Subgroups — C₅×#34320 #11957040

Order 1280.

2840 conjugacy classes of subgroups.

The subgroup lattice has 1156 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	C₅×#2374	C₂	1	2	yes	maximal, complemented
3	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2358	C₂	1	2	yes	maximal, complemented
8	C₅×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2342	C₂	1	2	yes	maximal, complemented
11	C₅×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2335	C₂	1	2	yes	maximal, complemented
14	C₅×#2333	C₂	1	2	yes	maximal, complemented
15	C₅×#2321	C₂	1	2	yes	maximal, complemented
16	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2273	C₂	1	2	yes	maximal, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#546	C₄	1	16	yes	complemented
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#121	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	2	yes	—
32	C₂×C₅×#120	C₂²	1	2	yes	—
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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	complemented
42	C₂×C₅×#117	C₂²	1	2	yes	complemented
43	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
51	C₅×#391	C₂²	1	1	yes	characteristic, complemented
52	C₅×#391	C₂²	1	1	yes	characteristic, complemented
53	C₅×#390	C₂²	1	1	yes	characteristic
54	C₅×#390	C₂²	1	1	yes	characteristic
55	C₅×#390	C₂²	1	2	yes	—
56	C₅×#390	C₂²	1	1	yes	characteristic
57	C₅×#390	C₂²	1	1	yes	characteristic
58	C₅×#390	C₂²	1	2	yes	—
59	C₅×#390	C₂²	1	1	yes	characteristic
60	C₅×#390	C₂²	1	1	yes	characteristic
61	C₅×#390	C₂²	1	2	yes	complemented
62	C₅×#390	C₂²	1	2	yes	complemented
63	C₅×#390	C₂²	1	2	yes	complemented
64	C₅×#389	C₂²	1	1	yes	characteristic, complemented
65	C₅×#389	C₂²	1	1	yes	characteristic, complemented
66	C₅×#389	C₂²	1	2	yes	complemented
67	C₅×#388	C₂²	1	2	yes	complemented
68	C₅×#388	C₂²	1	2	yes	complemented
69	C₅×#388	C₂²	1	2	yes	complemented
70	C₅×#388	C₂²	1	2	yes	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×#382	C₂²	1	1	yes	characteristic, complemented
92	C₅×#381	C₂²	1	2	yes	complemented
93	C₅×#380	C₂²	1	1	yes	characteristic
94	C₅×#380	C₂²	1	1	yes	characteristic, complemented
95	C₅×#380	C₂²	1	2	yes	complemented
96	C₅×#379	C₂²	1	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
104	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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, complemented
111	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	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	2	yes	complemented
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₄³×C₅	C₂²	1	1	yes	characteristic, complemented
124	#34320	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₅	C₂³	1	2	yes	—
126	C₂×C₅×#41	—	4	2	no	—
127	C₂×C₅×#41	—	4	2	no	—
128	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
129	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₅×D₄	—	4	2	no	—
131	C₂²×C₅×D₄	—	4	2	no	—
132	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
133	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₅×D₄	C₂³	1	2	yes	—
138	C₂²×C₅×D₄	C₂³	1	2	yes	—
139	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅	C₂³	1	2	yes	—
144	C₂³×C₄×C₅	C₂³	1	2	yes	—
145	C₂³×C₄×C₅	C₂³	1	2	yes	—
146	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅	C₂³	1	2	yes	—
148	C₂³×C₄×C₅	C₂³	1	2	yes	—
149	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
150	C₅×#124	C₂×C₄	1	8	yes	complemented
151	C₅×#123	C₂×C₄	1	16	yes	complemented
152	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
153	C₅×#121	C₂×C₄	1	8	yes	complemented
154	C₅×#121	C₂×C₄	1	16	yes	complemented
155	C₅×#120	C₂×C₄	1	16	yes	complemented
156	C₄×C₅×Q₈	—	4	2	no	—
157	C₄×C₅×Q₈	—	4	2	no	—
158	C₄×C₅×D₄	—	2	4	no	—
159	C₄×C₅×D₄	—	2	4	no	—
160	C₄×C₅×D₄	—	4	2	no	—
161	C₄×C₅×D₄	—	4	2	no	—
162	C₄×C₅×D₄	—	4	4	no	—
163	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
164	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
165	C₅×#117	—	4	4	no	—
166	C₅×#117	—	4	2	no	—
167	C₂×C₅×C₄⋊C₄	—	4	2	no	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
183	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
184	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
185	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
186	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
214	C₂×C₄²×C₅	—	4	2	no	—
215	C₂×C₄²×C₅	—	4	2	no	—
216	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₅	C₂³	1	2	yes	—
226	C₂×C₄²×C₅	C₂³	1	2	yes	—
227	C₂×C₄²×C₅	C₂³	1	2	yes	—
228	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₅	C₂³	1	2	yes	—
230	C₂×C₄²×C₅	C₂³	1	2	yes	—
231	C₂×C₄²×C₅	C₂³	1	2	yes	—
232	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	1	yes	characteristic
244	C₅×#95	C₂³	1	1	yes	characteristic
245	C₅×#95	C₂³	1	1	yes	characteristic
246	C₅×#95	C₂³	1	1	yes	characteristic
247	C₅×#95	C₂³	1	2	yes	—
248	C₅×#95	C₂³	1	2	yes	—
249	C₅×#95	C₂³	1	2	yes	—
250	C₅×#95	C₂³	1	2	yes	—
251	C₅×#95	C₂³	1	2	yes	—
252	C₅×#95	C₂³	1	2	yes	—
253	C₅×#95	C₂³	1	2	yes	—
254	C₂×#546	C₂×C₅	1	1	yes	characteristic
255	#2374	C₂×C₅	1	2	yes	complemented
256	#2367	C₂×C₅	1	1	yes	characteristic, complemented
257	#2363	C₂×C₅	1	1	yes	characteristic, complemented
258	#2363	C₂×C₅	1	2	yes	complemented
259	#2360	C₂×C₅	1	1	yes	characteristic, complemented
260	#2358	C₂×C₅	1	2	yes	complemented
261	#2357	C₂×C₅	1	1	yes	characteristic, complemented
262	#2352	C₂×C₅	1	1	yes	characteristic, complemented
263	#2342	C₂×C₅	1	2	yes	complemented
264	#2341	C₂×C₅	1	1	yes	characteristic, complemented
265	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
266	#2335	C₂×C₅	1	2	yes	complemented
267	#2333	C₂×C₅	1	2	yes	complemented
268	#2321	C₂×C₅	1	2	yes	complemented
269	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
270	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
271	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
272	#2297	C₂×C₅	1	1	yes	characteristic, complemented
273	#2293	C₂×C₅	1	1	yes	characteristic, complemented
274	C₂×#390	C₂×C₅	1	1	yes	characteristic, complemented
275	#2273	C₂×C₅	1	2	yes	complemented
276	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
277	C₂⁴×C₅	—	2	4	no	—
278	C₂⁴×C₅	—	2	4	no	—
279	C₂⁴×C₅	—	4	2	no	—
280	C₂⁴×C₅	—	4	2	no	—
281	C₂⁴×C₅	—	4	2	no	—
282	C₂⁴×C₅	—	4	2	no	—
283	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
284	C₂⁴×C₅	C₂⁴	1	2	yes	—
285	C₂⁴×C₅	C₂⁴	1	2	yes	—
286	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
287	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
288	C₅×#41	—	4	16	no	—
289	C₂×C₅×Q₈	—	2	2	no	—
290	C₂×C₅×Q₈	—	2	2	no	—
291	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	—	2	2	no	—
294	C₂×C₅×D₄	—	2	2	no	—
295	C₂×C₅×D₄	—	2	2	no	—
296	C₂×C₅×D₄	—	2	2	no	—
297	C₂×C₅×D₄	—	2	2	no	—
298	C₂×C₅×D₄	—	4	16	no	—
299	C₂×C₅×D₄	—	4	2	no	—
300	C₂×C₅×D₄	—	4	2	no	—
301	C₂×C₅×D₄	—	4	2	no	—
302	C₂×C₅×D₄	—	4	2	no	—
303	C₂×C₅×D₄	—	4	2	no	—
304	C₂×C₅×D₄	—	4	2	no	—
305	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
306	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
307	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
308	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
309	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
310	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
311	C₂²×C₄×C₅	—	2	2	no	—
312	C₂²×C₄×C₅	—	2	2	no	—
313	C₂²×C₄×C₅	—	2	2	no	—
314	C₂²×C₄×C₅	—	2	2	no	—
315	C₂²×C₄×C₅	—	2	2	no	—
316	C₂²×C₄×C₅	—	2	4	no	—
317	C₂²×C₄×C₅	—	2	2	no	—
318	C₂²×C₄×C₅	—	2	2	no	—
319	C₂²×C₄×C₅	—	2	2	no	—
320	C₂²×C₄×C₅	—	2	2	no	—
321	C₂²×C₄×C₅	—	2	4	no	—
322	C₂²×C₄×C₅	—	2	4	no	—
323	C₂²×C₄×C₅	—	4	1	no	—
324	C₂²×C₄×C₅	—	4	1	no	—
325	C₂²×C₄×C₅	—	4	1	no	—
326	C₂²×C₄×C₅	—	4	1	no	—
327	C₂²×C₄×C₅	—	4	2	no	—
328	C₂²×C₄×C₅	—	4	1	no	—
329	C₂²×C₄×C₅	—	4	2	no	—
330	C₂²×C₄×C₅	—	4	1	no	—
331	C₂²×C₄×C₅	—	4	2	no	—
332	C₂²×C₄×C₅	—	4	2	no	—
333	C₂²×C₄×C₅	—	4	2	no	—
334	C₂²×C₄×C₅	—	4	2	no	—
335	C₂²×C₄×C₅	—	4	2	no	—
336	C₂²×C₄×C₅	—	4	2	no	—
337	C₂²×C₄×C₅	—	4	2	no	—
338	C₂²×C₄×C₅	—	4	2	no	—
339	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
340	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
341	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
342	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
343	C₂²×C₄×C₅	#41	1	4	yes	complemented
344	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
363	C₅×C₄⋊C₄	—	2	2	no	—
364	C₅×C₄⋊C₄	—	2	2	no	—
365	C₅×C₄⋊C₄	—	2	2	no	—
366	C₅×C₄⋊C₄	—	2	2	no	—
367	C₅×C₄⋊C₄	—	2	4	no	—
368	C₅×C₄⋊C₄	—	2	2	no	—
369	C₅×C₄⋊C₄	—	2	2	no	—
370	C₅×C₄⋊C₄	—	4	2	no	—
371	C₅×C₄⋊C₄	—	4	2	no	—
372	C₅×C₄⋊C₄	—	4	2	no	—
373	C₅×C₄⋊C₄	—	4	2	no	—
374	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
375	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
376	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
377	C₅×C₂²⋊C₄	—	2	4	no	—
378	C₅×C₂²⋊C₄	—	2	2	no	—
379	C₅×C₂²⋊C₄	—	2	4	no	—
380	C₅×C₂²⋊C₄	—	2	4	no	—
381	C₅×C₂²⋊C₄	—	2	4	no	—
382	C₅×C₂²⋊C₄	—	2	4	no	—
383	C₅×C₂²⋊C₄	—	2	4	no	—
384	C₅×C₂²⋊C₄	—	2	4	no	—
385	C₅×C₂²⋊C₄	—	2	2	no	—
386	C₅×C₂²⋊C₄	—	2	2	no	—
387	C₅×C₂²⋊C₄	—	2	4	no	—
388	C₅×C₂²⋊C₄	—	2	4	no	—
389	C₅×C₂²⋊C₄	—	4	2	no	—
390	C₅×C₂²⋊C₄	—	4	2	no	—
391	C₅×C₂²⋊C₄	—	4	2	no	—
392	C₅×C₂²⋊C₄	—	4	2	no	—
393	C₅×C₂²⋊C₄	—	4	2	no	—
394	C₅×C₂²⋊C₄	—	4	2	no	—
395	C₅×C₂²⋊C₄	—	4	2	no	—
396	C₅×C₂²⋊C₄	—	4	2	no	—
397	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
398	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
399	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
400	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
401	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
402	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
403	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
404	C₅×C₂²⋊C₄	#41	1	4	yes	complemented
405	C₄²×C₅	—	2	2	no	—
406	C₄²×C₅	—	2	2	no	—
407	C₄²×C₅	—	2	2	no	—
408	C₄²×C₅	—	2	2	no	—
409	C₄²×C₅	—	2	2	no	—
410	C₄²×C₅	—	2	2	no	—
411	C₄²×C₅	—	2	2	no	—
412	C₄²×C₅	—	4	1	no	—
413	C₄²×C₅	—	4	1	no	—
414	C₄²×C₅	—	4	1	no	—
415	C₄²×C₅	—	4	1	no	—
416	C₄²×C₅	—	4	2	no	—
417	C₄²×C₅	—	4	1	no	—
418	C₄²×C₅	—	4	2	no	—
419	C₄²×C₅	—	4	2	no	—
420	C₄²×C₅	—	4	2	no	—
421	C₄²×C₅	—	4	2	no	—
422	C₄²×C₅	—	4	2	no	—
423	C₄²×C₅	C₂²×C₄	1	4	yes	—
424	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
425	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
426	#546	C₄×C₅	1	16	yes	complemented
427	C₂×#124	C₂²×C₅	1	1	yes	characteristic
428	C₂×#123	C₂²×C₅	1	2	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
430	C₂×#121	C₂²×C₅	1	2	yes	—
431	C₂×#121	C₂²×C₅	1	1	yes	characteristic
432	C₂×#120	C₂²×C₅	1	2	yes	—
433	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
434	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
435	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
442	C₂×#117	C₂²×C₅	1	2	yes	complemented
443	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
444	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
448	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
449	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
450	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
451	#391	C₂²×C₅	1	1	yes	characteristic, complemented
452	#391	C₂²×C₅	1	1	yes	characteristic, complemented
453	#390	C₂²×C₅	1	2	yes	—
454	#390	C₂²×C₅	1	1	yes	characteristic
455	#390	C₂²×C₅	1	1	yes	characteristic
456	#390	C₂²×C₅	1	1	yes	characteristic
457	#390	C₂²×C₅	1	1	yes	characteristic
458	#390	C₂²×C₅	1	2	yes	—
459	#390	C₂²×C₅	1	1	yes	characteristic
460	#390	C₂²×C₅	1	1	yes	characteristic
461	#390	C₂²×C₅	1	2	yes	complemented
462	#390	C₂²×C₅	1	2	yes	complemented
463	#390	C₂²×C₅	1	2	yes	complemented
464	#389	C₂²×C₅	1	2	yes	complemented
465	#389	C₂²×C₅	1	1	yes	characteristic, complemented
466	#389	C₂²×C₅	1	1	yes	characteristic, complemented
467	#388	C₂²×C₅	1	2	yes	complemented
468	#388	C₂²×C₅	1	2	yes	complemented
469	#388	C₂²×C₅	1	2	yes	complemented
470	#388	C₂²×C₅	1	2	yes	complemented
471	#388	C₂²×C₅	1	2	yes	complemented
472	#388	C₂²×C₅	1	2	yes	complemented
473	#388	C₂²×C₅	1	2	yes	complemented
474	#388	C₂²×C₅	1	2	yes	complemented
475	#388	C₂²×C₅	1	2	yes	complemented
476	#388	C₂²×C₅	1	2	yes	complemented
477	#388	C₂²×C₅	1	2	yes	complemented
478	#387	C₂²×C₅	1	2	yes	complemented
479	#387	C₂²×C₅	1	2	yes	complemented
480	#387	C₂²×C₅	1	2	yes	complemented
481	#386	C₂²×C₅	1	2	yes	—
482	#386	C₂²×C₅	1	2	yes	—
483	#386	C₂²×C₅	1	2	yes	—
484	#386	C₂²×C₅	1	2	yes	complemented
485	#386	C₂²×C₅	1	2	yes	complemented
486	#386	C₂²×C₅	1	2	yes	complemented
487	#386	C₂²×C₅	1	2	yes	complemented
488	#385	C₂²×C₅	1	2	yes	—
489	#385	C₂²×C₅	1	2	yes	—
490	#385	C₂²×C₅	1	2	yes	complemented
491	#382	C₂²×C₅	1	1	yes	characteristic, complemented
492	#381	C₂²×C₅	1	2	yes	complemented
493	#380	C₂²×C₅	1	1	yes	characteristic
494	#380	C₂²×C₅	1	2	yes	complemented
495	#380	C₂²×C₅	1	1	yes	characteristic, complemented
496	#379	C₂²×C₅	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
498	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
499	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
500	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
501	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
502	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
503	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
504	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
507	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
510	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
511	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
512	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
513	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
514	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
515	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
516	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
517	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
518	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
519	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
520	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
521	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
522	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
523	C₄³	C₂²×C₅	1	1	yes	characteristic, complemented
524	C₂³×C₅	—	2	1	no	—
525	C₂³×C₅	—	2	1	no	—
526	C₂³×C₅	—	2	1	no	—
527	C₂³×C₅	—	2	1	no	—
528	C₂³×C₅	—	2	2	no	—
529	C₂³×C₅	—	2	2	no	—
530	C₂³×C₅	—	2	2	no	—
531	C₂³×C₅	—	2	1	no	—
532	C₂³×C₅	—	2	1	no	—
533	C₂³×C₅	—	2	2	no	—
534	C₂³×C₅	—	2	2	no	—
535	C₂³×C₅	—	2	2	no	—
536	C₂³×C₅	—	2	1	no	—
537	C₂³×C₅	—	2	1	no	—
538	C₂³×C₅	—	2	2	no	—
539	C₂³×C₅	—	2	2	no	—
540	C₂³×C₅	—	2	1	no	—
541	C₂³×C₅	—	2	2	no	—
542	C₂³×C₅	—	2	2	no	—
543	C₂³×C₅	—	2	2	no	—
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	2	no	—
546	C₂³×C₅	—	2	16	no	—
547	C₂³×C₅	—	4	8	no	—
548	C₂³×C₅	—	4	8	no	—
549	C₂³×C₅	—	8	4	no	—
550	C₂³×C₅	—	8	4	no	—
551	C₂³×C₅	—	8	4	no	—
552	C₂³×C₅	—	8	4	no	—
553	C₂³×C₅	C₂³×C₄	1	4	yes	—
554	C₂³×C₅	C₂³×C₄	1	4	yes	—
555	C₂³×C₅	C₂³×C₄	1	2	yes	—
556	C₂³×C₅	C₂³×C₄	1	2	yes	—
557	C₂³×C₅	C₂×#41	1	2	yes	—
558	C₂³×C₅	C₂×#41	1	2	yes	—
559	C₂³×C₅	C₂⁵	1	1	yes	characteristic
560	C₅×Q₈	—	2	8	no	—
561	C₅×D₄	—	2	8	no	—
562	C₅×D₄	—	2	8	no	—
563	C₅×D₄	—	2	8	no	—
564	C₅×D₄	—	4	8	no	—
565	C₅×D₄	—	4	8	no	—
566	C₅×D₄	—	4	8	no	—
567	C₂×C₄×C₅	—	2	1	no	—
568	C₂×C₄×C₅	—	2	1	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	1	no	—
576	C₂×C₄×C₅	—	2	1	no	—
577	C₂×C₄×C₅	—	2	1	no	—
578	C₂×C₄×C₅	—	2	1	no	—
579	C₂×C₄×C₅	—	2	1	no	—
580	C₂×C₄×C₅	—	2	2	no	—
581	C₂×C₄×C₅	—	2	2	no	—
582	C₂×C₄×C₅	—	2	2	no	—
583	C₂×C₄×C₅	—	2	1	no	—
584	C₂×C₄×C₅	—	2	1	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	2	1	no	—
587	C₂×C₄×C₅	—	2	1	no	—
588	C₂×C₄×C₅	—	2	2	no	—
589	C₂×C₄×C₅	—	2	8	no	—
590	C₂×C₄×C₅	—	2	8	no	—
591	C₂×C₄×C₅	—	2	1	no	—
592	C₂×C₄×C₅	—	2	2	no	—
593	C₂×C₄×C₅	—	2	2	no	—
594	C₂×C₄×C₅	—	2	2	no	—
595	C₂×C₄×C₅	—	2	2	no	—
596	C₂×C₄×C₅	—	2	1	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	2	no	—
603	C₂×C₄×C₅	—	2	2	no	—
604	C₂×C₄×C₅	—	2	2	no	—
605	C₂×C₄×C₅	—	2	2	no	—
606	C₂×C₄×C₅	—	2	2	no	—
607	C₂×C₄×C₅	—	2	2	no	—
608	C₂×C₄×C₅	—	2	2	no	—
609	C₂×C₄×C₅	—	2	1	no	—
610	C₂×C₄×C₅	—	2	2	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	4	8	no	—
613	C₂×C₄×C₅	—	4	8	no	—
614	C₂×C₄×C₅	—	4	4	no	—
615	C₂×C₄×C₅	—	4	4	no	—
616	C₂×C₄×C₅	—	4	4	no	—
617	C₂×C₄×C₅	—	4	4	no	—
618	C₂×C₄×C₅	—	8	4	no	—
619	C₂×C₄×C₅	—	8	4	no	—
620	C₂×C₄×C₅	—	8	4	no	—
621	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
622	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
623	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
624	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
625	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
626	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
628	C₂×C₄×C₅	C₂×#41	1	2	yes	—
629	C₂×C₄×C₅	C₂×#41	1	2	yes	—
630	C₂×C₄×C₅	C₂×#41	1	2	yes	—
631	C₂×C₄×C₅	C₂×#41	1	2	yes	—
632	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
633	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
634	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
635	C₂⁵	C₂³×C₅	1	2	yes	—
636	C₂×#41	—	4	2	no	—
637	C₂×#41	—	4	2	no	—
638	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
639	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
640	C₂²×D₄	—	4	2	no	—
641	C₂²×D₄	—	4	2	no	—
642	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
643	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₅	1	2	yes	—
647	C₂²×D₄	C₂³×C₅	1	2	yes	—
648	C₂²×D₄	C₂³×C₅	1	2	yes	—
649	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₅	1	2	yes	—
654	C₂³×C₄	C₂³×C₅	1	2	yes	—
655	C₂³×C₄	C₂³×C₅	1	2	yes	—
656	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₅	1	2	yes	—
658	C₂³×C₄	C₂³×C₅	1	2	yes	—
659	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
660	#124	C₂×C₄×C₅	1	8	yes	complemented
661	#123	C₂×C₄×C₅	1	16	yes	complemented
662	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
663	#121	C₂×C₄×C₅	1	8	yes	complemented
664	#121	C₂×C₄×C₅	1	16	yes	complemented
665	#120	C₂×C₄×C₅	1	16	yes	complemented
666	C₄×Q₈	—	4	2	no	—
667	C₄×Q₈	—	4	2	no	—
668	C₄×D₄	—	2	4	no	—
669	C₄×D₄	—	2	4	no	—
670	C₄×D₄	—	4	2	no	—
671	C₄×D₄	—	4	2	no	—
672	C₄×D₄	—	4	4	no	—
673	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
674	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
675	#117	—	4	4	no	—
676	#117	—	4	2	no	—
677	C₂×C₄⋊C₄	—	4	2	no	—
678	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
692	C₂×C₂²⋊C₄	—	2	8	no	—
693	C₂×C₂²⋊C₄	—	2	8	no	—
694	C₂×C₂²⋊C₄	—	4	4	no	—
695	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
696	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
724	C₂×C₄²	—	4	2	no	—
725	C₂×C₄²	—	4	2	no	—
726	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₅	1	2	yes	—
734	C₂×C₄²	C₂³×C₅	1	2	yes	—
735	C₂×C₄²	C₂³×C₅	1	2	yes	—
736	C₂×C₄²	C₂³×C₅	1	2	yes	—
737	C₂×C₄²	C₂³×C₅	1	2	yes	—
738	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₅	1	2	yes	—
741	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
745	#95	C₂³×C₅	1	1	yes	characteristic
746	#95	C₂³×C₅	1	1	yes	characteristic
747	#95	C₂³×C₅	1	2	yes	—
748	#95	C₂³×C₅	1	2	yes	—
749	#95	C₂³×C₅	1	2	yes	—
750	#95	C₂³×C₅	1	2	yes	—
751	#95	C₂³×C₅	1	2	yes	—
752	#95	C₂³×C₅	1	2	yes	—
753	#95	C₂³×C₅	1	1	yes	characteristic
754	#95	C₂³×C₅	1	1	yes	characteristic
755	#95	C₂³×C₅	1	1	yes	characteristic
756	#95	C₂³×C₅	1	1	yes	characteristic
757	#95	C₂³×C₅	1	2	yes	—
758	#95	C₂³×C₅	1	2	yes	—
759	#95	C₂³×C₅	1	2	yes	—
760	#95	C₂³×C₅	1	2	yes	—
761	#95	C₂³×C₅	1	2	yes	—
762	#95	C₂³×C₅	1	2	yes	—
763	#95	C₂³×C₅	1	2	yes	—
764	C₂²×C₅	—	2	2	no	—
765	C₂²×C₅	—	2	2	no	—
766	C₂²×C₅	—	2	2	no	—
767	C₂²×C₅	—	2	2	no	—
768	C₂²×C₅	—	2	2	no	—
769	C₂²×C₅	—	2	2	no	—
770	C₂²×C₅	—	2	2	no	—
771	C₂²×C₅	—	2	4	no	—
772	C₂²×C₅	—	2	4	no	—
773	C₂²×C₅	—	2	2	no	—
774	C₂²×C₅	—	2	4	no	—
775	C₂²×C₅	—	2	4	no	—
776	C₂²×C₅	—	2	4	no	—
777	C₂²×C₅	—	2	2	no	—
778	C₂²×C₅	—	2	4	no	—
779	C₂²×C₅	—	4	1	no	—
780	C₂²×C₅	—	4	2	no	—
781	C₂²×C₅	—	4	2	no	—
782	C₂²×C₅	—	4	1	no	—
783	C₂²×C₅	—	4	2	no	—
784	C₂²×C₅	—	4	2	no	—
785	C₂²×C₅	—	4	2	no	—
786	C₂²×C₅	—	4	1	no	—
787	C₂²×C₅	—	4	2	no	—
788	C₂²×C₅	—	4	1	no	—
789	C₂²×C₅	—	4	2	no	—
790	C₂²×C₅	—	4	2	no	—
791	C₂²×C₅	—	8	16	no	—
792	C₂²×C₅	C₄×#41	1	4	yes	—
793	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
794	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
795	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
796	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂²×C₅	#585	1	1	yes	characteristic
800	C₄×C₅	—	2	2	no	—
801	C₄×C₅	—	2	2	no	—
802	C₄×C₅	—	2	2	no	—
803	C₄×C₅	—	2	4	no	—
804	C₄×C₅	—	2	2	no	—
805	C₄×C₅	—	2	4	no	—
806	C₄×C₅	—	2	2	no	—
807	C₄×C₅	—	2	2	no	—
808	C₄×C₅	—	2	2	no	—
809	C₄×C₅	—	2	2	no	—
810	C₄×C₅	—	2	2	no	—
811	C₄×C₅	—	4	1	no	—
812	C₄×C₅	—	4	1	no	—
813	C₄×C₅	—	4	2	no	—
814	C₄×C₅	—	4	2	no	—
815	C₄×C₅	—	4	2	no	—
816	C₄×C₅	—	4	1	no	—
817	C₄×C₅	—	4	2	no	—
818	C₄×C₅	#518	1	4	yes	—
819	C₂⁴	—	2	4	no	—
820	C₂⁴	—	2	4	no	—
821	C₂⁴	—	4	2	no	—
822	C₂⁴	—	4	2	no	—
823	C₂⁴	—	4	2	no	—
824	C₂⁴	—	4	2	no	—
825	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
826	C₂⁴	C₂⁴×C₅	1	2	yes	—
827	C₂⁴	C₂⁴×C₅	1	2	yes	—
828	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
829	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
830	#41	—	4	16	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	16	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
848	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
849	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
850	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
851	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
852	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	4	1	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
882	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
883	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
884	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
885	C₂²×C₄	C₅×#41	1	4	yes	complemented
886	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	4	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
917	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
918	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
940	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
941	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
942	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
943	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
944	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
945	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
946	C₂²⋊C₄	C₅×#41	1	4	yes	complemented
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	4	1	no	—
955	C₄²	—	4	1	no	—
956	C₄²	—	4	1	no	—
957	C₄²	—	4	1	no	—
958	C₄²	—	4	2	no	—
959	C₄²	—	4	2	no	—
960	C₄²	—	4	2	no	—
961	C₄²	—	4	2	no	—
962	C₄²	—	4	2	no	—
963	C₄²	—	4	2	no	—
964	C₄²	—	4	1	no	—
965	C₄²	C₂²×C₄×C₅	1	4	yes	—
966	C₂×C₅	—	2	4	no	—
967	C₂×C₅	—	4	2	no	—
968	C₂×C₅	—	4	4	no	—
969	C₂×C₅	—	4	4	no	—
970	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
971	C₂×C₅	C₂×#518	1	1	yes	characteristic
972	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂×C₅	#3505	1	1	yes	characteristic
974	C₂×C₅	#3508	1	1	yes	characteristic
975	C₂×C₅	#3514	1	1	yes	characteristic
976	C₂×C₅	#3519	1	1	yes	characteristic
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	16	no	—
1000	C₂³	—	4	8	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	8	4	no	—
1003	C₂³	—	8	4	no	—
1004	C₂³	—	8	4	no	—
1005	C₂³	—	8	4	no	—
1006	C₂³	C₂³×C₄×C₅	1	4	yes	—
1007	C₂³	C₂³×C₄×C₅	1	4	yes	—
1008	C₂³	C₂³×C₄×C₅	1	2	yes	—
1009	C₂³	C₂³×C₄×C₅	1	2	yes	—
1010	C₂³	C₂×C₅×#41	1	2	yes	—
1011	C₂³	C₂×C₅×#41	1	2	yes	—
1012	C₂³	C₂⁵×C₅	1	1	yes	characteristic
1013	Q₈	—	2	8	no	—
1014	D₄	—	2	8	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	4	8	no	—
1018	D₄	—	4	8	no	—
1019	D₄	—	4	8	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	2	8	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	4	8	no	—
1066	C₂×C₄	—	4	8	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	8	4	no	—
1072	C₂×C₄	—	8	4	no	—
1073	C₂×C₄	—	8	4	no	—
1074	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1075	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1076	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1077	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1078	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1079	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1080	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1081	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1082	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1083	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1084	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1085	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1086	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1087	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1088	C₅	#34320	1	1	yes	characteristic, direct product factor, Sylow
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	4	no	—
1100	C₂²	—	2	4	no	—
1101	C₂²	—	2	4	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	4	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	8	16	no	—
1117	C₂²	C₄×C₅×#41	1	4	yes	—
1118	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1119	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1120	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1121	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1122	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1123	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1124	C₂²	C₅×#585	1	1	yes	characteristic
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	4	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	4	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	C₅×#518	1	4	yes	—
1144	C₂	—	2	4	no	—
1145	C₂	—	4	4	no	—
1146	C₂	—	4	4	no	—
1147	C₂	—	4	2	no	—
1148	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
1149	C₂	C₂×C₅×#518	1	1	yes	characteristic
1150	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1151	C₂	C₅×#3505	1	1	yes	characteristic
1152	C₂	C₅×#3508	1	1	yes	characteristic
1153	C₂	C₅×#3514	1	1	yes	characteristic
1154	C₂	C₅×#3519	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#2374	C₂	semidirect
3. C₅×#2367	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2360	C₂	semidirect
7. C₅×#2358	C₂	semidirect
8. C₅×#2357	C₂	semidirect
9. C₅×#2352	C₂	semidirect
10. C₅×#2342	C₂	semidirect
11. C₅×#2341	C₂	semidirect
12. C₅×D₄×C₂²⋊C₄	C₂	semidirect
13. C₅×#2335	C₂	semidirect
14. C₅×#2333	C₂	semidirect
15. C₅×#2321	C₂	semidirect
16. C₄×C₅×#124	C₂	semidirect
17. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₅×#121	C₂	semidirect
19. C₅×#2297	C₂	semidirect
20. C₅×#2293	C₂	semidirect
21. C₂×C₅×#390	C₂	semidirect
22. C₅×#2273	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
26. C₅×#546	C₄	semidirect
33. C₂×C₄×C₅×Q₈	C₂²	semidirect
34. C₂×C₄×C₅×Q₈	C₂²	semidirect
41. C₂×C₄×C₅×D₄	C₂²	semidirect
42. C₂×C₅×#117	C₂²	semidirect
43. C₂×C₅×#117	C₂²	semidirect
50. C₂²×C₄²×C₅	C₂²	semidirect
51. C₅×#391	C₂²	semidirect
52. C₅×#391	C₂²	semidirect
61. C₅×#390	C₂²	semidirect
62. C₅×#390	C₂²	semidirect
63. C₅×#390	C₂²	semidirect
64. C₅×#389	C₂²	semidirect
65. C₅×#389	C₂²	semidirect
66. C₅×#389	C₂²	semidirect
67. C₅×#388	C₂²	semidirect
68. C₅×#388	C₂²	semidirect
69. C₅×#388	C₂²	semidirect
70. C₅×#388	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×#382	C₂²	semidirect
92. C₅×#381	C₂²	semidirect
94. C₅×#380	C₂²	semidirect
95. C₅×#380	C₂²	semidirect
97. C₄×C₅×C₄⋊C₄	C₂²	semidirect
98. C₄×C₅×C₄⋊C₄	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
110. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
111. C₄×C₅×C₂²⋊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. C₄³×C₅	C₂²	semidirect
124. #34320	C₅	direct (N × H)
128. C₂×C₅×#41	C₂×C₄	semidirect
132. C₂²×C₅×D₄	C₂×C₄	semidirect
150. C₅×#124	C₂×C₄	semidirect
151. C₅×#123	C₂×C₄	semidirect
152. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
153. C₅×#121	C₂×C₄	semidirect
154. C₅×#121	C₂×C₄	semidirect
155. C₅×#120	C₂×C₄	semidirect
163. C₄×C₅×D₄	C₂×C₄	semidirect
164. C₄×C₅×D₄	C₂×C₄	semidirect
185. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
255. #2374	C₂×C₅	semidirect
256. #2367	C₂×C₅	semidirect
257. #2363	C₂×C₅	semidirect
258. #2363	C₂×C₅	semidirect
259. #2360	C₂×C₅	semidirect
260. #2358	C₂×C₅	semidirect
261. #2357	C₂×C₅	semidirect
262. #2352	C₂×C₅	semidirect
263. #2342	C₂×C₅	semidirect
264. #2341	C₂×C₅	semidirect
265. D₄×C₂²⋊C₄	C₂×C₅	semidirect
266. #2335	C₂×C₅	semidirect
267. #2333	C₂×C₅	semidirect
268. #2321	C₂×C₅	semidirect
269. C₄×#124	C₂×C₅	semidirect
270. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
271. C₄×#121	C₂×C₅	semidirect
272. #2297	C₂×C₅	semidirect
273. #2293	C₂×C₅	semidirect
274. C₂×#390	C₂×C₅	semidirect
275. #2273	C₂×C₅	semidirect
276. C₄²×D₄	C₂×C₅	semidirect
343. C₂²×C₄×C₅	#41	semidirect
404. C₅×C₂²⋊C₄	#41	semidirect
426. #546	C₄×C₅	semidirect
433. C₂×C₄×Q₈	C₂²×C₅	semidirect
434. C₂×C₄×Q₈	C₂²×C₅	semidirect
441. C₂×C₄×D₄	C₂²×C₅	semidirect
442. C₂×#117	C₂²×C₅	semidirect
443. C₂×#117	C₂²×C₅	semidirect
450. C₂²×C₄²	C₂²×C₅	semidirect
451. #391	C₂²×C₅	semidirect
452. #391	C₂²×C₅	semidirect
461. #390	C₂²×C₅	semidirect
462. #390	C₂²×C₅	semidirect
463. #390	C₂²×C₅	semidirect
464. #389	C₂²×C₅	semidirect
465. #389	C₂²×C₅	semidirect
466. #389	C₂²×C₅	semidirect
467. #388	C₂²×C₅	semidirect
468. #388	C₂²×C₅	semidirect
469. #388	C₂²×C₅	semidirect
470. #388	C₂²×C₅	semidirect
471. #388	C₂²×C₅	semidirect
472. #388	C₂²×C₅	semidirect
473. #388	C₂²×C₅	semidirect
474. #388	C₂²×C₅	semidirect
475. #388	C₂²×C₅	semidirect
476. #388	C₂²×C₅	semidirect
477. #388	C₂²×C₅	semidirect
478. #387	C₂²×C₅	semidirect
479. #387	C₂²×C₅	semidirect
480. #387	C₂²×C₅	semidirect
484. #386	C₂²×C₅	semidirect
485. #386	C₂²×C₅	semidirect
486. #386	C₂²×C₅	semidirect
487. #386	C₂²×C₅	semidirect
490. #385	C₂²×C₅	semidirect
491. #382	C₂²×C₅	semidirect
492. #381	C₂²×C₅	semidirect
494. #380	C₂²×C₅	semidirect
495. #380	C₂²×C₅	semidirect
497. C₄×C₄⋊C₄	C₂²×C₅	semidirect
498. C₄×C₄⋊C₄	C₂²×C₅	semidirect
499. C₄×C₄⋊C₄	C₂²×C₅	semidirect
500. C₄×C₄⋊C₄	C₂²×C₅	semidirect
501. C₄×C₄⋊C₄	C₂²×C₅	semidirect
502. C₄×C₄⋊C₄	C₂²×C₅	semidirect
503. C₄×C₄⋊C₄	C₂²×C₅	semidirect
510. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
511. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
512. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
513. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
514. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
515. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
516. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
517. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
518. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
519. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
520. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
521. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
522. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
523. C₄³	C₂²×C₅	semidirect
638. C₂×#41	C₂×C₄×C₅	semidirect
642. C₂²×D₄	C₂×C₄×C₅	semidirect
660. #124	C₂×C₄×C₅	semidirect
661. #123	C₂×C₄×C₅	semidirect
662. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
663. #121	C₂×C₄×C₅	semidirect
664. #121	C₂×C₄×C₅	semidirect
665. #120	C₂×C₄×C₅	semidirect
673. C₄×D₄	C₂×C₄×C₅	semidirect
674. C₄×D₄	C₂×C₄×C₅	semidirect
695. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
885. C₂²×C₄	C₅×#41	semidirect
946. C₂²⋊C₄	C₅×#41	semidirect
1088. C₅	#34320	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
C₅×#2374	2
C₅×#2367	2
C₅×#2363	2
C₅×#2360	2
C₅×#2358	2
C₅×#2357	2
C₅×#2352	2
C₅×#2342	2
C₅×#2341	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2335	2
C₅×#2333	2
C₅×#2321	2
C₄×C₅×#124	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#121	2
C₅×#2297	2
C₅×#2293	2
C₂×C₅×#390	2
C₅×#2273	2
C₄²×C₅×D₄	2
#34320	5

Subgroups — C5×#34320 #11957040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34320 #11957040