Subgroups — C₅×#34288 #11957008

Order 1280.

3584 conjugacy classes of subgroups.

The subgroup lattice has 1198 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×C₅×#520	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×#2361	C₂	1	2	yes	maximal, complemented
6	C₅×#2361	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×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₄⋊C₄	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	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2325	C₂	1	2	yes	maximal, complemented
17	C₅×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#2322	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₅×#120	C₂	1	2	yes	maximal, complemented
21	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅×#385	C₂	1	2	yes	maximal, complemented
23	C₅×#2275	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	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
27	C₅×#546	C₄	1	16	yes	complemented
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	C₅×#520	—	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	2	yes	—
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
43	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
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	2	yes	complemented
50	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
51	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
52	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₅×#117	C₂²	1	2	yes	complemented
54	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
56	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
58	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
62	C₅×#391	C₂²	1	1	yes	characteristic, complemented
63	C₅×#391	C₂²	1	1	yes	characteristic, complemented
64	C₅×#390	C₂²	1	1	yes	characteristic
65	C₅×#390	C₂²	1	1	yes	characteristic
66	C₅×#390	C₂²	1	2	yes	complemented
67	C₅×#389	C₂²	1	1	yes	characteristic, complemented
68	C₅×#389	C₂²	1	2	yes	complemented
69	C₅×#389	C₂²	1	2	yes	complemented
70	C₅×#389	C₂²	1	1	yes	characteristic, complemented
71	C₅×#388	C₂²	1	1	yes	characteristic, complemented
72	C₅×#388	C₂²	1	1	yes	characteristic, 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×#388	C₂²	1	2	yes	complemented
79	C₅×#387	C₂²	1	1	yes	characteristic, complemented
80	C₅×#387	C₂²	1	1	yes	characteristic, complemented
81	C₅×#387	C₂²	1	2	yes	complemented
82	C₅×#387	C₂²	1	2	yes	complemented
83	C₅×#386	C₂²	1	1	yes	characteristic
84	C₅×#386	C₂²	1	1	yes	characteristic
85	C₅×#386	C₂²	1	2	yes	—
86	C₅×#386	C₂²	1	2	yes	—
87	C₅×#386	C₂²	1	2	yes	complemented
88	C₅×#386	C₂²	1	2	yes	complemented
89	C₅×#386	C₂²	1	2	yes	complemented
90	C₅×#386	C₂²	1	2	yes	complemented
91	C₅×#385	C₂²	1	1	yes	characteristic
92	C₅×#385	C₂²	1	2	yes	—
93	C₅×#385	C₂²	1	2	yes	—
94	C₅×#385	C₂²	1	2	yes	—
95	C₅×#385	C₂²	1	1	yes	characteristic
96	C₅×#385	C₂²	1	2	yes	complemented
97	C₅×#385	C₂²	1	2	yes	complemented
98	C₅×#385	C₂²	1	2	yes	complemented
99	C₅×#385	C₂²	1	2	yes	complemented
100	C₅×#385	C₂²	1	2	yes	complemented
101	C₅×#385	C₂²	1	2	yes	complemented
102	C₅×#385	C₂²	1	2	yes	complemented
103	C₅×#385	C₂²	1	2	yes	complemented
104	C₅×#384	C₂²	1	1	yes	characteristic, complemented
105	C₅×#381	C₂²	1	2	yes	complemented
106	C₅×#380	C₂²	1	1	yes	characteristic
107	C₅×#380	C₂²	1	1	yes	characteristic, complemented
108	C₅×#380	C₂²	1	2	yes	complemented
109	C₅×#379	C₂²	1	2	yes	—
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₅×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₅×#95	C₂²	1	2	yes	complemented
125	C₂×C₅×#95	C₂²	1	2	yes	complemented
126	#34288	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	—	4	4	no	—
143	C₂³×C₄×C₅	—	4	4	no	—
144	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅	C₂³	1	2	yes	—
151	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₅	C₂³	1	2	yes	—
153	C₂³×C₄×C₅	C₂³	1	2	yes	—
154	C₂³×C₄×C₅	C₂³	1	2	yes	—
155	C₂³×C₄×C₅	C₂³	1	2	yes	—
156	C₂³×C₄×C₅	C₂³	1	2	yes	—
157	C₂³×C₄×C₅	C₂³	1	2	yes	—
158	C₅×#124	C₂×C₄	1	8	yes	complemented
159	C₅×#123	C₂×C₄	1	16	yes	complemented
160	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
161	C₅×#121	C₂×C₄	1	8	yes	complemented
162	C₅×#121	C₂×C₄	1	16	yes	complemented
163	C₅×#120	C₂×C₄	1	16	yes	complemented
164	C₄×C₅×Q₈	—	2	4	no	—
165	C₄×C₅×Q₈	—	2	4	no	—
166	C₄×C₅×D₄	—	2	4	no	—
167	C₄×C₅×D₄	—	2	4	no	—
168	C₄×C₅×D₄	—	2	4	no	—
169	C₄×C₅×D₄	—	2	8	no	—
170	C₄×C₅×D₄	—	2	8	no	—
171	C₄×C₅×D₄	—	2	4	no	—
172	C₄×C₅×D₄	—	2	8	no	—
173	C₄×C₅×D₄	—	2	8	no	—
174	C₄×C₅×D₄	—	2	4	no	—
175	C₄×C₅×D₄	—	4	4	no	—
176	C₄×C₅×D₄	—	4	4	no	—
177	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
178	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
179	C₄×C₅×D₄	D₄	1	8	yes	complemented
180	C₅×#117	—	2	8	no	—
181	C₅×#117	—	2	4	no	—
182	C₂×C₅×C₄⋊C₄	—	2	8	no	—
183	C₂×C₅×C₄⋊C₄	—	2	4	no	—
184	C₂×C₅×C₄⋊C₄	—	2	4	no	—
185	C₂×C₅×C₄⋊C₄	—	4	4	no	—
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	2	yes	—
189	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
197	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
206	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
207	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
216	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
221	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
226	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₄²×C₅	—	2	4	no	—
234	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅	C₂³	1	2	yes	—
236	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	1	yes	characteristic
241	C₂×C₄²×C₅	C₂³	1	2	yes	—
242	C₂×C₄²×C₅	C₂³	1	2	yes	—
243	C₂×C₄²×C₅	C₂³	1	2	yes	—
244	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
246	C₅×#95	C₂³	1	1	yes	characteristic
247	C₅×#95	C₂³	1	1	yes	characteristic
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	C₅×#95	C₂³	1	1	yes	characteristic
255	C₅×#95	C₂³	1	1	yes	characteristic
256	C₅×#95	C₂³	1	1	yes	characteristic
257	C₅×#95	C₂³	1	2	yes	—
258	C₅×#95	C₂³	1	2	yes	—
259	C₅×#95	C₂³	1	2	yes	—
260	C₅×#95	C₂³	1	2	yes	—
261	C₅×#95	C₂³	1	1	yes	characteristic
262	C₅×#95	C₂³	1	1	yes	characteristic
263	C₅×#95	C₂³	1	1	yes	characteristic
264	C₅×#95	C₂³	1	1	yes	characteristic
265	C₅×#95	C₂³	1	2	yes	—
266	C₅×#95	C₂³	1	1	yes	characteristic
267	C₂×#546	C₂×C₅	1	1	yes	characteristic
268	C₂×#520	C₂×C₅	1	1	yes	characteristic, complemented
269	C₂²×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
270	#2367	C₂×C₅	1	1	yes	characteristic, complemented
271	#2361	C₂×C₅	1	2	yes	complemented
272	#2361	C₂×C₅	1	1	yes	characteristic, complemented
273	#2360	C₂×C₅	1	1	yes	characteristic, complemented
274	#2359	C₂×C₅	1	2	yes	complemented
275	#2358	C₂×C₅	1	2	yes	complemented
276	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
277	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
278	#2342	C₂×C₅	1	2	yes	complemented
279	#2339	C₂×C₅	1	1	yes	characteristic, complemented
280	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
281	#2326	C₂×C₅	1	1	yes	characteristic, complemented
282	#2325	C₂×C₅	1	2	yes	complemented
283	#2324	C₂×C₅	1	1	yes	characteristic, complemented
284	#2322	C₂×C₅	1	2	yes	complemented
285	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
286	C₄×#120	C₂×C₅	1	2	yes	complemented
287	#2290	C₂×C₅	1	1	yes	characteristic, complemented
288	C₂×#385	C₂×C₅	1	2	yes	complemented
289	#2275	C₂×C₅	1	1	yes	characteristic, complemented
290	C₂⁴×C₅	—	2	4	no	—
291	C₂⁴×C₅	—	2	4	no	—
292	C₂⁴×C₅	—	2	4	no	—
293	C₂⁴×C₅	—	2	4	no	—
294	C₂⁴×C₅	—	4	2	no	—
295	C₂⁴×C₅	—	4	2	no	—
296	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
297	C₂⁴×C₅	C₂⁴	1	2	yes	—
298	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
299	C₂⁴×C₅	C₂⁴	1	2	yes	—
300	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
301	C₅×#41	—	2	32	no	—
302	C₂×C₅×Q₈	—	2	2	no	—
303	C₂×C₅×Q₈	—	2	2	no	—
304	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
305	C₂×C₅×D₄	—	2	4	no	—
306	C₂×C₅×D₄	—	2	4	no	—
307	C₂×C₅×D₄	—	2	4	no	—
308	C₂×C₅×D₄	—	2	4	no	—
309	C₂×C₅×D₄	—	2	2	no	—
310	C₂×C₅×D₄	—	2	2	no	—
311	C₂×C₅×D₄	—	2	32	no	—
312	C₂×C₅×D₄	—	2	2	no	—
313	C₂×C₅×D₄	—	2	2	no	—
314	C₂×C₅×D₄	—	4	2	no	—
315	C₂×C₅×D₄	—	4	2	no	—
316	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
317	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
318	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
319	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
320	C₂×C₅×D₄	C₂²×C₄	1	8	yes	complemented
321	C₂×C₅×D₄	C₂²×C₄	1	8	yes	complemented
322	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
323	C₂×C₅×D₄	#41	1	4	yes	—
324	C₂²×C₄×C₅	—	2	4	no	—
325	C₂²×C₄×C₅	—	2	4	no	—
326	C₂²×C₄×C₅	—	2	2	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	2	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	4	no	—
335	C₂²×C₄×C₅	—	2	2	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	4	no	—
341	C₂²×C₄×C₅	—	2	4	no	—
342	C₂²×C₄×C₅	—	2	4	no	—
343	C₂²×C₄×C₅	—	2	4	no	—
344	C₂²×C₄×C₅	—	2	4	no	—
345	C₂²×C₄×C₅	—	4	2	no	—
346	C₂²×C₄×C₅	—	4	2	no	—
347	C₂²×C₄×C₅	—	4	2	no	—
348	C₂²×C₄×C₅	—	4	2	no	—
349	C₂²×C₄×C₅	—	4	2	no	—
350	C₂²×C₄×C₅	—	4	2	no	—
351	C₂²×C₄×C₅	—	4	2	no	—
352	C₂²×C₄×C₅	—	4	2	no	—
353	C₂²×C₄×C₅	—	4	1	no	—
354	C₂²×C₄×C₅	—	4	2	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	32	no	—
362	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
363	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
364	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	complemented
365	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
366	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
367	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
386	C₅×C₄⋊C₄	—	2	2	no	—
387	C₅×C₄⋊C₄	—	2	4	no	—
388	C₅×C₄⋊C₄	—	2	4	no	—
389	C₅×C₄⋊C₄	—	2	2	no	—
390	C₅×C₄⋊C₄	—	2	4	no	—
391	C₅×C₄⋊C₄	—	2	4	no	—
392	C₅×C₄⋊C₄	—	2	2	no	—
393	C₅×C₄⋊C₄	—	2	2	no	—
394	C₅×C₄⋊C₄	—	2	2	no	—
395	C₅×C₄⋊C₄	—	2	2	no	—
396	C₅×C₄⋊C₄	—	2	4	no	—
397	C₅×C₄⋊C₄	—	4	2	no	—
398	C₅×C₄⋊C₄	—	4	2	no	—
399	C₅×C₄⋊C₄	—	4	1	no	—
400	C₅×C₄⋊C₄	—	4	2	no	—
401	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
402	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
403	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
404	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
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	2	no	—
411	C₅×C₂²⋊C₄	—	2	4	no	—
412	C₅×C₂²⋊C₄	—	2	4	no	—
413	C₅×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
420	C₅×C₂²⋊C₄	—	4	2	no	—
421	C₅×C₂²⋊C₄	—	4	2	no	—
422	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
423	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
424	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
425	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
426	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
427	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
428	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
429	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
430	C₄²×C₅	—	2	2	no	—
431	C₄²×C₅	—	2	2	no	—
432	C₄²×C₅	—	2	2	no	—
433	C₄²×C₅	—	2	4	no	—
434	C₄²×C₅	—	2	4	no	—
435	C₄²×C₅	—	2	2	no	—
436	C₄²×C₅	—	2	2	no	—
437	C₄²×C₅	—	4	2	no	—
438	C₄²×C₅	—	4	2	no	—
439	C₄²×C₅	—	4	2	no	—
440	C₄²×C₅	C₂²×C₄	1	4	yes	complemented
441	C₄²×C₅	C₂×D₄	1	4	yes	—
442	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
444	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
445	#546	C₄×C₅	1	16	yes	complemented
446	C₂×#124	C₂²×C₅	1	1	yes	characteristic
447	C₂×#123	C₂²×C₅	1	2	yes	—
448	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
449	C₂×#121	C₂²×C₅	1	1	yes	characteristic
450	C₂×#121	C₂²×C₅	1	2	yes	—
451	C₂×#120	C₂²×C₅	1	2	yes	—
452	#520	—	2	8	no	—
453	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
454	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
455	C₂×C₄×D₄	—	2	8	no	—
456	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
464	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
468	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
469	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
470	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
471	C₂×#117	C₂²×C₅	1	2	yes	complemented
472	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
474	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
475	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
476	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
477	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
478	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
479	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
480	#391	C₂²×C₅	1	1	yes	characteristic, complemented
481	#391	C₂²×C₅	1	1	yes	characteristic, complemented
482	#390	C₂²×C₅	1	1	yes	characteristic
483	#390	C₂²×C₅	1	1	yes	characteristic
484	#390	C₂²×C₅	1	2	yes	complemented
485	#389	C₂²×C₅	1	2	yes	complemented
486	#389	C₂²×C₅	1	2	yes	complemented
487	#389	C₂²×C₅	1	1	yes	characteristic, complemented
488	#389	C₂²×C₅	1	1	yes	characteristic, complemented
489	#388	C₂²×C₅	1	2	yes	complemented
490	#388	C₂²×C₅	1	2	yes	complemented
491	#388	C₂²×C₅	1	2	yes	complemented
492	#388	C₂²×C₅	1	1	yes	characteristic, complemented
493	#388	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	1	yes	characteristic, complemented
497	#387	C₂²×C₅	1	1	yes	characteristic, complemented
498	#387	C₂²×C₅	1	2	yes	complemented
499	#387	C₂²×C₅	1	2	yes	complemented
500	#387	C₂²×C₅	1	1	yes	characteristic, complemented
501	#386	C₂²×C₅	1	2	yes	—
502	#386	C₂²×C₅	1	2	yes	—
503	#386	C₂²×C₅	1	1	yes	characteristic
504	#386	C₂²×C₅	1	1	yes	characteristic
505	#386	C₂²×C₅	1	2	yes	complemented
506	#386	C₂²×C₅	1	2	yes	complemented
507	#386	C₂²×C₅	1	2	yes	complemented
508	#386	C₂²×C₅	1	2	yes	complemented
509	#385	C₂²×C₅	1	1	yes	characteristic
510	#385	C₂²×C₅	1	2	yes	—
511	#385	C₂²×C₅	1	2	yes	—
512	#385	C₂²×C₅	1	1	yes	characteristic
513	#385	C₂²×C₅	1	2	yes	—
514	#385	C₂²×C₅	1	2	yes	complemented
515	#385	C₂²×C₅	1	2	yes	complemented
516	#385	C₂²×C₅	1	2	yes	complemented
517	#385	C₂²×C₅	1	2	yes	complemented
518	#385	C₂²×C₅	1	2	yes	complemented
519	#385	C₂²×C₅	1	2	yes	complemented
520	#385	C₂²×C₅	1	2	yes	complemented
521	#385	C₂²×C₅	1	2	yes	complemented
522	#384	C₂²×C₅	1	1	yes	characteristic, complemented
523	#381	C₂²×C₅	1	2	yes	complemented
524	#380	C₂²×C₅	1	1	yes	characteristic
525	#380	C₂²×C₅	1	1	yes	characteristic, complemented
526	#380	C₂²×C₅	1	2	yes	complemented
527	#379	C₂²×C₅	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
529	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
531	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
532	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
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	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
537	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
538	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
539	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
540	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
541	#376	C₂²×C₅	1	1	yes	characteristic, complemented
542	C₂×#95	C₂²×C₅	1	2	yes	complemented
543	C₂×#95	C₂²×C₅	1	2	yes	complemented
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	1	no	—
546	C₂³×C₅	—	2	2	no	—
547	C₂³×C₅	—	2	1	no	—
548	C₂³×C₅	—	2	2	no	—
549	C₂³×C₅	—	2	2	no	—
550	C₂³×C₅	—	2	2	no	—
551	C₂³×C₅	—	2	1	no	—
552	C₂³×C₅	—	2	16	no	—
553	C₂³×C₅	—	2	16	no	—
554	C₂³×C₅	—	2	1	no	—
555	C₂³×C₅	—	2	2	no	—
556	C₂³×C₅	—	2	1	no	—
557	C₂³×C₅	—	2	2	no	—
558	C₂³×C₅	—	2	1	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	2	no	—
564	C₂³×C₅	—	2	1	no	—
565	C₂³×C₅	—	2	2	no	—
566	C₂³×C₅	—	4	8	no	—
567	C₂³×C₅	—	4	8	no	—
568	C₂³×C₅	—	4	8	no	—
569	C₂³×C₅	—	4	8	no	—
570	C₂³×C₅	—	4	8	no	—
571	C₂³×C₅	C₂³×C₄	1	4	yes	—
572	C₂³×C₅	C₂³×C₄	1	2	yes	—
573	C₂³×C₅	C₂³×C₄	1	4	yes	—
574	C₂³×C₅	C₂³×C₄	1	2	yes	—
575	C₂³×C₅	C₂²×D₄	1	4	yes	—
576	C₂³×C₅	C₂×#41	1	4	yes	—
577	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
578	C₂³×C₅	2₋¹⁺⁴	1	2	yes	—
579	C₂³×C₅	C₂⁵	1	1	yes	characteristic
580	C₅×Q₈	—	2	8	no	—
581	C₅×D₄	—	2	16	no	—
582	C₅×D₄	—	2	16	no	—
583	C₅×D₄	—	2	8	no	—
584	C₅×D₄	—	2	8	no	—
585	C₅×D₄	—	4	8	no	—
586	C₅×D₄	C₄×D₄	1	16	yes	complemented
587	C₂×C₄×C₅	—	2	8	no	—
588	C₂×C₄×C₅	—	2	16	no	—
589	C₂×C₄×C₅	—	2	1	no	—
590	C₂×C₄×C₅	—	2	2	no	—
591	C₂×C₄×C₅	—	2	1	no	—
592	C₂×C₄×C₅	—	2	1	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	1	no	—
595	C₂×C₄×C₅	—	2	2	no	—
596	C₂×C₄×C₅	—	2	1	no	—
597	C₂×C₄×C₅	—	2	2	no	—
598	C₂×C₄×C₅	—	2	2	no	—
599	C₂×C₄×C₅	—	2	2	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	1	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	1	no	—
606	C₂×C₄×C₅	—	2	1	no	—
607	C₂×C₄×C₅	—	2	2	no	—
608	C₂×C₄×C₅	—	2	1	no	—
609	C₂×C₄×C₅	—	2	8	no	—
610	C₂×C₄×C₅	—	2	8	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	2	no	—
616	C₂×C₄×C₅	—	2	1	no	—
617	C₂×C₄×C₅	—	2	1	no	—
618	C₂×C₄×C₅	—	2	2	no	—
619	C₂×C₄×C₅	—	2	1	no	—
620	C₂×C₄×C₅	—	2	2	no	—
621	C₂×C₄×C₅	—	2	1	no	—
622	C₂×C₄×C₅	—	2	1	no	—
623	C₂×C₄×C₅	—	2	2	no	—
624	C₂×C₄×C₅	—	2	2	no	—
625	C₂×C₄×C₅	—	2	2	no	—
626	C₂×C₄×C₅	—	2	1	no	—
627	C₂×C₄×C₅	—	2	2	no	—
628	C₂×C₄×C₅	—	2	1	no	—
629	C₂×C₄×C₅	—	2	1	no	—
630	C₂×C₄×C₅	—	2	1	no	—
631	C₂×C₄×C₅	—	2	2	no	—
632	C₂×C₄×C₅	—	2	1	no	—
633	C₂×C₄×C₅	—	2	1	no	—
634	C₂×C₄×C₅	—	2	1	no	—
635	C₂×C₄×C₅	—	4	8	no	—
636	C₂×C₄×C₅	—	4	8	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	8	no	—
642	C₂×C₄×C₅	—	8	4	no	—
643	C₂×C₄×C₅	—	8	4	no	—
644	C₂×C₄×C₅	—	8	4	no	—
645	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
646	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
647	C₂×C₄×C₅	C₂³×C₄	1	4	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	2	yes	—
652	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
653	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
654	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
655	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
656	C₂×C₄×C₅	C₂×#41	1	2	yes	—
657	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
658	C₂⁵	C₂³×C₅	1	2	yes	—
659	C₂×#41	—	2	4	no	—
660	C₂×#41	—	2	4	no	—
661	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
662	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
663	C₂²×D₄	—	2	4	no	—
664	C₂²×D₄	—	2	4	no	—
665	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
666	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₅	1	2	yes	—
668	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₅	1	2	yes	—
670	C₂²×D₄	C₂³×C₅	1	2	yes	—
671	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
672	C₂³×C₄	—	2	8	no	—
673	C₂³×C₄	—	4	4	no	—
674	C₂³×C₄	—	4	4	no	—
675	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₅	1	2	yes	—
678	C₂³×C₄	C₂³×C₅	1	2	yes	—
679	C₂³×C₄	C₂³×C₅	1	2	yes	—
680	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₅	1	2	yes	—
682	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅	1	2	yes	—
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	#124	C₂×C₄×C₅	1	8	yes	complemented
690	#123	C₂×C₄×C₅	1	16	yes	complemented
691	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
692	#121	C₂×C₄×C₅	1	8	yes	complemented
693	#121	C₂×C₄×C₅	1	16	yes	complemented
694	#120	C₂×C₄×C₅	1	16	yes	complemented
695	C₄×Q₈	—	2	4	no	—
696	C₄×Q₈	—	2	4	no	—
697	C₄×D₄	—	2	4	no	—
698	C₄×D₄	—	2	4	no	—
699	C₄×D₄	—	2	4	no	—
700	C₄×D₄	—	2	8	no	—
701	C₄×D₄	—	2	8	no	—
702	C₄×D₄	—	2	4	no	—
703	C₄×D₄	—	2	8	no	—
704	C₄×D₄	—	2	8	no	—
705	C₄×D₄	—	2	4	no	—
706	C₄×D₄	—	4	4	no	—
707	C₄×D₄	—	4	4	no	—
708	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
709	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
710	C₄×D₄	C₅×D₄	1	8	yes	complemented
711	#117	—	2	8	no	—
712	#117	—	2	4	no	—
713	C₂×C₄⋊C₄	—	2	8	no	—
714	C₂×C₄⋊C₄	—	2	4	no	—
715	C₂×C₄⋊C₄	—	2	4	no	—
716	C₂×C₄⋊C₄	—	4	4	no	—
717	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	—	4	4	no	—
738	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
739	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
749	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
764	C₂×C₄²	—	2	4	no	—
765	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₅	1	2	yes	—
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	2	yes	—
773	C₂×C₄²	C₂³×C₅	1	2	yes	—
774	C₂×C₄²	C₂³×C₅	1	2	yes	—
775	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
777	#95	C₂³×C₅	1	1	yes	characteristic
778	#95	C₂³×C₅	1	1	yes	characteristic
779	#95	C₂³×C₅	1	2	yes	—
780	#95	C₂³×C₅	1	2	yes	—
781	#95	C₂³×C₅	1	2	yes	—
782	#95	C₂³×C₅	1	2	yes	—
783	#95	C₂³×C₅	1	2	yes	—
784	#95	C₂³×C₅	1	2	yes	—
785	#95	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	1	yes	characteristic
793	#95	C₂³×C₅	1	1	yes	characteristic
794	#95	C₂³×C₅	1	1	yes	characteristic
795	#95	C₂³×C₅	1	1	yes	characteristic
796	#95	C₂³×C₅	1	2	yes	—
797	#95	C₂³×C₅	1	1	yes	characteristic
798	C₂²×C₅	—	2	2	no	—
799	C₂²×C₅	—	2	4	no	—
800	C₂²×C₅	—	2	4	no	—
801	C₂²×C₅	—	2	2	no	—
802	C₂²×C₅	—	2	2	no	—
803	C₂²×C₅	—	2	4	no	—
804	C₂²×C₅	—	2	2	no	—
805	C₂²×C₅	—	2	4	no	—
806	C₂²×C₅	—	2	4	no	—
807	C₂²×C₅	—	2	2	no	—
808	C₂²×C₅	—	2	2	no	—
809	C₂²×C₅	—	2	4	no	—
810	C₂²×C₅	—	2	2	no	—
811	C₂²×C₅	—	2	4	no	—
812	C₂²×C₅	—	2	2	no	—
813	C₂²×C₅	—	2	4	no	—
814	C₂²×C₅	—	2	2	no	—
815	C₂²×C₅	—	2	4	no	—
816	C₂²×C₅	—	4	32	no	—
817	C₂²×C₅	—	4	2	no	—
818	C₂²×C₅	—	4	1	no	—
819	C₂²×C₅	—	4	1	no	—
820	C₂²×C₅	—	4	2	no	—
821	C₂²×C₅	—	4	1	no	—
822	C₂²×C₅	—	4	2	no	—
823	C₂²×C₅	—	4	1	no	—
824	C₂²×C₅	—	4	2	no	—
825	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
826	C₂²×C₅	#520	1	4	yes	complemented
827	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
828	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
829	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
830	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
832	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
833	C₂²×C₅	#585	1	1	yes	characteristic
834	C₄×C₅	—	2	2	no	—
835	C₄×C₅	—	2	2	no	—
836	C₄×C₅	—	2	4	no	—
837	C₄×C₅	—	2	2	no	—
838	C₄×C₅	—	2	2	no	—
839	C₄×C₅	—	2	4	no	—
840	C₄×C₅	—	2	2	no	—
841	C₄×C₅	—	2	2	no	—
842	C₄×C₅	—	2	4	no	—
843	C₄×C₅	—	2	2	no	—
844	C₄×C₅	—	4	2	no	—
845	C₄×C₅	—	4	1	no	—
846	C₄×C₅	—	4	2	no	—
847	C₄×C₅	—	4	1	no	—
848	C₄×C₅	—	4	1	no	—
849	C₄×C₅	—	4	2	no	—
850	C₄×C₅	—	4	1	no	—
851	C₄×C₅	—	4	1	no	—
852	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
853	C₂⁴	—	2	4	no	—
854	C₂⁴	—	2	4	no	—
855	C₂⁴	—	2	4	no	—
856	C₂⁴	—	2	4	no	—
857	C₂⁴	—	4	2	no	—
858	C₂⁴	—	4	2	no	—
859	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
860	C₂⁴	C₂⁴×C₅	1	2	yes	—
861	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
862	C₂⁴	C₂⁴×C₅	1	2	yes	—
863	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
864	#41	—	2	32	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	4	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	32	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
880	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
881	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
882	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
883	C₂×D₄	C₂²×C₄×C₅	1	8	yes	complemented
884	C₂×D₄	C₂²×C₄×C₅	1	8	yes	complemented
885	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
886	C₂×D₄	C₅×#41	1	4	yes	—
887	C₂²×C₄	—	2	4	no	—
888	C₂²×C₄	—	2	4	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	4	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	2	4	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	4	no	—
905	C₂²×C₄	—	2	4	no	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	—	4	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	1	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	2	no	—
919	C₂²×C₄	—	4	2	no	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	32	no	—
925	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
926	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
927	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	complemented
928	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
929	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
930	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
936	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
940	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	4	no	—
951	C₄⋊C₄	—	2	4	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	4	no	—
954	C₄⋊C₄	—	2	4	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	4	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	1	no	—
964	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
965	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
966	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
967	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	2	4	no	—
970	C₂²⋊C₄	—	2	4	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
986	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
987	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
988	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
989	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
990	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
991	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
992	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	4	no	—
997	C₄²	—	2	4	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	4	2	no	—
1001	C₄²	—	4	2	no	—
1002	C₄²	—	4	2	no	—
1003	C₄²	C₂²×C₄×C₅	1	4	yes	complemented
1004	C₄²	C₂×C₅×D₄	1	4	yes	—
1005	C₂×C₅	—	2	4	no	—
1006	C₂×C₅	—	2	8	no	—
1007	C₂×C₅	—	4	2	no	—
1008	C₂×C₅	—	4	4	no	—
1009	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
1010	C₂×C₅	C₂×#520	1	1	yes	characteristic
1011	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1012	C₂×C₅	#3484	1	1	yes	characteristic
1013	C₂×C₅	#3489	1	1	yes	characteristic
1014	C₂×C₅	#3513	1	1	yes	characteristic
1015	C₂×C₅	#3520	1	1	yes	characteristic
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	16	no	—
1025	C₂³	—	2	16	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	4	8	no	—
1039	C₂³	—	4	8	no	—
1040	C₂³	—	4	8	no	—
1041	C₂³	—	4	8	no	—
1042	C₂³	—	4	8	no	—
1043	C₂³	C₂³×C₄×C₅	1	4	yes	—
1044	C₂³	C₂³×C₄×C₅	1	2	yes	—
1045	C₂³	C₂³×C₄×C₅	1	4	yes	—
1046	C₂³	C₂³×C₄×C₅	1	2	yes	—
1047	C₂³	C₂²×C₅×D₄	1	4	yes	—
1048	C₂³	C₂×C₅×#41	1	4	yes	—
1049	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
1050	C₂³	C₅×2₋¹⁺⁴	1	2	yes	—
1051	C₂³	C₂⁵×C₅	1	1	yes	characteristic
1052	Q₈	—	2	8	no	—
1053	D₄	—	2	16	no	—
1054	D₄	—	2	16	no	—
1055	D₄	—	2	8	no	—
1056	D₄	—	2	8	no	—
1057	D₄	—	4	8	no	—
1058	D₄	C₄×C₅×D₄	1	16	yes	complemented
1059	C₂×C₄	—	2	8	no	—
1060	C₂×C₄	—	2	16	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	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	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	8	no	—
1082	C₂×C₄	—	2	8	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	4	8	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	8	no	—
1111	C₂×C₄	—	4	8	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	8	no	—
1114	C₂×C₄	—	8	4	no	—
1115	C₂×C₄	—	8	4	no	—
1116	C₂×C₄	—	8	4	no	—
1117	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1118	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1119	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1120	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1121	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1122	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1123	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1124	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1125	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1126	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
1127	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
1128	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1129	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1130	C₅	#34288	1	1	yes	characteristic, direct product factor, Sylow
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	4	no	—
1133	C₂²	—	2	4	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	4	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	4	no	—
1139	C₂²	—	2	4	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	4	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	4	32	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
1159	C₂²	C₅×#520	1	4	yes	complemented
1160	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1161	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
1162	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1163	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1164	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1166	C₂²	C₅×#585	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	4	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	4	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	4	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	1	no	—
1185	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
1186	C₂	—	2	4	no	—
1187	C₂	—	2	8	no	—
1188	C₂	—	4	4	no	—
1189	C₂	—	4	2	no	—
1190	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
1191	C₂	C₂×C₅×#520	1	1	yes	characteristic
1192	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1193	C₂	C₅×#3484	1	1	yes	characteristic
1194	C₂	C₅×#3489	1	1	yes	characteristic
1195	C₂	C₅×#3513	1	1	yes	characteristic
1196	C₂	C₅×#3520	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. C₂×C₅×#520	C₂	semidirect
3. C₂²×C₄×C₅×D₄	C₂	semidirect
4. C₅×#2367	C₂	semidirect
5. C₅×#2361	C₂	semidirect
6. C₅×#2361	C₂	semidirect
7. C₅×#2360	C₂	semidirect
8. C₅×#2359	C₂	semidirect
9. C₅×#2358	C₂	semidirect
10. C₅×D₄×C₄⋊C₄	C₂	semidirect
11. C₅×D₄×C₄⋊C₄	C₂	semidirect
12. C₅×#2342	C₂	semidirect
13. C₅×#2339	C₂	semidirect
14. C₅×D₄×C₂²⋊C₄	C₂	semidirect
15. C₅×#2326	C₂	semidirect
16. C₅×#2325	C₂	semidirect
17. C₅×#2324	C₂	semidirect
18. C₅×#2322	C₂	semidirect
19. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
20. C₄×C₅×#120	C₂	semidirect
21. C₅×#2290	C₂	semidirect
22. C₂×C₅×#385	C₂	semidirect
23. C₅×#2275	C₂	semidirect
27. C₅×#546	C₄	semidirect
35. C₂×C₄×C₅×Q₈	C₂²	semidirect
36. C₂×C₄×C₅×Q₈	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂²	semidirect
50. C₂×C₄×C₅×D₄	C₂²	semidirect
51. C₂×C₄×C₅×D₄	C₂²	semidirect
52. C₂×C₅×#117	C₂²	semidirect
53. C₂×C₅×#117	C₂²	semidirect
55. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
56. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
57. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
62. C₅×#391	C₂²	semidirect
63. C₅×#391	C₂²	semidirect
66. C₅×#390	C₂²	semidirect
67. C₅×#389	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×#388	C₂²	semidirect
79. C₅×#387	C₂²	semidirect
80. C₅×#387	C₂²	semidirect
81. C₅×#387	C₂²	semidirect
82. C₅×#387	C₂²	semidirect
87. C₅×#386	C₂²	semidirect
88. C₅×#386	C₂²	semidirect
89. C₅×#386	C₂²	semidirect
90. C₅×#386	C₂²	semidirect
96. C₅×#385	C₂²	semidirect
97. C₅×#385	C₂²	semidirect
98. C₅×#385	C₂²	semidirect
99. C₅×#385	C₂²	semidirect
100. C₅×#385	C₂²	semidirect
101. C₅×#385	C₂²	semidirect
102. C₅×#385	C₂²	semidirect
103. C₅×#385	C₂²	semidirect
104. C₅×#384	C₂²	semidirect
105. C₅×#381	C₂²	semidirect
107. C₅×#380	C₂²	semidirect
108. C₅×#380	C₂²	semidirect
110. C₄×C₅×C₄⋊C₄	C₂²	semidirect
111. C₄×C₅×C₄⋊C₄	C₂²	semidirect
112. C₄×C₅×C₄⋊C₄	C₂²	semidirect
113. C₄×C₅×C₄⋊C₄	C₂²	semidirect
114. C₄×C₅×C₄⋊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. C₅×#376	C₂²	semidirect
124. C₂×C₅×#95	C₂²	semidirect
125. C₂×C₅×#95	C₂²	semidirect
126. #34288	C₅	direct (N × H)
130. C₂×C₅×#41	C₂×C₄	semidirect
134. C₂²×C₅×D₄	C₂×C₄	semidirect
158. C₅×#124	C₂×C₄	semidirect
159. C₅×#123	C₂×C₄	semidirect
160. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
161. C₅×#121	C₂×C₄	semidirect
162. C₅×#121	C₂×C₄	semidirect
163. C₅×#120	C₂×C₄	semidirect
177. C₄×C₅×D₄	C₂×C₄	semidirect
178. C₄×C₅×D₄	C₂×C₄	semidirect
179. C₄×C₅×D₄	D₄	semidirect
207. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
268. C₂×#520	C₂×C₅	semidirect
269. C₂²×C₄×D₄	C₂×C₅	semidirect
270. #2367	C₂×C₅	semidirect
271. #2361	C₂×C₅	semidirect
272. #2361	C₂×C₅	semidirect
273. #2360	C₂×C₅	semidirect
274. #2359	C₂×C₅	semidirect
275. #2358	C₂×C₅	semidirect
276. D₄×C₄⋊C₄	C₂×C₅	semidirect
277. D₄×C₄⋊C₄	C₂×C₅	semidirect
278. #2342	C₂×C₅	semidirect
279. #2339	C₂×C₅	semidirect
280. D₄×C₂²⋊C₄	C₂×C₅	semidirect
281. #2326	C₂×C₅	semidirect
282. #2325	C₂×C₅	semidirect
283. #2324	C₂×C₅	semidirect
284. #2322	C₂×C₅	semidirect
285. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
286. C₄×#120	C₂×C₅	semidirect
287. #2290	C₂×C₅	semidirect
288. C₂×#385	C₂×C₅	semidirect
289. #2275	C₂×C₅	semidirect
304. C₂×C₅×Q₈	C₂²×C₄	semidirect
320. C₂×C₅×D₄	C₂²×C₄	semidirect
321. C₂×C₅×D₄	C₂²×C₄	semidirect
363. C₂²×C₄×C₅	C₂²×C₄	semidirect
364. C₂²×C₄×C₅	C₂²×C₄	semidirect
365. C₂²×C₄×C₅	C₂²×C₄	semidirect
401. C₅×C₄⋊C₄	C₂²×C₄	semidirect
402. C₅×C₄⋊C₄	C₂²×C₄	semidirect
403. C₅×C₄⋊C₄	C₂²×C₄	semidirect
424. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
425. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
426. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
427. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
428. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
440. C₄²×C₅	C₂²×C₄	semidirect
445. #546	C₄×C₅	semidirect
453. C₂×C₄×Q₈	C₂²×C₅	semidirect
454. C₂×C₄×Q₈	C₂²×C₅	semidirect
467. C₂×C₄×D₄	C₂²×C₅	semidirect
468. C₂×C₄×D₄	C₂²×C₅	semidirect
469. C₂×C₄×D₄	C₂²×C₅	semidirect
470. C₂×#117	C₂²×C₅	semidirect
471. C₂×#117	C₂²×C₅	semidirect
473. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
474. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
475. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
480. #391	C₂²×C₅	semidirect
481. #391	C₂²×C₅	semidirect
484. #390	C₂²×C₅	semidirect
485. #389	C₂²×C₅	semidirect
486. #389	C₂²×C₅	semidirect
487. #389	C₂²×C₅	semidirect
488. #389	C₂²×C₅	semidirect
489. #388	C₂²×C₅	semidirect
490. #388	C₂²×C₅	semidirect
491. #388	C₂²×C₅	semidirect
492. #388	C₂²×C₅	semidirect
493. #388	C₂²×C₅	semidirect
494. #388	C₂²×C₅	semidirect
495. #388	C₂²×C₅	semidirect
496. #388	C₂²×C₅	semidirect
497. #387	C₂²×C₅	semidirect
498. #387	C₂²×C₅	semidirect
499. #387	C₂²×C₅	semidirect
500. #387	C₂²×C₅	semidirect
505. #386	C₂²×C₅	semidirect
506. #386	C₂²×C₅	semidirect
507. #386	C₂²×C₅	semidirect
508. #386	C₂²×C₅	semidirect
514. #385	C₂²×C₅	semidirect
515. #385	C₂²×C₅	semidirect
516. #385	C₂²×C₅	semidirect
517. #385	C₂²×C₅	semidirect
518. #385	C₂²×C₅	semidirect
519. #385	C₂²×C₅	semidirect
520. #385	C₂²×C₅	semidirect
521. #385	C₂²×C₅	semidirect
522. #384	C₂²×C₅	semidirect
523. #381	C₂²×C₅	semidirect
525. #380	C₂²×C₅	semidirect
526. #380	C₂²×C₅	semidirect
528. C₄×C₄⋊C₄	C₂²×C₅	semidirect
529. C₄×C₄⋊C₄	C₂²×C₅	semidirect
530. C₄×C₄⋊C₄	C₂²×C₅	semidirect
531. C₄×C₄⋊C₄	C₂²×C₅	semidirect
532. C₄×C₄⋊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. #376	C₂²×C₅	semidirect
542. C₂×#95	C₂²×C₅	semidirect
543. C₂×#95	C₂²×C₅	semidirect
586. C₅×D₄	C₄×D₄	semidirect
661. C₂×#41	C₂×C₄×C₅	semidirect
665. C₂²×D₄	C₂×C₄×C₅	semidirect
689. #124	C₂×C₄×C₅	semidirect
690. #123	C₂×C₄×C₅	semidirect
691. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
692. #121	C₂×C₄×C₅	semidirect
693. #121	C₂×C₄×C₅	semidirect
694. #120	C₂×C₄×C₅	semidirect
708. C₄×D₄	C₂×C₄×C₅	semidirect
709. C₄×D₄	C₂×C₄×C₅	semidirect
710. C₄×D₄	C₅×D₄	semidirect
738. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
826. C₂²×C₅	#520	semidirect
867. C₂×Q₈	C₂²×C₄×C₅	semidirect
883. C₂×D₄	C₂²×C₄×C₅	semidirect
884. C₂×D₄	C₂²×C₄×C₅	semidirect
926. C₂²×C₄	C₂²×C₄×C₅	semidirect
927. C₂²×C₄	C₂²×C₄×C₅	semidirect
928. C₂²×C₄	C₂²×C₄×C₅	semidirect
964. C₄⋊C₄	C₂²×C₄×C₅	semidirect
965. C₄⋊C₄	C₂²×C₄×C₅	semidirect
966. C₄⋊C₄	C₂²×C₄×C₅	semidirect
987. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
988. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
989. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
990. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
991. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
1003. C₄²	C₂²×C₄×C₅	semidirect
1058. D₄	C₄×C₅×D₄	semidirect
1130. C₅	#34288	direct (N × H)
1159. C₂²	C₅×#520	semidirect

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×C₅×#520	2
C₂²×C₄×C₅×D₄	2
C₅×#2367	2
C₅×#2361	2
C₅×#2360	2
C₅×#2359	2
C₅×#2358	2
C₅×D₄×C₄⋊C₄	2
C₅×#2342	2
C₅×#2339	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2326	2
C₅×#2325	2
C₅×#2324	2
C₅×#2322	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#120	2
C₅×#2290	2
C₂×C₅×#385	2
C₅×#2275	2
#34288	5

Subgroups — C5×#34288 #11957008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34288 #11957008