Subgroups — C₅×#34284 #11957004

Order 1280.

2286 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#542	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	2	yes	maximal, complemented
3	C₅×#2373	C₂	1	2	yes	maximal, complemented
4	C₅×#2372	C₂	1	2	yes	maximal, complemented
5	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2367	C₂	1	2	yes	maximal, complemented
7	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2363	C₂	1	1	yes	maximal, characteristic
11	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2361	C₂	1	1	yes	maximal, characteristic
13	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2335	C₂	1	2	yes	maximal, complemented
15	C₅×#2332	C₂	1	2	yes	maximal, complemented
16	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
19	C₅×#2298	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#542	C₄	1	16	yes	complemented
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#126	C₂²	1	2	yes	—
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×#124	C₂²	1	2	yes	—
29	C₂×C₅×#123	C₂²	1	2	yes	—
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
36	C₂×C₄×C₅×Q₈	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	2	yes	—
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	1	yes	characteristic
42	C₂×C₅×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅	C₂²	1	2	yes	—
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	1	yes	characteristic
47	C₅×#391	C₂²	1	2	yes	—
48	C₅×#391	C₂²	1	2	yes	—
49	C₅×#391	C₂²	1	2	yes	—
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	2	yes	—
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#389	C₂²	1	1	yes	characteristic
55	C₅×#389	C₂²	1	2	yes	—
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×#388	C₂²	1	1	yes	characteristic
60	C₅×#388	C₂²	1	1	yes	characteristic
61	C₅×#388	C₂²	1	1	yes	characteristic
62	C₅×#388	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#388	C₂²	1	2	yes	—
71	C₅×#388	C₂²	1	2	yes	—
72	C₅×#388	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#387	C₂²	1	1	yes	characteristic
76	C₅×#387	C₂²	1	1	yes	characteristic
77	C₅×#387	C₂²	1	1	yes	characteristic
78	C₅×#387	C₂²	1	1	yes	characteristic
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#386	C₂²	1	2	yes	—
84	C₅×#386	C₂²	1	2	yes	—
85	C₅×#385	C₂²	1	2	yes	—
86	C₅×#385	C₂²	1	2	yes	—
87	C₅×#385	C₂²	1	2	yes	—
88	C₅×#385	C₂²	1	2	yes	—
89	C₅×#381	C₂²	1	2	yes	—
90	C₅×#380	C₂²	1	2	yes	—
91	C₄×C₅×C₄⋊C₄	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	1	yes	characteristic
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
109	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
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	C₅×#376	C₂²	1	1	yes	characteristic
121	C₅×#376	C₂²	1	2	yes	—
122	C₅×#376	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	1	yes	characteristic
124	#34284	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂³	1	2	yes	—
127	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₅×D₄	C₂³	1	2	yes	—
129	C₂³×C₄×C₅	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	2	yes	—
134	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
135	C₅×#126	C₂×C₄	1	16	yes	complemented
136	C₅×#124	C₂×C₄	1	8	yes	complemented
137	C₅×#124	C₂×C₄	1	16	yes	complemented
138	C₅×#123	C₂×C₄	1	16	yes	complemented
139	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
140	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
141	C₅×#121	C₂×C₄	1	8	yes	—
142	C₄×C₅×Q₈	—	2	4	no	—
143	C₄×C₅×Q₈	—	2	4	no	—
144	C₄×C₅×Q₈	—	4	4	no	—
145	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
146	C₄×C₅×D₄	—	2	4	no	—
147	C₄×C₅×D₄	—	2	4	no	—
148	C₄×C₅×D₄	—	4	4	no	—
149	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
150	C₅×#117	—	2	4	no	—
151	C₅×#117	C₂×C₄	1	8	yes	complemented
152	C₂×C₅×C₄⋊C₄	—	2	4	no	—
153	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
193	C₂×C₄²×C₅	—	4	4	no	—
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	2	yes	—
200	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₂×C₄²×C₅	C₂³	1	2	yes	—
209	C₂×C₄²×C₅	C₂³	1	2	yes	—
210	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	2	yes	—
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
216	C₅×#95	C₂³	1	1	yes	characteristic
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	1	yes	characteristic
221	C₅×#95	C₂³	1	1	yes	characteristic
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	1	yes	characteristic
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	1	yes	characteristic
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	1	yes	characteristic
243	C₅×#95	C₂³	1	1	yes	characteristic
244	C₂×#542	C₂×C₅	1	1	yes	characteristic
245	#2373	C₂×C₅	1	2	yes	complemented
246	#2373	C₂×C₅	1	2	yes	complemented
247	#2372	C₂×C₅	1	2	yes	complemented
248	#2369	C₂×C₅	1	1	yes	characteristic, complemented
249	#2367	C₂×C₅	1	1	yes	characteristic, complemented
250	#2367	C₂×C₅	1	1	yes	characteristic, complemented
251	#2367	C₂×C₅	1	2	yes	complemented
252	#2365	C₂×C₅	1	1	yes	characteristic, complemented
253	#2363	C₂×C₅	1	1	yes	characteristic
254	#2362	C₂×C₅	1	1	yes	characteristic, complemented
255	#2361	C₂×C₅	1	1	yes	characteristic
256	#2360	C₂×C₅	1	1	yes	characteristic, complemented
257	#2335	C₂×C₅	1	2	yes	complemented
258	#2332	C₂×C₅	1	2	yes	complemented
259	#2319	C₂×C₅	1	1	yes	characteristic, complemented
260	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
261	C₄×#123	C₂×C₅	1	2	yes	complemented
262	#2298	C₂×C₅	1	1	yes	characteristic, complemented
263	#2295	C₂×C₅	1	1	yes	characteristic, complemented
264	#2276	C₂×C₅	1	1	yes	characteristic, complemented
265	#2274	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₅	C₂⁴	1	2	yes	—
269	C₂×C₅×Q₈	—	2	2	no	—
270	C₂×C₅×Q₈	—	2	2	no	—
271	C₂×C₅×Q₈	—	4	2	no	—
272	C₂×C₅×Q₈	—	4	2	no	—
273	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
274	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
275	C₂×C₅×D₄	—	2	2	no	—
276	C₂×C₅×D₄	—	2	2	no	—
277	C₂×C₅×D₄	—	4	2	no	—
278	C₂×C₅×D₄	—	4	2	no	—
279	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
280	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
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	4	no	—
285	C₂²×C₄×C₅	—	2	4	no	—
286	C₂²×C₄×C₅	—	2	4	no	—
287	C₂²×C₄×C₅	—	2	4	no	—
288	C₂²×C₄×C₅	—	4	2	no	—
289	C₂²×C₄×C₅	—	4	2	no	—
290	C₂²×C₄×C₅	—	4	2	no	—
291	C₂²×C₄×C₅	—	4	2	no	—
292	C₂²×C₄×C₅	—	4	2	no	—
293	C₂²×C₄×C₅	—	4	2	no	—
294	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
295	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	C₅×C₄⋊C₄	—	2	4	no	—
318	C₅×C₄⋊C₄	—	2	2	no	—
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	4	no	—
321	C₅×C₄⋊C₄	—	2	4	no	—
322	C₅×C₄⋊C₄	—	2	4	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	4	1	no	—
326	C₅×C₄⋊C₄	—	4	2	no	—
327	C₅×C₄⋊C₄	—	4	2	no	—
328	C₅×C₄⋊C₄	—	4	1	no	—
329	C₅×C₄⋊C₄	—	4	2	no	—
330	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
331	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
332	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
333	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
334	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
335	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
336	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
337	C₅×C₄⋊C₄	#41	1	4	yes	—
338	C₅×C₄⋊C₄	#41	1	4	yes	—
339	C₅×C₂²⋊C₄	—	2	4	no	—
340	C₅×C₂²⋊C₄	—	2	4	no	—
341	C₅×C₂²⋊C₄	—	2	4	no	—
342	C₅×C₂²⋊C₄	—	2	2	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	4	2	no	—
345	C₅×C₂²⋊C₄	—	4	1	no	—
346	C₅×C₂²⋊C₄	—	4	1	no	—
347	C₅×C₂²⋊C₄	—	4	2	no	—
348	C₅×C₂²⋊C₄	—	4	2	no	—
349	C₅×C₂²⋊C₄	—	4	2	no	—
350	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
351	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
352	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
353	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
354	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
355	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
356	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
357	C₄²×C₅	—	2	4	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	—	2	2	no	—
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	4	no	—
366	C₄²×C₅	—	2	2	no	—
367	C₄²×C₅	—	4	2	no	—
368	C₄²×C₅	—	4	2	no	—
369	C₄²×C₅	—	4	1	no	—
370	C₄²×C₅	—	4	2	no	—
371	C₄²×C₅	—	4	2	no	—
372	C₄²×C₅	—	4	1	no	—
373	C₄²×C₅	—	4	2	no	—
374	C₄²×C₅	—	4	2	no	—
375	C₄²×C₅	—	4	2	no	—
376	C₄²×C₅	C₂²×C₄	1	4	yes	—
377	C₄²×C₅	C₂²×C₄	1	4	yes	—
378	C₄²×C₅	C₂²×C₄	1	8	yes	—
379	#542	C₄×C₅	1	16	yes	complemented
380	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₂×#126	C₂²×C₅	1	2	yes	—
382	C₂×#124	C₂²×C₅	1	1	yes	characteristic
383	C₂×#124	C₂²×C₅	1	2	yes	—
384	C₂×#123	C₂²×C₅	1	2	yes	—
385	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
387	C₂×#121	C₂²×C₅	1	1	yes	characteristic
388	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
390	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
396	C₂×#117	C₂²×C₅	1	1	yes	characteristic
397	C₂×#117	C₂²×C₅	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
399	C₂²×C₄²	C₂²×C₅	1	2	yes	—
400	#391	C₂²×C₅	1	2	yes	—
401	#391	C₂²×C₅	1	2	yes	—
402	#391	C₂²×C₅	1	1	yes	characteristic
403	#391	C₂²×C₅	1	1	yes	characteristic
404	#391	C₂²×C₅	1	2	yes	—
405	#390	C₂²×C₅	1	1	yes	characteristic
406	#390	C₂²×C₅	1	1	yes	characteristic
407	#390	C₂²×C₅	1	2	yes	—
408	#389	C₂²×C₅	1	1	yes	characteristic
409	#389	C₂²×C₅	1	1	yes	characteristic
410	#389	C₂²×C₅	1	2	yes	—
411	#389	C₂²×C₅	1	2	yes	—
412	#389	C₂²×C₅	1	1	yes	characteristic
413	#389	C₂²×C₅	1	1	yes	characteristic
414	#388	C₂²×C₅	1	2	yes	—
415	#388	C₂²×C₅	1	2	yes	—
416	#388	C₂²×C₅	1	2	yes	—
417	#388	C₂²×C₅	1	2	yes	—
418	#388	C₂²×C₅	1	2	yes	—
419	#388	C₂²×C₅	1	2	yes	—
420	#388	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	1	yes	characteristic
426	#388	C₂²×C₅	1	1	yes	characteristic
427	#388	C₂²×C₅	1	1	yes	characteristic
428	#387	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
435	#387	C₂²×C₅	1	1	yes	characteristic
436	#387	C₂²×C₅	1	2	yes	—
437	#387	C₂²×C₅	1	1	yes	characteristic
438	#386	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	#381	C₂²×C₅	1	2	yes	—
445	#380	C₂²×C₅	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
475	#376	C₂²×C₅	1	1	yes	characteristic
476	#376	C₂²×C₅	1	2	yes	—
477	#376	C₂²×C₅	1	2	yes	—
478	C₄³	C₂²×C₅	1	1	yes	characteristic
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	2	no	—
481	C₂³×C₅	—	2	2	no	—
482	C₂³×C₅	—	2	1	no	—
483	C₂³×C₅	—	2	1	no	—
484	C₂³×C₅	—	2	2	no	—
485	C₂³×C₅	—	2	1	no	—
486	C₂³×C₅	—	2	2	no	—
487	C₂³×C₅	—	2	2	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	2	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	C₂³×C₄	1	2	yes	—
492	C₂³×C₅	C₂³×C₄	1	4	yes	—
493	C₂³×C₅	C₂⁵	1	1	yes	characteristic
494	C₅×Q₈	—	2	8	no	—
495	C₅×Q₈	—	4	8	no	—
496	C₅×D₄	—	2	8	no	—
497	C₅×D₄	—	4	8	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	2	no	—
500	C₂×C₄×C₅	—	2	2	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	2	no	—
509	C₂×C₄×C₅	—	2	2	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	2	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	8	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	2	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	2	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	1	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	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	2	no	—
547	C₂×C₄×C₅	—	4	8	no	—
548	C₂×C₄×C₅	—	4	8	no	—
549	C₂×C₄×C₅	—	4	8	no	—
550	C₂×C₄×C₅	—	8	4	no	—
551	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
552	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
553	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
554	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
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	2	yes	—
560	C₂×C₄×C₅	C₂×#41	1	4	yes	—
561	C₂×C₄×C₅	C₂×#41	1	4	yes	—
562	C₂×C₄×C₅	C₂×#41	1	2	yes	—
563	C₂×C₄×C₅	C₂×#41	1	2	yes	—
564	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
566	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₅	1	2	yes	—
568	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₅	1	2	yes	—
570	C₂³×C₄	C₂³×C₅	1	2	yes	—
571	C₂³×C₄	C₂³×C₅	1	2	yes	—
572	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₅	1	2	yes	—
574	C₂³×C₄	C₂³×C₅	1	2	yes	—
575	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
576	#126	C₂×C₄×C₅	1	16	yes	complemented
577	#124	C₂×C₄×C₅	1	8	yes	complemented
578	#124	C₂×C₄×C₅	1	16	yes	complemented
579	#123	C₂×C₄×C₅	1	16	yes	complemented
580	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
581	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
582	#121	C₂×C₄×C₅	1	8	yes	—
583	C₄×Q₈	—	2	4	no	—
584	C₄×Q₈	—	2	4	no	—
585	C₄×Q₈	—	4	4	no	—
586	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	4	no	—
589	C₄×D₄	—	4	4	no	—
590	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
591	#117	—	2	4	no	—
592	#117	C₂×C₄×C₅	1	8	yes	complemented
593	C₂×C₄⋊C₄	—	2	4	no	—
594	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
634	C₂×C₄²	—	4	4	no	—
635	C₂×C₄²	C₂³×C₅	1	2	yes	—
636	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₅	1	2	yes	—
639	C₂×C₄²	C₂³×C₅	1	2	yes	—
640	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
646	C₂×C₄²	C₂³×C₅	1	2	yes	—
647	C₂×C₄²	C₂³×C₅	1	2	yes	—
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	2	yes	—
654	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	1	yes	characteristic
658	#95	C₂³×C₅	1	2	yes	—
659	#95	C₂³×C₅	1	2	yes	—
660	#95	C₂³×C₅	1	2	yes	—
661	#95	C₂³×C₅	1	1	yes	characteristic
662	#95	C₂³×C₅	1	1	yes	characteristic
663	#95	C₂³×C₅	1	2	yes	—
664	#95	C₂³×C₅	1	2	yes	—
665	#95	C₂³×C₅	1	1	yes	characteristic
666	#95	C₂³×C₅	1	2	yes	—
667	#95	C₂³×C₅	1	2	yes	—
668	#95	C₂³×C₅	1	1	yes	characteristic
669	#95	C₂³×C₅	1	2	yes	—
670	#95	C₂³×C₅	1	1	yes	characteristic
671	#95	C₂³×C₅	1	2	yes	—
672	#95	C₂³×C₅	1	1	yes	characteristic
673	#95	C₂³×C₅	1	2	yes	—
674	#95	C₂³×C₅	1	1	yes	characteristic
675	#95	C₂³×C₅	1	2	yes	—
676	#95	C₂³×C₅	1	2	yes	—
677	#95	C₂³×C₅	1	2	yes	—
678	#95	C₂³×C₅	1	2	yes	—
679	#95	C₂³×C₅	1	1	yes	characteristic
680	#95	C₂³×C₅	1	1	yes	characteristic
681	#95	C₂³×C₅	1	2	yes	—
682	#95	C₂³×C₅	1	2	yes	—
683	#95	C₂³×C₅	1	1	yes	characteristic
684	#95	C₂³×C₅	1	1	yes	characteristic
685	C₂²×C₅	—	2	2	no	—
686	C₂²×C₅	—	2	4	no	—
687	C₂²×C₅	—	2	4	no	—
688	C₂²×C₅	—	2	2	no	—
689	C₂²×C₅	—	2	2	no	—
690	C₂²×C₅	—	2	4	no	—
691	C₂²×C₅	—	4	2	no	—
692	C₂²×C₅	—	4	1	no	—
693	C₂²×C₅	—	4	2	no	—
694	C₂²×C₅	—	4	1	no	—
695	C₂²×C₅	—	4	2	no	—
696	C₂²×C₅	—	4	1	no	—
697	C₂²×C₅	—	4	1	no	—
698	C₂²×C₅	—	4	2	no	—
699	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
700	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
701	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
702	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
704	C₂²×C₅	#585	1	1	yes	characteristic
705	C₂²×C₅	#585	1	1	yes	characteristic
706	C₄×C₅	—	2	2	no	—
707	C₄×C₅	—	2	4	no	—
708	C₄×C₅	—	2	2	no	—
709	C₄×C₅	—	2	4	no	—
710	C₄×C₅	—	2	4	no	—
711	C₄×C₅	—	2	2	no	—
712	C₄×C₅	—	2	2	no	—
713	C₄×C₅	—	2	2	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	2	4	no	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	4	no	—
718	C₄×C₅	—	4	1	no	—
719	C₄×C₅	—	4	2	no	—
720	C₄×C₅	—	4	1	no	—
721	C₄×C₅	—	4	1	no	—
722	C₄×C₅	—	4	1	no	—
723	C₄×C₅	—	4	1	no	—
724	C₄×C₅	—	4	1	no	—
725	C₄×C₅	—	4	2	no	—
726	C₄×C₅	C₄×#41	1	4	yes	—
727	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
728	C₂⁴	C₂⁴×C₅	1	2	yes	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	4	2	no	—
732	C₂×Q₈	—	4	2	no	—
733	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
734	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
740	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
755	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
791	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
792	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
793	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
794	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
795	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
796	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
797	C₄⋊C₄	C₅×#41	1	4	yes	—
798	C₄⋊C₄	C₅×#41	1	4	yes	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	1	no	—
807	C₂²⋊C₄	—	4	1	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
811	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
817	C₄²	—	2	4	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	2	4	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	1	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	1	no	—
836	C₄²	C₂²×C₄×C₅	1	4	yes	—
837	C₄²	C₂²×C₄×C₅	1	4	yes	—
838	C₄²	C₂²×C₄×C₅	1	8	yes	—
839	C₂×C₅	—	4	2	no	—
840	C₂×C₅	—	4	4	no	—
841	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
842	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
843	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂×C₅	#3513	1	1	yes	characteristic
845	C₂×C₅	#3518	1	1	yes	characteristic
846	C₂×C₅	#3520	1	1	yes	characteristic
847	C₂×C₅	#3524	1	1	yes	characteristic
848	C₂³	—	2	1	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	C₂³×C₄×C₅	1	2	yes	—
861	C₂³	C₂³×C₄×C₅	1	4	yes	—
862	C₂³	C₂⁵×C₅	1	1	yes	characteristic
863	Q₈	—	2	8	no	—
864	Q₈	—	4	8	no	—
865	D₄	—	2	8	no	—
866	D₄	—	4	8	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	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	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	4	8	no	—
917	C₂×C₄	—	4	8	no	—
918	C₂×C₄	—	4	8	no	—
919	C₂×C₄	—	8	4	no	—
920	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
921	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
922	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
923	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
924	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
925	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
926	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
927	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
928	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
929	C₂×C₄	C₂×C₅×#41	1	4	yes	—
930	C₂×C₄	C₂×C₅×#41	1	4	yes	—
931	C₂×C₄	C₂×C₅×#41	1	2	yes	—
932	C₂×C₄	C₂×C₅×#41	1	2	yes	—
933	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
934	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
935	C₅	#34284	1	1	yes	characteristic, direct product factor, Sylow
936	C₂²	—	2	2	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
951	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
952	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
953	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
955	C₂²	C₅×#585	1	1	yes	characteristic
956	C₂²	C₅×#585	1	1	yes	characteristic
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	4	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	C₄×C₅×#41	1	4	yes	—
978	C₂	—	4	2	no	—
979	C₂	—	4	4	no	—
980	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
981	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
983	C₂	C₅×#3513	1	1	yes	characteristic
984	C₂	C₅×#3518	1	1	yes	characteristic
985	C₂	C₅×#3520	1	1	yes	characteristic
986	C₂	C₅×#3524	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×#121	C₂²
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×#2373	C₂	semidirect
4. C₅×#2372	C₂	semidirect
5. C₅×#2369	C₂	semidirect
6. C₅×#2367	C₂	semidirect
7. C₅×#2367	C₂	semidirect
8. C₅×#2367	C₂	semidirect
9. C₅×#2365	C₂	semidirect
11. C₅×#2362	C₂	semidirect
13. C₅×#2360	C₂	semidirect
14. C₅×#2335	C₂	semidirect
15. C₅×#2332	C₂	semidirect
16. C₅×#2319	C₂	semidirect
17. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₅×#123	C₂	semidirect
19. C₅×#2298	C₂	semidirect
20. C₅×#2295	C₂	semidirect
21. C₅×#2276	C₂	semidirect
22. C₅×#2274	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
24. C₅×#542	C₄	semidirect
124. #34284	C₅	direct (N × H)
134. C₅×C₄⋊Q₈	C₂×C₄	semidirect
135. C₅×#126	C₂×C₄	semidirect
136. C₅×#124	C₂×C₄	semidirect
137. C₅×#124	C₂×C₄	semidirect
138. C₅×#123	C₂×C₄	semidirect
139. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
140. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
145. C₄×C₅×Q₈	C₂×C₄	semidirect
149. C₄×C₅×D₄	C₂×C₄	semidirect
151. C₅×#117	C₂×C₄	semidirect
245. #2373	C₂×C₅	semidirect
246. #2373	C₂×C₅	semidirect
247. #2372	C₂×C₅	semidirect
248. #2369	C₂×C₅	semidirect
249. #2367	C₂×C₅	semidirect
250. #2367	C₂×C₅	semidirect
251. #2367	C₂×C₅	semidirect
252. #2365	C₂×C₅	semidirect
254. #2362	C₂×C₅	semidirect
256. #2360	C₂×C₅	semidirect
257. #2335	C₂×C₅	semidirect
258. #2332	C₂×C₅	semidirect
259. #2319	C₂×C₅	semidirect
260. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
261. C₄×#123	C₂×C₅	semidirect
262. #2298	C₂×C₅	semidirect
263. #2295	C₂×C₅	semidirect
264. #2276	C₂×C₅	semidirect
265. #2274	C₂×C₅	semidirect
266. C₄²×D₄	C₂×C₅	semidirect
379. #542	C₄×C₅	semidirect
575. C₄⋊Q₈	C₂×C₄×C₅	semidirect
576. #126	C₂×C₄×C₅	semidirect
577. #124	C₂×C₄×C₅	semidirect
578. #124	C₂×C₄×C₅	semidirect
579. #123	C₂×C₄×C₅	semidirect
580. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
581. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
586. C₄×Q₈	C₂×C₄×C₅	semidirect
590. C₄×D₄	C₂×C₄×C₅	semidirect
592. #117	C₂×C₄×C₅	semidirect
935. C₅	#34284	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×#542	2
C₅×#2373	2
C₅×#2372	2
C₅×#2369	2
C₅×#2367	2
C₅×#2365	2
C₅×#2363	2
C₅×#2362	2
C₅×#2361	2
C₅×#2360	2
C₅×#2335	2
C₅×#2332	2
C₅×#2319	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#123	2
C₅×#2298	2
C₅×#2295	2
C₅×#2276	2
C₅×#2274	2
C₄²×C₅×D₄	2
#34284	5

Subgroups — C5×#34284 #11957004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34284 #11957004