Subgroups — C₅×#34307 #11957027

Order 1280.

2136 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	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
5	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2356	C₂	1	2	yes	maximal, complemented
9	C₅×#2356	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2352	C₂	1	1	yes	maximal, characteristic
11	C₅×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2346	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2337	C₂	1	2	yes	maximal
14	C₅×#2334	C₂	1	2	yes	maximal, complemented
15	C₅×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#126	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2295	C₂	1	2	yes	maximal, complemented
20	C₅×#2290	C₂	1	1	yes	maximal, characteristic
21	C₅×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#556	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×#126	C₂²	1	2	yes	—
28	C₂×C₅×#124	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×Q₈	C₂²	1	2	yes	—
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×#117	C₂²	1	1	yes	characteristic
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	1	yes	characteristic
39	C₂×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
42	C₅×#391	C₂²	1	2	yes	—
43	C₅×#391	C₂²	1	2	yes	—
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	2	yes	—
47	C₅×#391	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	C₂²	1	1	yes	characteristic
54	C₅×#389	C₂²	1	2	yes	—
55	C₅×#388	C₂²	1	1	yes	characteristic
56	C₅×#388	C₂²	1	1	yes	characteristic
57	C₅×#388	C₂²	1	2	yes	—
58	C₅×#388	C₂²	1	2	yes	—
59	C₅×#388	C₂²	1	2	yes	—
60	C₅×#388	C₂²	1	2	yes	—
61	C₅×#388	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×#387	C₂²	1	1	yes	characteristic
67	C₅×#387	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	1	yes	characteristic
78	C₅×#386	C₂²	1	1	yes	characteristic
79	C₅×#386	C₂²	1	2	yes	—
80	C₅×#385	C₂²	1	1	yes	characteristic
81	C₅×#385	C₂²	1	1	yes	characteristic
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	2	yes	—
84	C₅×#383	C₂²	1	2	yes	—
85	C₅×#383	C₂²	1	2	yes	—
86	C₅×#382	C₂²	1	1	yes	characteristic
87	C₅×#382	C₂²	1	2	yes	—
88	C₅×#380	C₂²	1	1	yes	characteristic
89	C₅×#380	C₂²	1	1	yes	characteristic
90	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
95	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₅×#376	C₂²	1	2	yes	—
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	2	yes	—
122	C₅×#376	C₂²	1	2	yes	—
123	C₄³×C₅	C₂²	1	2	yes	—
124	#34307	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	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅	C₂³	1	2	yes	—
132	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
133	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
134	C₅×#126	C₂×C₄	1	16	yes	complemented
135	C₅×#126	C₂×C₄	1	16	yes	complemented
136	C₅×#124	C₂×C₄	1	16	yes	—
137	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
138	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
139	C₄×C₅×Q₈	—	2	4	no	—
140	C₄×C₅×Q₈	—	2	4	no	—
141	C₄×C₅×Q₈	C₂×C₄	1	16	yes	complemented
142	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
143	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
144	C₅×#117	—	2	4	no	—
145	C₅×#117	—	2	4	no	—
146	C₅×#117	C₂×C₄	1	8	yes	complemented
147	C₅×#117	C₂×C₄	1	8	yes	complemented
148	C₂×C₅×C₄⋊C₄	—	2	4	no	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅	—	2	4	no	—
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	2	yes	—
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	2	yes	—
194	C₂×C₄²×C₅	C₂³	1	2	yes	—
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₂×C₄²×C₅	C₂³	1	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	2	yes	—
200	C₂×C₄²×C₅	C₂³	1	2	yes	—
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
205	C₂×C₄²×C₅	C₂³	1	2	yes	—
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
210	C₅×#95	C₂³	1	1	yes	characteristic
211	C₅×#95	C₂³	1	2	yes	—
212	C₅×#95	C₂³	1	1	yes	characteristic
213	C₅×#95	C₂³	1	1	yes	characteristic
214	C₅×#95	C₂³	1	2	yes	—
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
232	C₅×#95	C₂³	1	1	yes	characteristic
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	1	yes	characteristic
235	C₅×#95	C₂³	1	2	yes	—
236	C₅×#95	C₂³	1	2	yes	—
237	C₅×#95	C₂³	1	1	yes	characteristic
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
241	C₂×#556	C₂×C₅	1	1	yes	characteristic
242	#2373	C₂×C₅	1	2	yes	complemented
243	#2373	C₂×C₅	1	2	yes	complemented
244	#2372	C₂×C₅	1	2	yes	—
245	#2369	C₂×C₅	1	1	yes	characteristic, complemented
246	#2362	C₂×C₅	1	1	yes	characteristic, complemented
247	#2360	C₂×C₅	1	1	yes	characteristic, complemented
248	#2356	C₂×C₅	1	1	yes	characteristic, complemented
249	#2356	C₂×C₅	1	2	yes	complemented
250	#2352	C₂×C₅	1	1	yes	characteristic
251	#2347	C₂×C₅	1	1	yes	characteristic, complemented
252	#2346	C₂×C₅	1	1	yes	characteristic, complemented
253	#2337	C₂×C₅	1	2	yes	—
254	#2334	C₂×C₅	1	2	yes	complemented
255	#2331	C₂×C₅	1	1	yes	characteristic, complemented
256	#2323	C₂×C₅	1	1	yes	characteristic, complemented
257	C₄×#126	C₂×C₅	1	2	yes	complemented
258	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
259	#2295	C₂×C₅	1	2	yes	complemented
260	#2290	C₂×C₅	1	1	yes	characteristic
261	#2276	C₂×C₅	1	1	yes	characteristic, complemented
262	#2274	C₂×C₅	1	1	yes	characteristic, complemented
263	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
264	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₅×Q₈	—	2	2	no	—
267	C₂×C₅×Q₈	—	2	2	no	—
268	C₂×C₅×Q₈	—	4	2	no	—
269	C₂×C₅×Q₈	—	4	2	no	—
270	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
271	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
272	C₂×C₅×D₄	—	4	1	no	—
273	C₂×C₅×D₄	—	4	1	no	—
274	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
275	C₂²×C₄×C₅	—	2	2	no	—
276	C₂²×C₄×C₅	—	2	2	no	—
277	C₂²×C₄×C₅	—	2	2	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	4	no	—
283	C₂²×C₄×C₅	—	4	1	no	—
284	C₂²×C₄×C₅	—	4	1	no	—
285	C₂²×C₄×C₅	—	4	1	no	—
286	C₂²×C₄×C₅	—	4	2	no	—
287	C₂²×C₄×C₅	—	4	2	no	—
288	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
289	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	2	yes	—
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	2	no	—
314	C₅×C₄⋊C₄	—	2	2	no	—
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	4	no	—
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	—	4	1	no	—
321	C₅×C₄⋊C₄	—	4	2	no	—
322	C₅×C₄⋊C₄	—	4	2	no	—
323	C₅×C₄⋊C₄	—	4	2	no	—
324	C₅×C₄⋊C₄	—	4	2	no	—
325	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
326	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
327	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
328	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
330	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
331	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
332	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
333	C₅×C₄⋊C₄	#41	1	4	yes	—
334	C₅×C₂²⋊C₄	—	2	2	no	—
335	C₅×C₂²⋊C₄	—	2	4	no	—
336	C₅×C₂²⋊C₄	—	2	2	no	—
337	C₅×C₂²⋊C₄	—	2	2	no	—
338	C₅×C₂²⋊C₄	—	4	2	no	—
339	C₅×C₂²⋊C₄	—	4	1	no	—
340	C₅×C₂²⋊C₄	—	4	1	no	—
341	C₅×C₂²⋊C₄	—	4	2	no	—
342	C₅×C₂²⋊C₄	—	4	1	no	—
343	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
344	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
345	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
346	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
347	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
348	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	2	2	no	—
352	C₄²×C₅	—	2	4	no	—
353	C₄²×C₅	—	2	2	no	—
354	C₄²×C₅	—	2	4	no	—
355	C₄²×C₅	—	2	4	no	—
356	C₄²×C₅	—	2	2	no	—
357	C₄²×C₅	—	2	4	no	—
358	C₄²×C₅	—	4	2	no	—
359	C₄²×C₅	—	4	2	no	—
360	C₄²×C₅	—	4	2	no	—
361	C₄²×C₅	—	4	2	no	—
362	C₄²×C₅	—	4	2	no	—
363	C₄²×C₅	—	4	2	no	—
364	C₄²×C₅	—	4	2	no	—
365	C₄²×C₅	—	4	2	no	—
366	C₄²×C₅	C₂²×C₄	1	8	yes	—
367	C₄²×C₅	C₂²×C₄	1	8	yes	—
368	C₄²×C₅	C₂²×C₄	1	4	yes	—
369	C₄²×C₅	C₂²×C₄	1	8	yes	—
370	C₄²×C₅	#41	1	4	yes	—
371	#556	C₄×C₅	1	16	yes	complemented
372	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
373	C₂×#126	C₂²×C₅	1	2	yes	—
374	C₂×#126	C₂²×C₅	1	2	yes	—
375	C₂×#124	C₂²×C₅	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
383	C₂×#117	C₂²×C₅	1	1	yes	characteristic
384	C₂×#117	C₂²×C₅	1	1	yes	characteristic
385	C₂×#117	C₂²×C₅	1	1	yes	characteristic
386	C₂×#117	C₂²×C₅	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
389	#391	C₂²×C₅	1	1	yes	characteristic
390	#391	C₂²×C₅	1	2	yes	—
391	#391	C₂²×C₅	1	2	yes	—
392	#391	C₂²×C₅	1	2	yes	—
393	#391	C₂²×C₅	1	1	yes	characteristic
394	#391	C₂²×C₅	1	2	yes	—
395	#389	C₂²×C₅	1	2	yes	—
396	#389	C₂²×C₅	1	1	yes	characteristic
397	#389	C₂²×C₅	1	1	yes	characteristic
398	#389	C₂²×C₅	1	1	yes	characteristic
399	#389	C₂²×C₅	1	2	yes	—
400	#389	C₂²×C₅	1	1	yes	characteristic
401	#389	C₂²×C₅	1	2	yes	—
402	#388	C₂²×C₅	1	1	yes	characteristic
403	#388	C₂²×C₅	1	2	yes	—
404	#388	C₂²×C₅	1	2	yes	—
405	#388	C₂²×C₅	1	2	yes	—
406	#388	C₂²×C₅	1	2	yes	—
407	#388	C₂²×C₅	1	2	yes	—
408	#388	C₂²×C₅	1	2	yes	—
409	#388	C₂²×C₅	1	2	yes	—
410	#388	C₂²×C₅	1	2	yes	—
411	#388	C₂²×C₅	1	2	yes	—
412	#388	C₂²×C₅	1	1	yes	characteristic
413	#387	C₂²×C₅	1	2	yes	—
414	#387	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	2	yes	—
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	1	yes	characteristic
422	#387	C₂²×C₅	1	2	yes	—
423	#387	C₂²×C₅	1	1	yes	characteristic
424	#386	C₂²×C₅	1	1	yes	characteristic
425	#386	C₂²×C₅	1	2	yes	—
426	#386	C₂²×C₅	1	1	yes	characteristic
427	#385	C₂²×C₅	1	1	yes	characteristic
428	#385	C₂²×C₅	1	2	yes	—
429	#385	C₂²×C₅	1	2	yes	—
430	#385	C₂²×C₅	1	1	yes	characteristic
431	#383	C₂²×C₅	1	2	yes	—
432	#383	C₂²×C₅	1	2	yes	—
433	#382	C₂²×C₅	1	1	yes	characteristic
434	#382	C₂²×C₅	1	2	yes	—
435	#380	C₂²×C₅	1	1	yes	characteristic
436	#380	C₂²×C₅	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
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	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
462	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
465	#376	C₂²×C₅	1	1	yes	characteristic
466	#376	C₂²×C₅	1	2	yes	—
467	#376	C₂²×C₅	1	2	yes	—
468	#376	C₂²×C₅	1	2	yes	—
469	#376	C₂²×C₅	1	2	yes	—
470	C₄³	C₂²×C₅	1	2	yes	—
471	C₂³×C₅	—	2	1	no	—
472	C₂³×C₅	—	2	1	no	—
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	2	1	no	—
476	C₂³×C₅	—	2	1	no	—
477	C₂³×C₅	—	2	1	no	—
478	C₂³×C₅	—	2	1	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	2	1	no	—
482	C₂³×C₅	—	2	1	no	—
483	C₂³×C₅	C₂³×C₄	1	2	yes	—
484	C₂³×C₅	C₂³×C₄	1	2	yes	—
485	C₂³×C₅	C₂⁵	1	1	yes	characteristic
486	C₅×Q₈	—	2	8	no	—
487	C₅×Q₈	—	4	8	no	—
488	C₅×D₄	—	4	4	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	2	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	2	no	—
500	C₂×C₄×C₅	—	2	1	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	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	2	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	8	no	—
514	C₂×C₄×C₅	—	2	8	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	1	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	2	no	—
523	C₂×C₄×C₅	—	2	2	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	1	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	2	no	—
532	C₂×C₄×C₅	—	2	2	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	4	4	no	—
540	C₂×C₄×C₅	—	4	4	no	—
541	C₂×C₄×C₅	—	8	4	no	—
542	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
543	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
546	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
547	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
548	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
549	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
550	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
551	C₂×C₄×C₅	C₂×#41	1	2	yes	—
552	C₂×C₄×C₅	C₂×#41	1	4	yes	—
553	C₂×C₄×C₅	C₂×#41	1	2	yes	—
554	C₂×C₄×C₅	C₂×#41	1	2	yes	—
555	C₂×C₄×C₅	C₂×#41	1	2	yes	—
556	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
557	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
558	C₂²×Q₈	C₂³×C₅	1	2	yes	—
559	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₅	1	2	yes	—
564	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
565	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
566	#126	C₂×C₄×C₅	1	16	yes	complemented
567	#126	C₂×C₄×C₅	1	16	yes	complemented
568	#124	C₂×C₄×C₅	1	16	yes	—
569	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
570	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
571	C₄×Q₈	—	2	4	no	—
572	C₄×Q₈	—	2	4	no	—
573	C₄×Q₈	C₂×C₄×C₅	1	16	yes	complemented
574	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
575	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
576	#117	—	2	4	no	—
577	#117	—	2	4	no	—
578	#117	C₂×C₄×C₅	1	8	yes	complemented
579	#117	C₂×C₄×C₅	1	8	yes	complemented
580	C₂×C₄⋊C₄	—	2	4	no	—
581	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
619	C₂×C₄²	—	2	4	no	—
620	C₂×C₄²	C₂³×C₅	1	2	yes	—
621	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₅	1	2	yes	—
624	C₂×C₄²	C₂³×C₅	1	2	yes	—
625	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₅	1	2	yes	—
627	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅	1	2	yes	—
630	C₂×C₄²	C₂³×C₅	1	2	yes	—
631	C₂×C₄²	C₂³×C₅	1	2	yes	—
632	C₂×C₄²	C₂³×C₅	1	2	yes	—
633	C₂×C₄²	C₂³×C₅	1	2	yes	—
634	C₂×C₄²	C₂³×C₅	1	2	yes	—
635	C₂×C₄²	C₂³×C₅	1	2	yes	—
636	C₂×C₄²	C₂³×C₅	1	2	yes	—
637	C₂×C₄²	C₂³×C₅	1	2	yes	—
638	C₂×C₄²	C₂³×C₅	1	2	yes	—
639	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₅	1	2	yes	—
641	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
642	#95	C₂³×C₅	1	1	yes	characteristic
643	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	1	yes	characteristic
645	#95	C₂³×C₅	1	1	yes	characteristic
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	#95	C₂³×C₅	1	2	yes	—
652	#95	C₂³×C₅	1	1	yes	characteristic
653	#95	C₂³×C₅	1	1	yes	characteristic
654	#95	C₂³×C₅	1	1	yes	characteristic
655	#95	C₂³×C₅	1	2	yes	—
656	#95	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	2	yes	—
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	2	yes	—
663	#95	C₂³×C₅	1	2	yes	—
664	#95	C₂³×C₅	1	1	yes	characteristic
665	#95	C₂³×C₅	1	2	yes	—
666	#95	C₂³×C₅	1	1	yes	characteristic
667	#95	C₂³×C₅	1	2	yes	—
668	#95	C₂³×C₅	1	2	yes	—
669	#95	C₂³×C₅	1	1	yes	characteristic
670	#95	C₂³×C₅	1	2	yes	—
671	#95	C₂³×C₅	1	2	yes	—
672	#95	C₂³×C₅	1	2	yes	—
673	C₂²×C₅	—	2	2	no	—
674	C₂²×C₅	—	2	2	no	—
675	C₂²×C₅	—	2	2	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	4	1	no	—
680	C₂²×C₅	—	4	1	no	—
681	C₂²×C₅	—	4	1	no	—
682	C₂²×C₅	—	4	1	no	—
683	C₂²×C₅	—	4	1	no	—
684	C₂²×C₅	—	4	1	no	—
685	C₂²×C₅	—	4	1	no	—
686	C₂²×C₅	—	4	1	no	—
687	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
688	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂²×C₅	#585	1	1	yes	characteristic
692	C₂²×C₅	#585	1	1	yes	characteristic
693	C₂²×C₅	#585	1	1	yes	characteristic
694	C₄×C₅	—	2	2	no	—
695	C₄×C₅	—	2	2	no	—
696	C₄×C₅	—	2	4	no	—
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	4	no	—
699	C₄×C₅	—	2	4	no	—
700	C₄×C₅	—	2	4	no	—
701	C₄×C₅	—	2	2	no	—
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	2	2	no	—
705	C₄×C₅	—	2	4	no	—
706	C₄×C₅	—	4	1	no	—
707	C₄×C₅	—	4	2	no	—
708	C₄×C₅	—	4	1	no	—
709	C₄×C₅	—	4	1	no	—
710	C₄×C₅	—	4	1	no	—
711	C₄×C₅	—	4	2	no	—
712	C₄×C₅	—	4	1	no	—
713	C₄×C₅	—	4	2	no	—
714	C₄×C₅	C₄×#41	1	4	yes	—
715	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
716	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	4	2	no	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
722	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
740	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₅	1	2	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	2	yes	—
759	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	4	1	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
777	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
778	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
779	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
780	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
781	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
782	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
783	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
784	C₄⋊C₄	C₅×#41	1	4	yes	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	1	no	—
791	C₂²⋊C₄	—	4	1	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	1	no	—
794	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
795	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
796	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
797	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
798	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
799	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	4	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	C₂²×C₄×C₅	1	8	yes	—
818	C₄²	C₂²×C₄×C₅	1	8	yes	—
819	C₄²	C₂²×C₄×C₅	1	4	yes	—
820	C₄²	C₂²×C₄×C₅	1	8	yes	—
821	C₄²	C₅×#41	1	4	yes	—
822	C₂×C₅	—	4	2	no	—
823	C₂×C₅	—	4	2	no	—
824	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
825	C₂×C₅	#3428	1	1	yes	characteristic
826	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
827	C₂×C₅	#3493	1	1	yes	characteristic
828	C₂×C₅	#3495	1	1	yes	characteristic
829	C₂×C₅	#3518	1	1	yes	characteristic
830	C₂×C₅	#3521	1	1	yes	characteristic
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	C₂³×C₄×C₅	1	2	yes	—
844	C₂³	C₂³×C₄×C₅	1	2	yes	—
845	C₂³	C₂⁵×C₅	1	1	yes	characteristic
846	Q₈	—	2	8	no	—
847	Q₈	—	4	8	no	—
848	D₄	—	4	4	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	8	no	—
874	C₂×C₄	—	2	8	no	—
875	C₂×C₄	—	2	1	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	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
903	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
904	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
905	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
906	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
908	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
909	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
910	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
911	C₂×C₄	C₂×C₅×#41	1	2	yes	—
912	C₂×C₄	C₂×C₅×#41	1	4	yes	—
913	C₂×C₄	C₂×C₅×#41	1	2	yes	—
914	C₂×C₄	C₂×C₅×#41	1	2	yes	—
915	C₂×C₄	C₂×C₅×#41	1	2	yes	—
916	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
917	C₅	#34307	1	1	yes	characteristic, direct product factor, Sylow
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
933	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
934	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
935	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
936	C₂²	C₅×#585	1	1	yes	characteristic
937	C₂²	C₅×#585	1	1	yes	characteristic
938	C₂²	C₅×#585	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	4	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	C₄×C₅×#41	1	4	yes	—
960	C₂	—	4	2	no	—
961	C₂	—	4	2	no	—
962	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
963	C₂	C₅×#3428	1	1	yes	characteristic
964	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
965	C₂	C₅×#3493	1	1	yes	characteristic
966	C₂	C₅×#3495	1	1	yes	characteristic
967	C₂	C₅×#3518	1	1	yes	characteristic
968	C₂	C₅×#3521	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×#2373	C₂	semidirect
5. C₅×#2369	C₂	semidirect
6. C₅×#2362	C₂	semidirect
7. C₅×#2360	C₂	semidirect
8. C₅×#2356	C₂	semidirect
9. C₅×#2356	C₂	semidirect
11. C₅×#2347	C₂	semidirect
12. C₅×#2346	C₂	semidirect
14. C₅×#2334	C₂	semidirect
15. C₅×#2331	C₂	semidirect
16. C₅×#2323	C₂	semidirect
17. C₄×C₅×#126	C₂	semidirect
18. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
19. C₅×#2295	C₂	semidirect
21. C₅×#2276	C₂	semidirect
22. C₅×#2274	C₂	semidirect
23. C₄×C₅×#117	C₂	semidirect
24. C₅×#556	C₄	semidirect
124. #34307	C₅	direct (N × H)
133. C₅×C₄⋊Q₈	C₂×C₄	semidirect
134. C₅×#126	C₂×C₄	semidirect
135. C₅×#126	C₂×C₄	semidirect
137. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
138. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
141. C₄×C₅×Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
146. C₅×#117	C₂×C₄	semidirect
147. C₅×#117	C₂×C₄	semidirect
242. #2373	C₂×C₅	semidirect
243. #2373	C₂×C₅	semidirect
245. #2369	C₂×C₅	semidirect
246. #2362	C₂×C₅	semidirect
247. #2360	C₂×C₅	semidirect
248. #2356	C₂×C₅	semidirect
249. #2356	C₂×C₅	semidirect
251. #2347	C₂×C₅	semidirect
252. #2346	C₂×C₅	semidirect
254. #2334	C₂×C₅	semidirect
255. #2331	C₂×C₅	semidirect
256. #2323	C₂×C₅	semidirect
257. C₄×#126	C₂×C₅	semidirect
258. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
259. #2295	C₂×C₅	semidirect
261. #2276	C₂×C₅	semidirect
262. #2274	C₂×C₅	semidirect
263. C₄×#117	C₂×C₅	semidirect
371. #556	C₄×C₅	semidirect
565. C₄⋊Q₈	C₂×C₄×C₅	semidirect
566. #126	C₂×C₄×C₅	semidirect
567. #126	C₂×C₄×C₅	semidirect
569. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
570. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
573. C₄×Q₈	C₂×C₄×C₅	semidirect
574. C₄×Q₈	C₂×C₄×C₅	semidirect
578. #117	C₂×C₄×C₅	semidirect
579. #117	C₂×C₄×C₅	semidirect
917. C₅	#34307	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×#556	2
C₅×#2373	2
C₅×#2372	2
C₅×#2369	2
C₅×#2362	2
C₅×#2360	2
C₅×#2356	2
C₅×#2352	2
C₅×#2347	2
C₅×#2346	2
C₅×#2337	2
C₅×#2334	2
C₅×#2331	2
C₅×#2323	2
C₄×C₅×#126	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₅×#2290	2
C₅×#2276	2
C₅×#2274	2
C₄×C₅×#117	2
#34307	5

Subgroups — C5×#34307 #11957027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34307 #11957027