Subgroups — C₄×C₅×#546 #11956877

Order 1280.

3720 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2364	C₂	1	2	yes	maximal, complemented
6	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2359	C₂	1	2	yes	maximal, complemented
9	C₅×#2358	C₂	1	2	yes	maximal, complemented
10	C₅×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2342	C₂	1	2	yes	maximal, complemented
13	C₅×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#121	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₅×#120	C₂	1	2	yes	maximal, complemented
21	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
27	C₅×#546	C₄	1	16	yes	direct product factor
28	C₂×C₅×#124	C₂²	1	1	yes	characteristic
29	C₂×C₅×#123	C₂²	1	2	yes	—
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	1	yes	characteristic
32	C₂×C₅×#121	C₂²	1	2	yes	—
33	C₂×C₅×#120	C₂²	1	2	yes	—
34	C₄×C₅×#41	—	2	8	no	—
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₅×D₄	—	2	8	no	—
38	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
42	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
45	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
51	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
52	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
53	C₂×C₅×#117	C₂²	1	2	yes	complemented
54	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
61	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
63	C₅×#391	C₂²	1	1	yes	characteristic, complemented
64	C₅×#391	C₂²	1	1	yes	characteristic, complemented
65	C₅×#390	C₂²	1	1	yes	characteristic
66	C₅×#390	C₂²	1	1	yes	characteristic
67	C₅×#390	C₂²	1	2	yes	complemented
68	C₅×#389	C₂²	1	1	yes	characteristic, complemented
69	C₅×#389	C₂²	1	2	yes	complemented
70	C₅×#389	C₂²	1	1	yes	characteristic, complemented
71	C₅×#388	C₂²	1	2	yes	complemented
72	C₅×#388	C₂²	1	2	yes	complemented
73	C₅×#388	C₂²	1	2	yes	complemented
74	C₅×#388	C₂²	1	2	yes	complemented
75	C₅×#388	C₂²	1	2	yes	complemented
76	C₅×#388	C₂²	1	2	yes	complemented
77	C₅×#388	C₂²	1	2	yes	complemented
78	C₅×#387	C₂²	1	2	yes	complemented
79	C₅×#387	C₂²	1	2	yes	complemented
80	C₅×#387	C₂²	1	2	yes	complemented
81	C₅×#386	C₂²	1	2	yes	—
82	C₅×#386	C₂²	1	2	yes	—
83	C₅×#386	C₂²	1	2	yes	—
84	C₅×#386	C₂²	1	2	yes	complemented
85	C₅×#386	C₂²	1	2	yes	complemented
86	C₅×#386	C₂²	1	2	yes	complemented
87	C₅×#386	C₂²	1	2	yes	complemented
88	C₅×#385	C₂²	1	2	yes	—
89	C₅×#385	C₂²	1	2	yes	—
90	C₅×#385	C₂²	1	2	yes	complemented
91	C₅×#385	C₂²	1	2	yes	complemented
92	C₅×#385	C₂²	1	2	yes	complemented
93	C₅×#382	C₂²	1	1	yes	characteristic, complemented
94	C₅×#381	C₂²	1	2	yes	complemented
95	C₅×#380	C₂²	1	1	yes	characteristic
96	C₅×#380	C₂²	1	1	yes	characteristic, complemented
97	C₅×#380	C₂²	1	2	yes	complemented
98	C₅×#379	C₂²	1	2	yes	—
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
106	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₅×#95	C₂²	1	2	yes	complemented
124	C₂×C₅×#95	C₂²	1	2	yes	complemented
125	C₄³×C₅	C₂²	1	1	yes	characteristic, complemented
126	C₄×#546	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁵×C₅	C₂³	1	2	yes	—
128	C₂×C₅×#41	—	2	4	no	—
129	C₂×C₅×#41	—	2	4	no	—
130	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
131	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₅×D₄	—	2	4	no	—
133	C₂²×C₅×D₄	—	2	4	no	—
134	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
135	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₅×D₄	C₂³	1	2	yes	—
139	C₂²×C₅×D₄	C₂³	1	2	yes	—
140	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅	—	2	8	no	—
142	C₂³×C₄×C₅	—	2	8	no	—
143	C₂³×C₄×C₅	—	4	4	no	—
144	C₂³×C₄×C₅	C₂³	1	2	yes	—
145	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅	C₂³	1	2	yes	—
147	C₂³×C₄×C₅	C₂³	1	2	yes	—
148	C₂³×C₄×C₅	C₂³	1	2	yes	—
149	C₂³×C₄×C₅	C₂³	1	2	yes	—
150	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₅	C₂³	1	2	yes	—
152	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅	C₂³	1	2	yes	—
155	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₅	C₂³	1	2	yes	—
157	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₅	C₂³	1	2	yes	—
159	C₅×#124	C₂×C₄	1	8	yes	complemented
160	C₅×#123	C₂×C₄	1	16	yes	complemented
161	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
162	C₅×#121	C₂×C₄	1	8	yes	complemented
163	C₅×#121	C₂×C₄	1	16	yes	complemented
164	C₅×#120	C₂×C₄	1	16	yes	complemented
165	C₄×C₅×Q₈	—	2	4	no	—
166	C₄×C₅×Q₈	—	2	4	no	—
167	C₄×C₅×D₄	—	2	4	no	—
168	C₄×C₅×D₄	—	2	4	no	—
169	C₄×C₅×D₄	—	2	4	no	—
170	C₄×C₅×D₄	—	2	8	no	—
171	C₄×C₅×D₄	—	2	8	no	—
172	C₄×C₅×D₄	—	2	4	no	—
173	C₄×C₅×D₄	—	2	4	no	—
174	C₄×C₅×D₄	—	2	8	no	—
175	C₄×C₅×D₄	—	2	8	no	—
176	C₄×C₅×D₄	—	2	4	no	—
177	C₄×C₅×D₄	—	2	4	no	—
178	C₄×C₅×D₄	—	4	4	no	—
179	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
180	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
181	C₄×C₅×D₄	D₄	1	8	yes	complemented
182	C₅×#117	—	2	4	no	—
183	C₅×#117	—	2	8	no	—
184	C₂×C₅×C₄⋊C₄	—	2	4	no	—
185	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
200	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
201	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
202	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₅	—	2	8	no	—
227	C₂×C₄²×C₅	—	2	4	no	—
228	C₂×C₄²×C₅	—	2	4	no	—
229	C₂×C₄²×C₅	—	4	4	no	—
230	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅	C₂³	1	2	yes	—
233	C₂×C₄²×C₅	C₂³	1	2	yes	—
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₅	C₂³	1	2	yes	—
241	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₅	C₂³	1	2	yes	—
243	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₅	C₂³	1	2	yes	—
246	C₂×C₄²×C₅	C₂³	1	2	yes	—
247	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
249	C₅×#95	C₂³	1	1	yes	characteristic
250	C₅×#95	C₂³	1	1	yes	characteristic
251	C₅×#95	C₂³	1	2	yes	—
252	C₅×#95	C₂³	1	2	yes	—
253	C₅×#95	C₂³	1	2	yes	—
254	C₅×#95	C₂³	1	2	yes	—
255	C₅×#95	C₂³	1	2	yes	—
256	C₅×#95	C₂³	1	2	yes	—
257	C₅×#95	C₂³	1	1	yes	characteristic
258	C₅×#95	C₂³	1	1	yes	characteristic
259	C₅×#95	C₂³	1	1	yes	characteristic
260	C₅×#95	C₂³	1	1	yes	characteristic
261	C₅×#95	C₂³	1	2	yes	—
262	C₅×#95	C₂³	1	2	yes	—
263	C₅×#95	C₂³	1	2	yes	—
264	C₅×#95	C₂³	1	2	yes	—
265	C₅×#95	C₂³	1	2	yes	—
266	C₅×#95	C₂³	1	2	yes	—
267	C₅×#95	C₂³	1	2	yes	—
268	C₂×#546	C₂×C₅	1	1	yes	characteristic
269	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
270	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
271	#2367	C₂×C₅	1	1	yes	characteristic, complemented
272	#2364	C₂×C₅	1	2	yes	complemented
273	#2363	C₂×C₅	1	1	yes	characteristic, complemented
274	#2360	C₂×C₅	1	1	yes	characteristic, complemented
275	#2359	C₂×C₅	1	2	yes	complemented
276	#2358	C₂×C₅	1	2	yes	complemented
277	#2352	C₂×C₅	1	1	yes	characteristic, complemented
278	#2349	C₂×C₅	1	1	yes	characteristic, complemented
279	#2342	C₂×C₅	1	2	yes	complemented
280	#2339	C₂×C₅	1	1	yes	characteristic, complemented
281	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
282	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
283	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
284	C₄×#123	C₂×C₅	1	2	yes	complemented
285	C₄×#121	C₂×C₅	1	2	yes	complemented
286	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
287	C₄×#120	C₂×C₅	1	2	yes	complemented
288	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
289	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
290	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
291	C₂⁴×C₅	—	2	4	no	—
292	C₂⁴×C₅	—	2	4	no	—
293	C₂⁴×C₅	—	2	4	no	—
294	C₂⁴×C₅	—	2	4	no	—
295	C₂⁴×C₅	—	4	2	no	—
296	C₂⁴×C₅	—	4	2	no	—
297	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
298	C₂⁴×C₅	C₂⁴	1	2	yes	—
299	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₅	C₂⁴	1	2	yes	—
301	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
302	C₅×#41	—	2	32	no	—
303	C₂×C₅×Q₈	—	2	2	no	—
304	C₂×C₅×Q₈	—	2	2	no	—
305	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
306	C₂×C₅×D₄	—	2	4	no	—
307	C₂×C₅×D₄	—	2	4	no	—
308	C₂×C₅×D₄	—	2	2	no	—
309	C₂×C₅×D₄	—	2	2	no	—
310	C₂×C₅×D₄	—	2	4	no	—
311	C₂×C₅×D₄	—	2	4	no	—
312	C₂×C₅×D₄	—	2	32	no	—
313	C₂×C₅×D₄	—	2	2	no	—
314	C₂×C₅×D₄	—	2	2	no	—
315	C₂×C₅×D₄	—	4	2	no	—
316	C₂×C₅×D₄	—	4	2	no	—
317	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
318	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
319	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
320	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
321	C₂×C₅×D₄	C₂²×C₄	1	8	yes	complemented
322	C₂×C₅×D₄	C₂²×C₄	1	8	yes	complemented
323	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
324	C₂×C₅×D₄	#41	1	4	yes	—
325	C₂²×C₄×C₅	—	2	4	no	—
326	C₂²×C₄×C₅	—	2	4	no	—
327	C₂²×C₄×C₅	—	2	2	no	—
328	C₂²×C₄×C₅	—	2	2	no	—
329	C₂²×C₄×C₅	—	2	2	no	—
330	C₂²×C₄×C₅	—	2	4	no	—
331	C₂²×C₄×C₅	—	2	2	no	—
332	C₂²×C₄×C₅	—	2	2	no	—
333	C₂²×C₄×C₅	—	2	4	no	—
334	C₂²×C₄×C₅	—	2	2	no	—
335	C₂²×C₄×C₅	—	2	4	no	—
336	C₂²×C₄×C₅	—	2	4	no	—
337	C₂²×C₄×C₅	—	2	4	no	—
338	C₂²×C₄×C₅	—	2	2	no	—
339	C₂²×C₄×C₅	—	2	4	no	—
340	C₂²×C₄×C₅	—	2	2	no	—
341	C₂²×C₄×C₅	—	2	2	no	—
342	C₂²×C₄×C₅	—	2	2	no	—
343	C₂²×C₄×C₅	—	2	4	no	—
344	C₂²×C₄×C₅	—	2	4	no	—
345	C₂²×C₄×C₅	—	2	4	no	—
346	C₂²×C₄×C₅	—	2	4	no	—
347	C₂²×C₄×C₅	—	2	4	no	—
348	C₂²×C₄×C₅	—	2	2	no	—
349	C₂²×C₄×C₅	—	2	2	no	—
350	C₂²×C₄×C₅	—	2	4	no	—
351	C₂²×C₄×C₅	—	2	4	no	—
352	C₂²×C₄×C₅	—	2	4	no	—
353	C₂²×C₄×C₅	—	2	2	no	—
354	C₂²×C₄×C₅	—	2	4	no	—
355	C₂²×C₄×C₅	—	4	2	no	—
356	C₂²×C₄×C₅	—	4	2	no	—
357	C₂²×C₄×C₅	—	4	2	no	—
358	C₂²×C₄×C₅	—	4	2	no	—
359	C₂²×C₄×C₅	—	4	2	no	—
360	C₂²×C₄×C₅	—	4	2	no	—
361	C₂²×C₄×C₅	—	4	1	no	—
362	C₂²×C₄×C₅	—	4	1	no	—
363	C₂²×C₄×C₅	—	4	2	no	—
364	C₂²×C₄×C₅	—	4	32	no	—
365	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
366	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
367	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	complemented
368	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
369	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
370	C₂²×C₄×C₅	#41	1	4	yes	complemented
371	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
390	C₅×C₄⋊C₄	—	2	4	no	—
391	C₅×C₄⋊C₄	—	2	2	no	—
392	C₅×C₄⋊C₄	—	2	4	no	—
393	C₅×C₄⋊C₄	—	2	4	no	—
394	C₅×C₄⋊C₄	—	2	2	no	—
395	C₅×C₄⋊C₄	—	2	2	no	—
396	C₅×C₄⋊C₄	—	2	2	no	—
397	C₅×C₄⋊C₄	—	2	2	no	—
398	C₅×C₄⋊C₄	—	4	2	no	—
399	C₅×C₄⋊C₄	—	4	2	no	—
400	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
401	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
402	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
403	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
404	C₅×C₂²⋊C₄	—	2	4	no	—
405	C₅×C₂²⋊C₄	—	2	4	no	—
406	C₅×C₂²⋊C₄	—	2	4	no	—
407	C₅×C₂²⋊C₄	—	2	4	no	—
408	C₅×C₂²⋊C₄	—	2	2	no	—
409	C₅×C₂²⋊C₄	—	2	4	no	—
410	C₅×C₂²⋊C₄	—	2	4	no	—
411	C₅×C₂²⋊C₄	—	2	4	no	—
412	C₅×C₂²⋊C₄	—	2	4	no	—
413	C₅×C₂²⋊C₄	—	2	4	no	—
414	C₅×C₂²⋊C₄	—	2	2	no	—
415	C₅×C₂²⋊C₄	—	2	2	no	—
416	C₅×C₂²⋊C₄	—	4	2	no	—
417	C₅×C₂²⋊C₄	—	4	2	no	—
418	C₅×C₂²⋊C₄	—	4	2	no	—
419	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
420	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
421	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
422	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
423	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
424	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
425	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
426	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
427	C₅×C₂²⋊C₄	#41	1	4	yes	complemented
428	C₄²×C₅	—	2	2	no	—
429	C₄²×C₅	—	2	2	no	—
430	C₄²×C₅	—	2	4	no	—
431	C₄²×C₅	—	2	2	no	—
432	C₄²×C₅	—	2	2	no	—
433	C₄²×C₅	—	2	2	no	—
434	C₄²×C₅	—	2	4	no	—
435	C₄²×C₅	—	2	2	no	—
436	C₄²×C₅	—	2	4	no	—
437	C₄²×C₅	—	2	2	no	—
438	C₄²×C₅	—	2	2	no	—
439	C₄²×C₅	—	2	2	no	—
440	C₄²×C₅	—	2	2	no	—
441	C₄²×C₅	—	2	4	no	—
442	C₄²×C₅	—	4	2	no	—
443	C₄²×C₅	—	4	2	no	—
444	C₄²×C₅	—	4	1	no	—
445	C₄²×C₅	C₂²×C₄	1	4	yes	complemented
446	C₄²×C₅	C₂×D₄	1	4	yes	—
447	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
448	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
449	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
450	#546	C₄×C₅	1	16	yes	direct product factor
451	C₂×#124	C₂²×C₅	1	1	yes	characteristic
452	C₂×#123	C₂²×C₅	1	2	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
454	C₂×#121	C₂²×C₅	1	1	yes	characteristic
455	C₂×#121	C₂²×C₅	1	2	yes	—
456	C₂×#120	C₂²×C₅	1	2	yes	—
457	C₄×#41	—	2	8	no	—
458	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
459	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
460	C₂×C₄×D₄	—	2	8	no	—
461	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
466	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
474	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
475	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
476	C₂×#117	C₂²×C₅	1	2	yes	complemented
477	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
478	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
480	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
481	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
482	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
483	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
484	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
485	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
486	#391	C₂²×C₅	1	1	yes	characteristic, complemented
487	#391	C₂²×C₅	1	1	yes	characteristic, complemented
488	#390	C₂²×C₅	1	1	yes	characteristic
489	#390	C₂²×C₅	1	1	yes	characteristic
490	#390	C₂²×C₅	1	2	yes	complemented
491	#389	C₂²×C₅	1	1	yes	characteristic, complemented
492	#389	C₂²×C₅	1	1	yes	characteristic, complemented
493	#389	C₂²×C₅	1	2	yes	complemented
494	#388	C₂²×C₅	1	2	yes	complemented
495	#388	C₂²×C₅	1	2	yes	complemented
496	#388	C₂²×C₅	1	2	yes	complemented
497	#388	C₂²×C₅	1	2	yes	complemented
498	#388	C₂²×C₅	1	2	yes	complemented
499	#388	C₂²×C₅	1	2	yes	complemented
500	#388	C₂²×C₅	1	2	yes	complemented
501	#387	C₂²×C₅	1	2	yes	complemented
502	#387	C₂²×C₅	1	2	yes	complemented
503	#387	C₂²×C₅	1	2	yes	complemented
504	#386	C₂²×C₅	1	2	yes	—
505	#386	C₂²×C₅	1	2	yes	—
506	#386	C₂²×C₅	1	2	yes	—
507	#386	C₂²×C₅	1	2	yes	complemented
508	#386	C₂²×C₅	1	2	yes	complemented
509	#386	C₂²×C₅	1	2	yes	complemented
510	#386	C₂²×C₅	1	2	yes	complemented
511	#385	C₂²×C₅	1	2	yes	—
512	#385	C₂²×C₅	1	2	yes	—
513	#385	C₂²×C₅	1	2	yes	complemented
514	#385	C₂²×C₅	1	2	yes	complemented
515	#385	C₂²×C₅	1	2	yes	complemented
516	#382	C₂²×C₅	1	1	yes	characteristic, complemented
517	#381	C₂²×C₅	1	2	yes	complemented
518	#380	C₂²×C₅	1	1	yes	characteristic
519	#380	C₂²×C₅	1	1	yes	characteristic, complemented
520	#380	C₂²×C₅	1	2	yes	complemented
521	#379	C₂²×C₅	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
523	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
524	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
525	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
526	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
527	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
528	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
529	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
531	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
534	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
535	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
536	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
537	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
538	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
539	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
540	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
541	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
542	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
543	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
544	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
545	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
546	C₂×#95	C₂²×C₅	1	2	yes	complemented
547	C₂×#95	C₂²×C₅	1	2	yes	complemented
548	C₄³	C₂²×C₅	1	1	yes	characteristic, complemented
549	C₂³×C₅	—	2	1	no	—
550	C₂³×C₅	—	2	2	no	—
551	C₂³×C₅	—	2	2	no	—
552	C₂³×C₅	—	2	1	no	—
553	C₂³×C₅	—	2	2	no	—
554	C₂³×C₅	—	2	1	no	—
555	C₂³×C₅	—	2	2	no	—
556	C₂³×C₅	—	2	1	no	—
557	C₂³×C₅	—	2	16	no	—
558	C₂³×C₅	—	2	16	no	—
559	C₂³×C₅	—	2	1	no	—
560	C₂³×C₅	—	2	2	no	—
561	C₂³×C₅	—	2	2	no	—
562	C₂³×C₅	—	2	1	no	—
563	C₂³×C₅	—	2	1	no	—
564	C₂³×C₅	—	2	2	no	—
565	C₂³×C₅	—	2	1	no	—
566	C₂³×C₅	—	2	2	no	—
567	C₂³×C₅	—	2	1	no	—
568	C₂³×C₅	—	2	2	no	—
569	C₂³×C₅	—	2	2	no	—
570	C₂³×C₅	—	2	1	no	—
571	C₂³×C₅	—	4	8	no	—
572	C₂³×C₅	—	4	8	no	—
573	C₂³×C₅	—	4	8	no	—
574	C₂³×C₅	—	4	8	no	—
575	C₂³×C₅	—	4	8	no	—
576	C₂³×C₅	C₂³×C₄	1	4	yes	—
577	C₂³×C₅	C₂³×C₄	1	2	yes	—
578	C₂³×C₅	C₂³×C₄	1	4	yes	—
579	C₂³×C₅	C₂³×C₄	1	2	yes	—
580	C₂³×C₅	C₂²×D₄	1	4	yes	—
581	C₂³×C₅	C₂×#41	1	4	yes	—
582	C₂³×C₅	C₂×#41	1	2	yes	—
583	C₂³×C₅	C₂×#41	1	2	yes	—
584	C₂³×C₅	C₂⁵	1	1	yes	characteristic
585	C₅×Q₈	—	2	8	no	—
586	C₅×D₄	—	2	16	no	—
587	C₅×D₄	—	2	16	no	—
588	C₅×D₄	—	2	8	no	—
589	C₅×D₄	—	2	8	no	—
590	C₅×D₄	—	4	8	no	—
591	C₅×D₄	C₄×D₄	1	16	yes	complemented
592	C₂×C₄×C₅	—	2	16	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	1	no	—
595	C₂×C₄×C₅	—	2	1	no	—
596	C₂×C₄×C₅	—	2	2	no	—
597	C₂×C₄×C₅	—	2	1	no	—
598	C₂×C₄×C₅	—	2	1	no	—
599	C₂×C₄×C₅	—	2	1	no	—
600	C₂×C₄×C₅	—	2	1	no	—
601	C₂×C₄×C₅	—	2	1	no	—
602	C₂×C₄×C₅	—	2	1	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	2	no	—
606	C₂×C₄×C₅	—	2	1	no	—
607	C₂×C₄×C₅	—	2	1	no	—
608	C₂×C₄×C₅	—	2	2	no	—
609	C₂×C₄×C₅	—	2	2	no	—
610	C₂×C₄×C₅	—	2	1	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	2	1	no	—
613	C₂×C₄×C₅	—	2	2	no	—
614	C₂×C₄×C₅	—	2	1	no	—
615	C₂×C₄×C₅	—	2	8	no	—
616	C₂×C₄×C₅	—	2	8	no	—
617	C₂×C₄×C₅	—	2	8	no	—
618	C₂×C₄×C₅	—	2	16	no	—
619	C₂×C₄×C₅	—	2	1	no	—
620	C₂×C₄×C₅	—	2	1	no	—
621	C₂×C₄×C₅	—	2	2	no	—
622	C₂×C₄×C₅	—	2	2	no	—
623	C₂×C₄×C₅	—	2	1	no	—
624	C₂×C₄×C₅	—	2	1	no	—
625	C₂×C₄×C₅	—	2	2	no	—
626	C₂×C₄×C₅	—	2	2	no	—
627	C₂×C₄×C₅	—	2	1	no	—
628	C₂×C₄×C₅	—	2	1	no	—
629	C₂×C₄×C₅	—	2	2	no	—
630	C₂×C₄×C₅	—	2	2	no	—
631	C₂×C₄×C₅	—	2	2	no	—
632	C₂×C₄×C₅	—	2	1	no	—
633	C₂×C₄×C₅	—	2	2	no	—
634	C₂×C₄×C₅	—	2	1	no	—
635	C₂×C₄×C₅	—	2	2	no	—
636	C₂×C₄×C₅	—	2	1	no	—
637	C₂×C₄×C₅	—	4	8	no	—
638	C₂×C₄×C₅	—	4	4	no	—
639	C₂×C₄×C₅	—	4	8	no	—
640	C₂×C₄×C₅	—	4	8	no	—
641	C₂×C₄×C₅	—	4	4	no	—
642	C₂×C₄×C₅	—	4	8	no	—
643	C₂×C₄×C₅	—	4	8	no	—
644	C₂×C₄×C₅	—	4	8	no	—
645	C₂×C₄×C₅	—	4	4	no	—
646	C₂×C₄×C₅	—	4	8	no	—
647	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
648	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
649	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
650	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
651	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
652	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
654	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
655	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
656	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
657	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₅	C₂×#41	1	2	yes	—
659	C₂×C₄×C₅	C₂×#41	1	2	yes	—
660	C₂×C₄×C₅	C₂×#41	1	2	yes	—
661	C₂×C₄×C₅	C₂×#41	1	2	yes	—
662	C₂×C₄×C₅	C₂×#41	1	2	yes	—
663	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
664	C₂⁵	C₂³×C₅	1	2	yes	—
665	C₂×#41	—	2	4	no	—
666	C₂×#41	—	2	4	no	—
667	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
668	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
669	C₂²×D₄	—	2	4	no	—
670	C₂²×D₄	—	2	4	no	—
671	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
672	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
673	C₂²×D₄	C₂³×C₅	1	2	yes	—
674	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₅	1	2	yes	—
676	C₂²×D₄	C₂³×C₅	1	2	yes	—
677	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
678	C₂³×C₄	—	2	8	no	—
679	C₂³×C₄	—	2	8	no	—
680	C₂³×C₄	—	4	4	no	—
681	C₂³×C₄	C₂³×C₅	1	2	yes	—
682	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅	1	2	yes	—
685	C₂³×C₄	C₂³×C₅	1	2	yes	—
686	C₂³×C₄	C₂³×C₅	1	2	yes	—
687	C₂³×C₄	C₂³×C₅	1	2	yes	—
688	C₂³×C₄	C₂³×C₅	1	2	yes	—
689	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₅	1	2	yes	—
692	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₅	1	2	yes	—
694	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₅	1	2	yes	—
696	#124	C₂×C₄×C₅	1	8	yes	complemented
697	#123	C₂×C₄×C₅	1	16	yes	complemented
698	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
699	#121	C₂×C₄×C₅	1	8	yes	complemented
700	#121	C₂×C₄×C₅	1	16	yes	complemented
701	#120	C₂×C₄×C₅	1	16	yes	complemented
702	C₄×Q₈	—	2	4	no	—
703	C₄×Q₈	—	2	4	no	—
704	C₄×D₄	—	2	4	no	—
705	C₄×D₄	—	2	4	no	—
706	C₄×D₄	—	2	4	no	—
707	C₄×D₄	—	2	8	no	—
708	C₄×D₄	—	2	8	no	—
709	C₄×D₄	—	2	4	no	—
710	C₄×D₄	—	2	4	no	—
711	C₄×D₄	—	2	8	no	—
712	C₄×D₄	—	2	8	no	—
713	C₄×D₄	—	2	4	no	—
714	C₄×D₄	—	2	4	no	—
715	C₄×D₄	—	4	4	no	—
716	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
717	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
718	C₄×D₄	C₅×D₄	1	8	yes	complemented
719	#117	—	2	4	no	—
720	#117	—	2	8	no	—
721	C₂×C₄⋊C₄	—	2	4	no	—
722	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	—	2	8	no	—
737	C₂×C₂²⋊C₄	—	2	8	no	—
738	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
739	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
763	C₂×C₄²	—	2	8	no	—
764	C₂×C₄²	—	2	4	no	—
765	C₂×C₄²	—	2	4	no	—
766	C₂×C₄²	—	4	4	no	—
767	C₂×C₄²	C₂³×C₅	1	2	yes	—
768	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₅	1	2	yes	—
777	C₂×C₄²	C₂³×C₅	1	2	yes	—
778	C₂×C₄²	C₂³×C₅	1	2	yes	—
779	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₅	1	2	yes	—
783	C₂×C₄²	C₂³×C₅	1	2	yes	—
784	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
786	#95	C₂³×C₅	1	1	yes	characteristic
787	#95	C₂³×C₅	1	1	yes	characteristic
788	#95	C₂³×C₅	1	2	yes	—
789	#95	C₂³×C₅	1	2	yes	—
790	#95	C₂³×C₅	1	2	yes	—
791	#95	C₂³×C₅	1	2	yes	—
792	#95	C₂³×C₅	1	2	yes	—
793	#95	C₂³×C₅	1	2	yes	—
794	#95	C₂³×C₅	1	1	yes	characteristic
795	#95	C₂³×C₅	1	1	yes	characteristic
796	#95	C₂³×C₅	1	1	yes	characteristic
797	#95	C₂³×C₅	1	1	yes	characteristic
798	#95	C₂³×C₅	1	2	yes	—
799	#95	C₂³×C₅	1	2	yes	—
800	#95	C₂³×C₅	1	2	yes	—
801	#95	C₂³×C₅	1	2	yes	—
802	#95	C₂³×C₅	1	2	yes	—
803	#95	C₂³×C₅	1	2	yes	—
804	#95	C₂³×C₅	1	2	yes	—
805	C₂²×C₅	—	2	2	no	—
806	C₂²×C₅	—	2	4	no	—
807	C₂²×C₅	—	2	4	no	—
808	C₂²×C₅	—	2	2	no	—
809	C₂²×C₅	—	2	2	no	—
810	C₂²×C₅	—	2	4	no	—
811	C₂²×C₅	—	2	2	no	—
812	C₂²×C₅	—	2	4	no	—
813	C₂²×C₅	—	2	2	no	—
814	C₂²×C₅	—	2	4	no	—
815	C₂²×C₅	—	2	4	no	—
816	C₂²×C₅	—	2	2	no	—
817	C₂²×C₅	—	2	2	no	—
818	C₂²×C₅	—	2	4	no	—
819	C₂²×C₅	—	2	2	no	—
820	C₂²×C₅	—	2	4	no	—
821	C₂²×C₅	—	2	2	no	—
822	C₂²×C₅	—	2	4	no	—
823	C₂²×C₅	—	4	32	no	—
824	C₂²×C₅	—	4	2	no	—
825	C₂²×C₅	—	4	1	no	—
826	C₂²×C₅	—	4	1	no	—
827	C₂²×C₅	—	4	2	no	—
828	C₂²×C₅	—	4	1	no	—
829	C₂²×C₅	—	4	2	no	—
830	C₂²×C₅	—	4	1	no	—
831	C₂²×C₅	—	4	2	no	—
832	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
833	C₂²×C₅	C₄×#41	1	4	yes	complemented
834	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
835	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
836	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
837	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
838	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
839	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
840	C₂²×C₅	#585	1	1	yes	characteristic
841	C₄×C₅	—	2	2	no	—
842	C₄×C₅	—	2	2	no	—
843	C₄×C₅	—	2	4	no	—
844	C₄×C₅	—	2	2	no	—
845	C₄×C₅	—	2	2	no	—
846	C₄×C₅	—	2	4	no	—
847	C₄×C₅	—	2	2	no	—
848	C₄×C₅	—	2	4	no	—
849	C₄×C₅	—	2	2	no	—
850	C₄×C₅	—	2	2	no	—
851	C₄×C₅	—	2	2	no	—
852	C₄×C₅	—	4	1	no	—
853	C₄×C₅	—	4	2	no	—
854	C₄×C₅	—	4	1	no	—
855	C₄×C₅	—	4	2	no	—
856	C₄×C₅	—	4	1	no	—
857	C₄×C₅	—	4	2	no	—
858	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
859	C₄×C₅	#546	1	4	yes	direct product factor
860	C₂⁴	—	2	4	no	—
861	C₂⁴	—	2	4	no	—
862	C₂⁴	—	2	4	no	—
863	C₂⁴	—	2	4	no	—
864	C₂⁴	—	4	2	no	—
865	C₂⁴	—	4	2	no	—
866	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
867	C₂⁴	C₂⁴×C₅	1	2	yes	—
868	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
869	C₂⁴	C₂⁴×C₅	1	2	yes	—
870	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
871	#41	—	2	32	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
875	C₂×D₄	—	2	4	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	4	no	—
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	32	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
887	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
888	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
889	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
890	C₂×D₄	C₂²×C₄×C₅	1	8	yes	complemented
891	C₂×D₄	C₂²×C₄×C₅	1	8	yes	complemented
892	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
893	C₂×D₄	C₅×#41	1	4	yes	—
894	C₂²×C₄	—	2	4	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	4	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	4	no	—
913	C₂²×C₄	—	2	4	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	2	4	no	—
916	C₂²×C₄	—	2	4	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	4	no	—
920	C₂²×C₄	—	2	4	no	—
921	C₂²×C₄	—	2	4	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	4	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	—	4	1	no	—
931	C₂²×C₄	—	4	1	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	32	no	—
934	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
935	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
936	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	complemented
937	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
938	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
939	C₂²×C₄	C₅×#41	1	4	yes	complemented
940	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
950	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
959	C₄⋊C₄	—	2	4	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	4	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
970	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
971	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
972	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	4	no	—
979	C₂²⋊C₄	—	2	4	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
989	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
990	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
991	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
992	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
993	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
994	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
995	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
996	C₂²⋊C₄	C₅×#41	1	4	yes	complemented
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	4	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	4	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	4	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	4	no	—
1011	C₄²	—	4	2	no	—
1012	C₄²	—	4	2	no	—
1013	C₄²	—	4	1	no	—
1014	C₄²	C₂²×C₄×C₅	1	4	yes	complemented
1015	C₄²	C₂×C₅×D₄	1	4	yes	—
1016	C₂×C₅	—	2	4	no	—
1017	C₂×C₅	—	2	8	no	—
1018	C₂×C₅	—	4	2	no	—
1019	C₂×C₅	—	4	4	no	—
1020	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
1021	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
1022	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1023	C₂×C₅	C₂×#546	1	1	yes	characteristic
1024	C₂×C₅	D₄×#41	1	1	yes	characteristic
1025	C₂×C₅	#3475	1	1	yes	characteristic
1026	C₂×C₅	#3481	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	16	no	—
1036	C₂³	—	2	16	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	4	8	no	—
1050	C₂³	—	4	8	no	—
1051	C₂³	—	4	8	no	—
1052	C₂³	—	4	8	no	—
1053	C₂³	—	4	8	no	—
1054	C₂³	C₂³×C₄×C₅	1	4	yes	—
1055	C₂³	C₂³×C₄×C₅	1	2	yes	—
1056	C₂³	C₂³×C₄×C₅	1	4	yes	—
1057	C₂³	C₂³×C₄×C₅	1	2	yes	—
1058	C₂³	C₂²×C₅×D₄	1	4	yes	—
1059	C₂³	C₂×C₅×#41	1	4	yes	—
1060	C₂³	C₂×C₅×#41	1	2	yes	—
1061	C₂³	C₂×C₅×#41	1	2	yes	—
1062	C₂³	C₂⁵×C₅	1	1	yes	characteristic
1063	Q₈	—	2	8	no	—
1064	D₄	—	2	16	no	—
1065	D₄	—	2	16	no	—
1066	D₄	—	2	8	no	—
1067	D₄	—	2	8	no	—
1068	D₄	—	4	8	no	—
1069	D₄	C₄×C₅×D₄	1	16	yes	complemented
1070	C₂×C₄	—	2	16	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	8	no	—
1094	C₂×C₄	—	2	8	no	—
1095	C₂×C₄	—	2	8	no	—
1096	C₂×C₄	—	2	16	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	4	8	no	—
1116	C₂×C₄	—	4	8	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	8	no	—
1119	C₂×C₄	—	4	8	no	—
1120	C₂×C₄	—	4	8	no	—
1121	C₂×C₄	—	4	4	no	—
1122	C₂×C₄	—	4	8	no	—
1123	C₂×C₄	—	4	8	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1126	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1127	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1128	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1129	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1130	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1131	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1132	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1133	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
1134	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1135	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1136	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1137	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1138	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1139	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1140	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1141	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1142	C₅	C₄×#546	1	1	yes	characteristic, direct product factor, Sylow
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	2	4	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	4	32	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
1171	C₂²	C₄×C₅×#41	1	4	yes	complemented
1172	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1173	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1174	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1175	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1176	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1177	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1178	C₂²	C₅×#585	1	1	yes	characteristic
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	4	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	4	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	4	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
1197	C₄	C₅×#546	1	4	yes	direct product factor
1198	C₂	—	2	4	no	—
1199	C₂	—	2	8	no	—
1200	C₂	—	4	4	no	—
1201	C₂	—	4	2	no	—
1202	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
1203	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
1204	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1205	C₂	C₂×C₅×#546	1	1	yes	characteristic
1206	C₂	C₅×D₄×#41	1	1	yes	characteristic
1207	C₂	C₅×#3475	1	1	yes	characteristic
1208	C₂	C₅×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₂×C₅×#546	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×C₅×#41	C₂	semidirect
3. C₂²×C₄×C₅×D₄	C₂	semidirect
4. C₅×#2367	C₂	semidirect
5. C₅×#2364	C₂	semidirect
6. C₅×#2363	C₂	semidirect
7. C₅×#2360	C₂	semidirect
8. C₅×#2359	C₂	semidirect
9. C₅×#2358	C₂	semidirect
10. C₅×#2352	C₂	semidirect
11. C₅×#2349	C₂	semidirect
12. C₅×#2342	C₂	semidirect
13. C₅×#2339	C₂	semidirect
14. C₅×D₄×C₂²⋊C₄	C₂	semidirect
15. C₄×C₅×#124	C₂	semidirect
16. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₅×#123	C₂	semidirect
18. C₄×C₅×#121	C₂	semidirect
19. C₄×C₅×#121	C₂	semidirect
20. C₄×C₅×#120	C₂	semidirect
21. C₄²×C₅×D₄	C₂	semidirect
22. C₄²×C₅×D₄	C₂	semidirect
23. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
27. C₅×#546	C₄	direct (N × H)
35. C₂×C₄×C₅×Q₈	C₂²	semidirect
36. C₂×C₄×C₅×Q₈	C₂²	semidirect
50. C₂×C₄×C₅×D₄	C₂²	semidirect
51. C₂×C₄×C₅×D₄	C₂²	semidirect
52. C₂×C₄×C₅×D₄	C₂²	semidirect
53. C₂×C₅×#117	C₂²	semidirect
54. C₂×C₅×#117	C₂²	semidirect
60. C₂²×C₄²×C₅	C₂²	semidirect
61. C₂²×C₄²×C₅	C₂²	semidirect
62. C₂²×C₄²×C₅	C₂²	semidirect
63. C₅×#391	C₂²	semidirect
64. C₅×#391	C₂²	semidirect
67. C₅×#390	C₂²	semidirect
68. C₅×#389	C₂²	semidirect
69. C₅×#389	C₂²	semidirect
70. C₅×#389	C₂²	semidirect
71. C₅×#388	C₂²	semidirect
72. C₅×#388	C₂²	semidirect
73. C₅×#388	C₂²	semidirect
74. C₅×#388	C₂²	semidirect
75. C₅×#388	C₂²	semidirect
76. C₅×#388	C₂²	semidirect
77. C₅×#388	C₂²	semidirect
78. C₅×#387	C₂²	semidirect
79. C₅×#387	C₂²	semidirect
80. C₅×#387	C₂²	semidirect
84. C₅×#386	C₂²	semidirect
85. C₅×#386	C₂²	semidirect
86. C₅×#386	C₂²	semidirect
87. C₅×#386	C₂²	semidirect
90. C₅×#385	C₂²	semidirect
91. C₅×#385	C₂²	semidirect
92. C₅×#385	C₂²	semidirect
93. C₅×#382	C₂²	semidirect
94. C₅×#381	C₂²	semidirect
96. C₅×#380	C₂²	semidirect
97. C₅×#380	C₂²	semidirect
99. C₄×C₅×C₄⋊C₄	C₂²	semidirect
100. C₄×C₅×C₄⋊C₄	C₂²	semidirect
101. C₄×C₅×C₄⋊C₄	C₂²	semidirect
102. C₄×C₅×C₄⋊C₄	C₂²	semidirect
103. C₄×C₅×C₄⋊C₄	C₂²	semidirect
104. C₄×C₅×C₄⋊C₄	C₂²	semidirect
105. C₄×C₅×C₄⋊C₄	C₂²	semidirect
112. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
113. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
114. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
115. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
116. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
117. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
119. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
123. C₂×C₅×#95	C₂²	semidirect
124. C₂×C₅×#95	C₂²	semidirect
125. C₄³×C₅	C₂²	semidirect
126. C₄×#546	C₅	direct (N × H)
130. C₂×C₅×#41	C₂×C₄	semidirect
134. C₂²×C₅×D₄	C₂×C₄	semidirect
159. C₅×#124	C₂×C₄	semidirect
160. C₅×#123	C₂×C₄	semidirect
161. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
162. C₅×#121	C₂×C₄	semidirect
163. C₅×#121	C₂×C₄	semidirect
164. C₅×#120	C₂×C₄	semidirect
179. C₄×C₅×D₄	C₂×C₄	semidirect
180. C₄×C₅×D₄	C₂×C₄	semidirect
181. C₄×C₅×D₄	D₄	semidirect
201. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
269. C₂×C₄×#41	C₂×C₅	semidirect
270. C₂²×C₄×D₄	C₂×C₅	semidirect
271. #2367	C₂×C₅	semidirect
272. #2364	C₂×C₅	semidirect
273. #2363	C₂×C₅	semidirect
274. #2360	C₂×C₅	semidirect
275. #2359	C₂×C₅	semidirect
276. #2358	C₂×C₅	semidirect
277. #2352	C₂×C₅	semidirect
278. #2349	C₂×C₅	semidirect
279. #2342	C₂×C₅	semidirect
280. #2339	C₂×C₅	semidirect
281. D₄×C₂²⋊C₄	C₂×C₅	semidirect
282. C₄×#124	C₂×C₅	semidirect
283. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
284. C₄×#123	C₂×C₅	semidirect
285. C₄×#121	C₂×C₅	semidirect
286. C₄×#121	C₂×C₅	semidirect
287. C₄×#120	C₂×C₅	semidirect
288. C₄²×D₄	C₂×C₅	semidirect
289. C₄²×D₄	C₂×C₅	semidirect
290. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
305. C₂×C₅×Q₈	C₂²×C₄	semidirect
321. C₂×C₅×D₄	C₂²×C₄	semidirect
322. C₂×C₅×D₄	C₂²×C₄	semidirect
366. C₂²×C₄×C₅	C₂²×C₄	semidirect
367. C₂²×C₄×C₅	C₂²×C₄	semidirect
368. C₂²×C₄×C₅	C₂²×C₄	semidirect
370. C₂²×C₄×C₅	#41	semidirect
400. C₅×C₄⋊C₄	C₂²×C₄	semidirect
401. C₅×C₄⋊C₄	C₂²×C₄	semidirect
402. C₅×C₄⋊C₄	C₂²×C₄	semidirect
421. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
422. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
423. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
424. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
425. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
427. C₅×C₂²⋊C₄	#41	semidirect
445. C₄²×C₅	C₂²×C₄	semidirect
450. #546	C₄×C₅	direct (N × H)
458. C₂×C₄×Q₈	C₂²×C₅	semidirect
459. C₂×C₄×Q₈	C₂²×C₅	semidirect
473. C₂×C₄×D₄	C₂²×C₅	semidirect
474. C₂×C₄×D₄	C₂²×C₅	semidirect
475. C₂×C₄×D₄	C₂²×C₅	semidirect
476. C₂×#117	C₂²×C₅	semidirect
477. C₂×#117	C₂²×C₅	semidirect
483. C₂²×C₄²	C₂²×C₅	semidirect
484. C₂²×C₄²	C₂²×C₅	semidirect
485. C₂²×C₄²	C₂²×C₅	semidirect
486. #391	C₂²×C₅	semidirect
487. #391	C₂²×C₅	semidirect
490. #390	C₂²×C₅	semidirect
491. #389	C₂²×C₅	semidirect
492. #389	C₂²×C₅	semidirect
493. #389	C₂²×C₅	semidirect
494. #388	C₂²×C₅	semidirect
495. #388	C₂²×C₅	semidirect
496. #388	C₂²×C₅	semidirect
497. #388	C₂²×C₅	semidirect
498. #388	C₂²×C₅	semidirect
499. #388	C₂²×C₅	semidirect
500. #388	C₂²×C₅	semidirect
501. #387	C₂²×C₅	semidirect
502. #387	C₂²×C₅	semidirect
503. #387	C₂²×C₅	semidirect
507. #386	C₂²×C₅	semidirect
508. #386	C₂²×C₅	semidirect
509. #386	C₂²×C₅	semidirect
510. #386	C₂²×C₅	semidirect
513. #385	C₂²×C₅	semidirect
514. #385	C₂²×C₅	semidirect
515. #385	C₂²×C₅	semidirect
516. #382	C₂²×C₅	semidirect
517. #381	C₂²×C₅	semidirect
519. #380	C₂²×C₅	semidirect
520. #380	C₂²×C₅	semidirect
522. C₄×C₄⋊C₄	C₂²×C₅	semidirect
523. C₄×C₄⋊C₄	C₂²×C₅	semidirect
524. C₄×C₄⋊C₄	C₂²×C₅	semidirect
525. C₄×C₄⋊C₄	C₂²×C₅	semidirect
526. C₄×C₄⋊C₄	C₂²×C₅	semidirect
527. C₄×C₄⋊C₄	C₂²×C₅	semidirect
528. C₄×C₄⋊C₄	C₂²×C₅	semidirect
535. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
536. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
537. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
538. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
539. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
540. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
541. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
542. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
543. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
544. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
545. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
546. C₂×#95	C₂²×C₅	semidirect
547. C₂×#95	C₂²×C₅	semidirect
548. C₄³	C₂²×C₅	semidirect
591. C₅×D₄	C₄×D₄	semidirect
667. C₂×#41	C₂×C₄×C₅	semidirect
671. C₂²×D₄	C₂×C₄×C₅	semidirect
696. #124	C₂×C₄×C₅	semidirect
697. #123	C₂×C₄×C₅	semidirect
698. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
699. #121	C₂×C₄×C₅	semidirect
700. #121	C₂×C₄×C₅	semidirect
701. #120	C₂×C₄×C₅	semidirect
716. C₄×D₄	C₂×C₄×C₅	semidirect
717. C₄×D₄	C₂×C₄×C₅	semidirect
718. C₄×D₄	C₅×D₄	semidirect
738. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
833. C₂²×C₅	C₄×#41	semidirect
859. C₄×C₅	#546	direct (N × H)
874. C₂×Q₈	C₂²×C₄×C₅	semidirect
890. C₂×D₄	C₂²×C₄×C₅	semidirect
891. C₂×D₄	C₂²×C₄×C₅	semidirect
935. C₂²×C₄	C₂²×C₄×C₅	semidirect
936. C₂²×C₄	C₂²×C₄×C₅	semidirect
937. C₂²×C₄	C₂²×C₄×C₅	semidirect
939. C₂²×C₄	C₅×#41	semidirect
969. C₄⋊C₄	C₂²×C₄×C₅	semidirect
970. C₄⋊C₄	C₂²×C₄×C₅	semidirect
971. C₄⋊C₄	C₂²×C₄×C₅	semidirect
990. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
991. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
992. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
993. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
994. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
996. C₂²⋊C₄	C₅×#41	semidirect
1014. C₄²	C₂²×C₄×C₅	semidirect
1069. D₄	C₄×C₅×D₄	semidirect
1142. C₅	C₄×#546	direct (N × H)
1171. C₂²	C₄×C₅×#41	semidirect
1197. C₄	C₅×#546	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#546	2
C₂×C₄×C₅×#41	2
C₂²×C₄×C₅×D₄	2
C₅×#2367	2
C₅×#2364	2
C₅×#2363	2
C₅×#2360	2
C₅×#2359	2
C₅×#2358	2
C₅×#2352	2
C₅×#2349	2
C₅×#2342	2
C₅×#2339	2
C₅×D₄×C₂²⋊C₄	2
C₄×C₅×#124	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#123	2
C₄×C₅×#121	2
C₄×C₅×#120	2
C₄²×C₅×D₄	2
C₂×C₄×C₅×C₂²⋊C₄	2
C₄×#546	5

Subgroups — C4×C5×#546 #11956877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#546 #11956877