Subgroups — C₅×#34314 #11957034

Order 1280.

2264 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#552	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	2	yes	maximal, complemented
3	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2370	C₂	1	2	yes	maximal, complemented
5	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2359	C₂	1	2	yes	maximal
8	C₅×#2352	C₂	1	1	yes	maximal, characteristic
9	C₅×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2347	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2343	C₂	1	2	yes	maximal, complemented
13	C₅×#2336	C₂	1	2	yes	maximal, complemented
14	C₅×#2334	C₂	1	2	yes	maximal, complemented
15	C₅×#2322	C₂	1	2	yes	maximal
16	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2274	C₂	1	2	yes	maximal, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
24	C₅×#552	C₄	1	16	yes	complemented
25	C₂×C₅×#126	C₂²	1	2	yes	—
26	C₂×C₅×#125	C₂²	1	1	yes	characteristic
27	C₂×C₅×#125	C₂²	1	2	yes	—
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×#117	C₂²	1	2	yes	—
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₂×C₅×#117	C₂²	1	2	yes	—
40	C₂×C₅×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	1	yes	characteristic
47	C₅×#391	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	2	yes	—
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	1	yes	characteristic
55	C₅×#389	C₂²	1	1	yes	characteristic
56	C₅×#389	C₂²	1	1	yes	characteristic
57	C₅×#389	C₂²	1	1	yes	characteristic
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#389	C₂²	1	2	yes	—
62	C₅×#388	C₂²	1	2	yes	—
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#388	C₂²	1	2	yes	—
65	C₅×#388	C₂²	1	2	yes	—
66	C₅×#388	C₂²	1	2	yes	—
67	C₅×#387	C₂²	1	2	yes	—
68	C₅×#387	C₂²	1	2	yes	—
69	C₅×#387	C₂²	1	2	yes	—
70	C₅×#387	C₂²	1	2	yes	—
71	C₅×#387	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#387	C₂²	1	2	yes	—
76	C₅×#387	C₂²	1	2	yes	—
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#386	C₂²	1	2	yes	—
81	C₅×#385	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	2	yes	—
84	C₅×#385	C₂²	1	2	yes	—
85	C₅×#385	C₂²	1	2	yes	—
86	C₅×#383	C₂²	1	2	yes	—
87	C₅×#382	C₂²	1	1	yes	characteristic
88	C₅×#382	C₂²	1	2	yes	—
89	C₅×#381	C₂²	1	2	yes	—
90	C₅×#380	C₂²	1	1	yes	characteristic
91	C₅×#380	C₂²	1	1	yes	characteristic
92	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
101	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	2	yes	—
122	C₂×C₅×#95	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34314	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₅×#126	C₂×C₄	1	16	yes	complemented
136	C₅×#125	C₂×C₄	1	16	yes	complemented
137	C₅×#125	C₂×C₄	1	8	yes	complemented
138	C₅×#123	C₂×C₄	1	16	yes	—
139	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
140	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
141	C₄×C₅×Q₈	—	4	2	no	—
142	C₄×C₅×Q₈	—	4	2	no	—
143	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
144	C₄×C₅×D₄	—	2	4	no	—
145	C₄×C₅×D₄	—	2	4	no	—
146	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
147	C₅×#117	—	2	8	no	—
148	C₅×#117	—	4	2	no	—
149	C₅×#117	C₂×C₄	1	8	yes	complemented
150	C₅×#117	C₂×C₄	1	16	yes	complemented
151	C₂×C₅×C₄⋊C₄	—	2	8	no	—
152	C₂×C₅×C₄⋊C₄	—	4	2	no	—
153	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
154	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
180	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	—	4	2	no	—
194	C₂×C₄²×C₅	—	4	2	no	—
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅	C₂³	1	2	yes	—
201	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅	C₂³	1	2	yes	—
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅	C₂³	1	2	yes	—
209	C₂×C₄²×C₅	C₂³	1	2	yes	—
210	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅	C₂³	1	2	yes	—
212	C₂×C₄²×C₅	C₂³	1	2	yes	—
213	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅	C₂³	1	2	yes	—
217	C₂×C₄²×C₅	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	2	yes	—
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	1	yes	characteristic
226	C₅×#95	C₂³	1	1	yes	characteristic
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	1	yes	characteristic
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	1	yes	characteristic
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
236	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
244	C₅×#95	C₂³	1	2	yes	—
245	C₂×#552	C₂×C₅	1	1	yes	characteristic
246	#2373	C₂×C₅	1	2	yes	complemented
247	#2370	C₂×C₅	1	1	yes	characteristic, complemented
248	#2370	C₂×C₅	1	2	yes	complemented
249	#2362	C₂×C₅	1	1	yes	characteristic, complemented
250	#2360	C₂×C₅	1	1	yes	characteristic, complemented
251	#2359	C₂×C₅	1	2	yes	—
252	#2352	C₂×C₅	1	1	yes	characteristic
253	#2351	C₂×C₅	1	1	yes	characteristic, complemented
254	#2347	C₂×C₅	1	1	yes	characteristic, complemented
255	#2344	C₂×C₅	1	1	yes	characteristic, complemented
256	#2343	C₂×C₅	1	2	yes	complemented
257	#2336	C₂×C₅	1	2	yes	complemented
258	#2334	C₂×C₅	1	2	yes	complemented
259	#2322	C₂×C₅	1	2	yes	—
260	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
261	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
262	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
263	#2296	C₂×C₅	1	1	yes	characteristic, complemented
264	#2295	C₂×C₅	1	1	yes	characteristic, complemented
265	C₂×#389	C₂×C₅	1	1	yes	characteristic, complemented
266	#2274	C₂×C₅	1	2	yes	complemented
267	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
268	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₅×Q₈	—	2	2	no	—
271	C₂×C₅×Q₈	—	2	2	no	—
272	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
273	C₂×C₅×D₄	—	2	2	no	—
274	C₂×C₅×D₄	—	2	2	no	—
275	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₅	—	2	4	no	—
277	C₂²×C₄×C₅	—	2	4	no	—
278	C₂²×C₄×C₅	—	2	2	no	—
279	C₂²×C₄×C₅	—	2	2	no	—
280	C₂²×C₄×C₅	—	2	2	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	2	no	—
283	C₂²×C₄×C₅	—	2	4	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	2	2	no	—
286	C₂²×C₄×C₅	—	2	2	no	—
287	C₂²×C₄×C₅	—	2	2	no	—
288	C₂²×C₄×C₅	—	4	1	no	—
289	C₂²×C₄×C₅	—	4	1	no	—
290	C₂²×C₄×C₅	—	4	1	no	—
291	C₂²×C₄×C₅	—	4	1	no	—
292	C₂²×C₄×C₅	—	4	1	no	—
293	C₂²×C₄×C₅	—	4	1	no	—
294	C₂²×C₄×C₅	—	4	2	no	—
295	C₂²×C₄×C₅	—	4	2	no	—
296	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
297	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
298	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
299	C₂²×C₄×C₅	#41	1	4	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₅×C₄⋊C₄	—	2	4	no	—
322	C₅×C₄⋊C₄	—	2	4	no	—
323	C₅×C₄⋊C₄	—	2	4	no	—
324	C₅×C₄⋊C₄	—	2	4	no	—
325	C₅×C₄⋊C₄	—	2	4	no	—
326	C₅×C₄⋊C₄	—	2	4	no	—
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	2	2	no	—
331	C₅×C₄⋊C₄	—	2	2	no	—
332	C₅×C₄⋊C₄	—	2	4	no	—
333	C₅×C₄⋊C₄	—	2	2	no	—
334	C₅×C₄⋊C₄	—	4	2	no	—
335	C₅×C₄⋊C₄	—	4	2	no	—
336	C₅×C₄⋊C₄	—	4	2	no	—
337	C₅×C₄⋊C₄	—	4	2	no	—
338	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
339	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
340	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
341	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
342	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
343	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
344	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
345	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
346	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
347	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
348	C₅×C₂²⋊C₄	—	2	4	no	—
349	C₅×C₂²⋊C₄	—	2	2	no	—
350	C₅×C₂²⋊C₄	—	2	2	no	—
351	C₅×C₂²⋊C₄	—	2	2	no	—
352	C₅×C₂²⋊C₄	—	4	2	no	—
353	C₅×C₂²⋊C₄	—	4	2	no	—
354	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
355	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
356	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
357	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
358	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
359	C₅×C₂²⋊C₄	#41	1	4	yes	—
360	C₄²×C₅	—	2	4	no	—
361	C₄²×C₅	—	2	4	no	—
362	C₄²×C₅	—	2	2	no	—
363	C₄²×C₅	—	2	2	no	—
364	C₄²×C₅	—	2	2	no	—
365	C₄²×C₅	—	2	2	no	—
366	C₄²×C₅	—	2	2	no	—
367	C₄²×C₅	—	2	2	no	—
368	C₄²×C₅	—	2	2	no	—
369	C₄²×C₅	—	4	1	no	—
370	C₄²×C₅	—	4	1	no	—
371	C₄²×C₅	—	4	1	no	—
372	C₄²×C₅	—	4	1	no	—
373	C₄²×C₅	—	4	1	no	—
374	C₄²×C₅	—	4	2	no	—
375	C₄²×C₅	—	4	2	no	—
376	C₄²×C₅	—	4	2	no	—
377	C₄²×C₅	—	4	2	no	—
378	C₄²×C₅	—	4	2	no	—
379	C₄²×C₅	—	4	2	no	—
380	C₄²×C₅	C₂²×C₄	1	8	yes	—
381	C₄²×C₅	C₂²×C₄	1	8	yes	—
382	C₄²×C₅	C₂²×C₄	1	4	yes	—
383	#552	C₄×C₅	1	16	yes	complemented
384	C₂×#126	C₂²×C₅	1	2	yes	—
385	C₂×#125	C₂²×C₅	1	1	yes	characteristic
386	C₂×#125	C₂²×C₅	1	2	yes	—
387	C₂×#123	C₂²×C₅	1	2	yes	—
388	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
389	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
396	C₂×#117	C₂²×C₅	1	2	yes	—
397	C₂×#117	C₂²×C₅	1	1	yes	characteristic
398	C₂×#117	C₂²×C₅	1	2	yes	—
399	C₂×#117	C₂²×C₅	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
401	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
405	#391	C₂²×C₅	1	1	yes	characteristic
406	#391	C₂²×C₅	1	1	yes	characteristic
407	#389	C₂²×C₅	1	1	yes	characteristic
408	#389	C₂²×C₅	1	1	yes	characteristic
409	#389	C₂²×C₅	1	2	yes	—
410	#389	C₂²×C₅	1	2	yes	—
411	#389	C₂²×C₅	1	2	yes	—
412	#389	C₂²×C₅	1	2	yes	—
413	#389	C₂²×C₅	1	2	yes	—
414	#389	C₂²×C₅	1	1	yes	characteristic
415	#389	C₂²×C₅	1	1	yes	characteristic
416	#389	C₂²×C₅	1	1	yes	characteristic
417	#389	C₂²×C₅	1	1	yes	characteristic
418	#389	C₂²×C₅	1	1	yes	characteristic
419	#389	C₂²×C₅	1	2	yes	—
420	#389	C₂²×C₅	1	1	yes	characteristic
421	#388	C₂²×C₅	1	2	yes	—
422	#388	C₂²×C₅	1	2	yes	—
423	#388	C₂²×C₅	1	2	yes	—
424	#388	C₂²×C₅	1	2	yes	—
425	#388	C₂²×C₅	1	2	yes	—
426	#387	C₂²×C₅	1	2	yes	—
427	#387	C₂²×C₅	1	2	yes	—
428	#387	C₂²×C₅	1	2	yes	—
429	#387	C₂²×C₅	1	2	yes	—
430	#387	C₂²×C₅	1	2	yes	—
431	#387	C₂²×C₅	1	2	yes	—
432	#387	C₂²×C₅	1	2	yes	—
433	#387	C₂²×C₅	1	2	yes	—
434	#387	C₂²×C₅	1	2	yes	—
435	#387	C₂²×C₅	1	2	yes	—
436	#387	C₂²×C₅	1	2	yes	—
437	#387	C₂²×C₅	1	2	yes	—
438	#387	C₂²×C₅	1	2	yes	—
439	#386	C₂²×C₅	1	2	yes	—
440	#385	C₂²×C₅	1	2	yes	—
441	#385	C₂²×C₅	1	2	yes	—
442	#385	C₂²×C₅	1	2	yes	—
443	#385	C₂²×C₅	1	2	yes	—
444	#385	C₂²×C₅	1	2	yes	—
445	#383	C₂²×C₅	1	2	yes	—
446	#382	C₂²×C₅	1	1	yes	characteristic
447	#382	C₂²×C₅	1	2	yes	—
448	#381	C₂²×C₅	1	2	yes	—
449	#380	C₂²×C₅	1	1	yes	characteristic
450	#380	C₂²×C₅	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
473	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
476	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
477	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
478	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
480	#376	C₂²×C₅	1	2	yes	—
481	C₂×#95	C₂²×C₅	1	2	yes	—
482	C₄³	C₂²×C₅	1	1	yes	characteristic
483	C₂³×C₅	—	2	1	no	—
484	C₂³×C₅	—	2	1	no	—
485	C₂³×C₅	—	2	1	no	—
486	C₂³×C₅	—	2	1	no	—
487	C₂³×C₅	—	2	1	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	—	2	1	no	—
492	C₂³×C₅	—	2	1	no	—
493	C₂³×C₅	C₂³×C₄	1	2	yes	—
494	C₂³×C₅	C₂³×C₄	1	2	yes	—
495	C₂³×C₅	C₂×#41	1	2	yes	—
496	C₂³×C₅	C₂×#41	1	2	yes	—
497	C₂³×C₅	C₂⁵	1	1	yes	characteristic
498	C₅×Q₈	—	2	8	no	—
499	C₅×D₄	—	2	8	no	—
500	C₂×C₄×C₅	—	2	16	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	2	no	—
506	C₂×C₄×C₅	—	2	2	no	—
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	8	no	—
528	C₂×C₄×C₅	—	2	8	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	2	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	2	no	—
539	C₂×C₄×C₅	—	2	2	no	—
540	C₂×C₄×C₅	—	2	2	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	2	no	—
544	C₂×C₄×C₅	—	2	2	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	2	2	no	—
548	C₂×C₄×C₅	—	2	2	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	4	4	no	—
551	C₂×C₄×C₅	—	4	4	no	—
552	C₂×C₄×C₅	—	4	4	no	—
553	C₂×C₄×C₅	—	4	4	no	—
554	C₂×C₄×C₅	—	8	4	no	—
555	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
556	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
557	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
558	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
559	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
560	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
561	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
562	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
563	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
564	C₂×C₄×C₅	C₂×#41	1	2	yes	—
565	C₂×C₄×C₅	C₂×#41	1	2	yes	—
566	C₂×C₄×C₅	C₂×#41	1	2	yes	—
567	C₂×C₄×C₅	C₂×#41	1	2	yes	—
568	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
569	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
570	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
571	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₅	1	2	yes	—
576	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₅	1	2	yes	—
579	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
581	#126	C₂×C₄×C₅	1	16	yes	complemented
582	#125	C₂×C₄×C₅	1	16	yes	complemented
583	#125	C₂×C₄×C₅	1	8	yes	complemented
584	#123	C₂×C₄×C₅	1	16	yes	—
585	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
586	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
587	C₄×Q₈	—	4	2	no	—
588	C₄×Q₈	—	4	2	no	—
589	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	4	no	—
592	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
593	#117	—	2	8	no	—
594	#117	—	4	2	no	—
595	#117	C₂×C₄×C₅	1	8	yes	complemented
596	#117	C₂×C₄×C₅	1	16	yes	complemented
597	C₂×C₄⋊C₄	—	2	8	no	—
598	C₂×C₄⋊C₄	—	4	2	no	—
599	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
600	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
639	C₂×C₄²	—	4	2	no	—
640	C₂×C₄²	—	4	2	no	—
641	C₂×C₄²	C₂³×C₅	1	2	yes	—
642	C₂×C₄²	C₂³×C₅	1	2	yes	—
643	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₅	1	2	yes	—
651	C₂×C₄²	C₂³×C₅	1	2	yes	—
652	C₂×C₄²	C₂³×C₅	1	2	yes	—
653	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₅	1	2	yes	—
655	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₅	1	2	yes	—
657	C₂×C₄²	C₂³×C₅	1	2	yes	—
658	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₅	1	2	yes	—
662	C₂×C₄²	C₂³×C₅	1	2	yes	—
663	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
664	#95	C₂³×C₅	1	2	yes	—
665	#95	C₂³×C₅	1	2	yes	—
666	#95	C₂³×C₅	1	2	yes	—
667	#95	C₂³×C₅	1	2	yes	—
668	#95	C₂³×C₅	1	2	yes	—
669	#95	C₂³×C₅	1	2	yes	—
670	#95	C₂³×C₅	1	2	yes	—
671	#95	C₂³×C₅	1	1	yes	characteristic
672	#95	C₂³×C₅	1	1	yes	characteristic
673	#95	C₂³×C₅	1	1	yes	characteristic
674	#95	C₂³×C₅	1	1	yes	characteristic
675	#95	C₂³×C₅	1	1	yes	characteristic
676	#95	C₂³×C₅	1	1	yes	characteristic
677	#95	C₂³×C₅	1	2	yes	—
678	#95	C₂³×C₅	1	2	yes	—
679	#95	C₂³×C₅	1	2	yes	—
680	#95	C₂³×C₅	1	2	yes	—
681	#95	C₂³×C₅	1	2	yes	—
682	#95	C₂³×C₅	1	2	yes	—
683	#95	C₂³×C₅	1	2	yes	—
684	#95	C₂³×C₅	1	2	yes	—
685	#95	C₂³×C₅	1	2	yes	—
686	#95	C₂³×C₅	1	2	yes	—
687	#95	C₂³×C₅	1	2	yes	—
688	#95	C₂³×C₅	1	2	yes	—
689	#95	C₂³×C₅	1	2	yes	—
690	#95	C₂³×C₅	1	2	yes	—
691	C₂²×C₅	—	2	2	no	—
692	C₂²×C₅	—	2	2	no	—
693	C₂²×C₅	—	2	2	no	—
694	C₂²×C₅	—	2	2	no	—
695	C₂²×C₅	—	2	2	no	—
696	C₂²×C₅	—	2	2	no	—
697	C₂²×C₅	—	2	2	no	—
698	C₂²×C₅	—	2	2	no	—
699	C₂²×C₅	—	2	2	no	—
700	C₂²×C₅	—	4	1	no	—
701	C₂²×C₅	—	4	1	no	—
702	C₂²×C₅	—	4	1	no	—
703	C₂²×C₅	—	4	1	no	—
704	C₂²×C₅	C₄×#41	1	4	yes	—
705	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
706	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
707	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
708	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
709	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
711	C₂²×C₅	#585	1	1	yes	characteristic
712	C₄×C₅	—	2	4	no	—
713	C₄×C₅	—	2	4	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	2	2	no	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	4	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	4	no	—
720	C₄×C₅	—	2	2	no	—
721	C₄×C₅	—	2	2	no	—
722	C₄×C₅	—	2	2	no	—
723	C₄×C₅	—	2	2	no	—
724	C₄×C₅	—	2	2	no	—
725	C₄×C₅	—	4	1	no	—
726	C₄×C₅	—	4	2	no	—
727	C₄×C₅	—	4	2	no	—
728	C₄×C₅	—	4	1	no	—
729	C₄×C₅	—	4	2	no	—
730	C₄×C₅	—	4	2	no	—
731	C₄×C₅	—	4	1	no	—
732	C₄×C₅	#520	1	4	yes	—
733	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
734	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	1	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
762	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
763	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
764	C₂²×C₄	C₅×#41	1	4	yes	—
765	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
804	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
805	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
806	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
807	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
808	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
809	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
810	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
811	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
812	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
824	C₂²⋊C₄	C₅×#41	1	4	yes	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	4	1	no	—
835	C₄²	—	4	1	no	—
836	C₄²	—	4	1	no	—
837	C₄²	—	4	1	no	—
838	C₄²	—	4	2	no	—
839	C₄²	—	4	2	no	—
840	C₄²	—	4	2	no	—
841	C₄²	—	4	1	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	C₂²×C₄×C₅	1	8	yes	—
846	C₄²	C₂²×C₄×C₅	1	8	yes	—
847	C₄²	C₂²×C₄×C₅	1	4	yes	—
848	C₂×C₅	—	2	4	no	—
849	C₂×C₅	—	4	2	no	—
850	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
851	C₂×C₅	C₂×#520	1	1	yes	characteristic
852	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂×C₅	#3505	1	1	yes	characteristic
854	C₂×C₅	#3509	1	1	yes	characteristic
855	C₂×C₅	#3515	1	1	yes	characteristic
856	C₂×C₅	#3520	1	1	yes	characteristic
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	C₂³×C₄×C₅	1	2	yes	—
868	C₂³	C₂³×C₄×C₅	1	2	yes	—
869	C₂³	C₂×C₅×#41	1	2	yes	—
870	C₂³	C₂×C₅×#41	1	2	yes	—
871	C₂³	C₂⁵×C₅	1	1	yes	characteristic
872	Q₈	—	2	8	no	—
873	D₄	—	2	8	no	—
874	C₂×C₄	—	2	16	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	8	no	—
902	C₂×C₄	—	2	8	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	4	4	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	8	4	no	—
929	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
930	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
931	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
932	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
933	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
934	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
935	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
936	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
937	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
938	C₂×C₄	C₂×C₅×#41	1	2	yes	—
939	C₂×C₄	C₂×C₅×#41	1	2	yes	—
940	C₂×C₄	C₂×C₅×#41	1	2	yes	—
941	C₂×C₄	C₂×C₅×#41	1	2	yes	—
942	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
943	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
944	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
945	C₅	#34314	1	1	yes	characteristic, direct product factor, Sylow
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	C₄×C₅×#41	1	4	yes	—
960	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
961	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
962	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
963	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
964	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
965	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
966	C₂²	C₅×#585	1	1	yes	characteristic
967	C₄	—	2	4	no	—
968	C₄	—	2	4	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	4	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	C₅×#520	1	4	yes	—
988	C₂	—	2	4	no	—
989	C₂	—	4	2	no	—
990	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
991	C₂	C₂×C₅×#520	1	1	yes	characteristic
992	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
993	C₂	C₅×#3505	1	1	yes	characteristic
994	C₂	C₅×#3509	1	1	yes	characteristic
995	C₂	C₅×#3515	1	1	yes	characteristic
996	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	C₂²×C₅×D₄	C₂³
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×#2373	C₂	semidirect
3. C₅×#2370	C₂	semidirect
4. C₅×#2370	C₂	semidirect
5. C₅×#2362	C₂	semidirect
6. C₅×#2360	C₂	semidirect
9. C₅×#2351	C₂	semidirect
10. C₅×#2347	C₂	semidirect
11. C₅×#2344	C₂	semidirect
12. C₅×#2343	C₂	semidirect
13. C₅×#2336	C₂	semidirect
14. C₅×#2334	C₂	semidirect
16. C₄×C₅×#125	C₂	semidirect
17. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
19. C₅×#2296	C₂	semidirect
20. C₅×#2295	C₂	semidirect
21. C₂×C₅×#389	C₂	semidirect
22. C₅×#2274	C₂	semidirect
24. C₅×#552	C₄	semidirect
124. #34314	C₅	direct (N × H)
135. C₅×#126	C₂×C₄	semidirect
136. C₅×#125	C₂×C₄	semidirect
137. C₅×#125	C₂×C₄	semidirect
139. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
140. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
143. C₄×C₅×Q₈	C₂×C₄	semidirect
149. C₅×#117	C₂×C₄	semidirect
150. C₅×#117	C₂×C₄	semidirect
153. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
246. #2373	C₂×C₅	semidirect
247. #2370	C₂×C₅	semidirect
248. #2370	C₂×C₅	semidirect
249. #2362	C₂×C₅	semidirect
250. #2360	C₂×C₅	semidirect
253. #2351	C₂×C₅	semidirect
254. #2347	C₂×C₅	semidirect
255. #2344	C₂×C₅	semidirect
256. #2343	C₂×C₅	semidirect
257. #2336	C₂×C₅	semidirect
258. #2334	C₂×C₅	semidirect
260. C₄×#125	C₂×C₅	semidirect
261. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
262. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
263. #2296	C₂×C₅	semidirect
264. #2295	C₂×C₅	semidirect
265. C₂×#389	C₂×C₅	semidirect
266. #2274	C₂×C₅	semidirect
383. #552	C₄×C₅	semidirect
581. #126	C₂×C₄×C₅	semidirect
582. #125	C₂×C₄×C₅	semidirect
583. #125	C₂×C₄×C₅	semidirect
585. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
586. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
589. C₄×Q₈	C₂×C₄×C₅	semidirect
595. #117	C₂×C₄×C₅	semidirect
596. #117	C₂×C₄×C₅	semidirect
599. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
945. C₅	#34314	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×#552	2
C₅×#2373	2
C₅×#2370	2
C₅×#2362	2
C₅×#2360	2
C₅×#2359	2
C₅×#2352	2
C₅×#2351	2
C₅×#2347	2
C₅×#2344	2
C₅×#2343	2
C₅×#2336	2
C₅×#2334	2
C₅×#2322	2
C₄×C₅×#125	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2296	2
C₅×#2295	2
C₂×C₅×#389	2
C₅×#2274	2
C₄²×C₅×D₄	2
#34314	5

Subgroups — C5×#34314 #11957034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34314 #11957034