Subgroups — C₅×#34975 #11957695

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2533	C₂	1	2	yes	maximal, complemented
2	C₅×#2528	C₂	1	2	yes	maximal, complemented
3	C₅×#2514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2506	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2496	C₂	1	1	yes	maximal, characteristic
6	C₅×#2489	C₂	1	1	yes	maximal, characteristic
7	C₅×#2478	C₂	1	2	yes	maximal
8	C₅×#2475	C₂	1	2	yes	maximal
9	C₅×#2453	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2429	C₂	1	1	yes	maximal, characteristic
12	C₅×#2421	C₂	1	1	yes	maximal, characteristic
13	C₅×#2402	C₂	1	2	yes	maximal, complemented
14	C₅×#2401	C₂	1	2	yes	maximal
15	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#125	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#126	C₂	1	2	yes	maximal
19	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
20	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
21	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#126	C₂²	1	2	yes	—
26	C₂×C₅×#125	C₂²	1	2	yes	—
27	C₂×C₅×#125	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×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×C₅×#117	C₂²	1	1	yes	characteristic
35	C₂×C₅×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₅×#401	C₂²	1	2	yes	—
38	C₅×#400	C₂²	1	2	yes	—
39	C₅×#400	C₂²	1	2	yes	—
40	C₅×#400	C₂²	1	2	yes	—
41	C₅×#400	C₂²	1	2	yes	—
42	C₅×#400	C₂²	1	2	yes	—
43	C₅×#400	C₂²	1	2	yes	—
44	C₅×#400	C₂²	1	2	yes	—
45	C₅×#398	C₂²	1	2	yes	—
46	C₅×#398	C₂²	1	2	yes	—
47	C₅×#398	C₂²	1	2	yes	—
48	C₅×#398	C₂²	1	2	yes	—
49	C₅×#397	C₂²	1	2	yes	—
50	C₅×#397	C₂²	1	2	yes	—
51	C₅×#397	C₂²	1	2	yes	—
52	C₅×#396	C₂²	1	2	yes	—
53	C₅×#391	C₂²	1	1	yes	characteristic
54	C₅×#391	C₂²	1	1	yes	characteristic
55	C₅×#391	C₂²	1	1	yes	characteristic
56	C₅×#391	C₂²	1	1	yes	characteristic
57	C₅×#391	C₂²	1	1	yes	characteristic
58	C₅×#391	C₂²	1	1	yes	characteristic
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#389	C₂²	1	2	yes	—
62	C₅×#389	C₂²	1	1	yes	characteristic
63	C₅×#389	C₂²	1	1	yes	characteristic
64	C₅×#389	C₂²	1	1	yes	characteristic
65	C₅×#389	C₂²	1	1	yes	characteristic
66	C₅×#389	C₂²	1	1	yes	characteristic
67	C₅×#389	C₂²	1	1	yes	characteristic
68	C₅×#389	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×#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×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#387	C₂²	1	2	yes	—
84	C₅×#387	C₂²	1	2	yes	—
85	C₅×#385	C₂²	1	2	yes	—
86	C₅×#385	C₂²	1	2	yes	—
87	C₅×#384	C₂²	1	1	yes	characteristic
88	C₅×#383	C₂²	1	2	yes	—
89	C₅×#382	C₂²	1	2	yes	—
90	C₅×#382	C₂²	1	1	yes	characteristic
91	C₅×#380	C₂²	1	1	yes	characteristic
92	C₅×#380	C₂²	1	1	yes	characteristic
93	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	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×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₅×#376	C₂²	1	1	yes	characteristic
118	C₅×#376	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	2	yes	—
120	C₄³×C₅	C₂²	1	1	yes	characteristic
121	C₄³×C₅	C₂²	1	1	yes	characteristic
122	C₄³×C₅	C₂²	1	2	yes	—
123	#34975	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₅×C₄⋊Q₈	—	2	4	no	—
130	C₅×#126	—	2	8	no	—
131	C₅×#125	—	2	8	no	—
132	C₅×#125	—	2	4	no	—
133	C₅×C₂²⋊Q₈	—	2	4	no	—
134	C₅×C₂²⋊Q₈	—	2	4	no	—
135	C₄×C₅×Q₈	—	2	4	no	—
136	C₄×C₅×Q₈	—	2	4	no	—
137	C₄×C₅×Q₈	—	2	4	no	—
138	C₄×C₅×Q₈	—	2	4	no	—
139	C₅×#117	—	2	4	no	—
140	C₅×#117	—	2	4	no	—
141	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
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	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅	—	2	4	no	—
178	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₅	C₂³	1	2	yes	—
187	C₂×C₄²×C₅	C₂³	1	2	yes	—
188	C₂×C₄²×C₅	C₂³	1	2	yes	—
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	1	yes	characteristic
201	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₅×#95	C₂³	1	1	yes	characteristic
203	C₅×#95	C₂³	1	1	yes	characteristic
204	C₅×#95	C₂³	1	1	yes	characteristic
205	C₅×#95	C₂³	1	1	yes	characteristic
206	C₅×#95	C₂³	1	1	yes	characteristic
207	C₅×#95	C₂³	1	1	yes	characteristic
208	C₅×#95	C₂³	1	1	yes	characteristic
209	C₅×#95	C₂³	1	1	yes	characteristic
210	C₅×#95	C₂³	1	2	yes	—
211	C₅×#95	C₂³	1	2	yes	—
212	C₅×#95	C₂³	1	2	yes	—
213	C₅×#95	C₂³	1	2	yes	—
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	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	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	2	yes	—
230	C₅×#95	C₂³	1	2	yes	—
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	#2533	C₂×C₅	1	2	yes	complemented
237	#2528	C₂×C₅	1	2	yes	complemented
238	#2514	C₂×C₅	1	1	yes	characteristic, complemented
239	#2506	C₂×C₅	1	1	yes	characteristic, complemented
240	#2496	C₂×C₅	1	1	yes	characteristic
241	#2489	C₂×C₅	1	1	yes	characteristic
242	#2478	C₂×C₅	1	2	yes	—
243	#2475	C₂×C₅	1	2	yes	—
244	#2453	C₂×C₅	1	1	yes	characteristic, complemented
245	#2446	C₂×C₅	1	1	yes	characteristic, complemented
246	#2429	C₂×C₅	1	1	yes	characteristic
247	#2421	C₂×C₅	1	1	yes	characteristic
248	#2402	C₂×C₅	1	2	yes	complemented
249	#2401	C₂×C₅	1	2	yes	—
250	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
251	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
252	C₄×#125	C₂×C₅	1	2	yes	complemented
253	C₄×#126	C₂×C₅	1	2	yes	—
254	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
255	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
256	#2295	C₂×C₅	1	1	yes	characteristic, complemented
257	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
258	C₄×#117	C₂×C₅	1	1	yes	characteristic
259	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
260	C₂×C₅×Q₈	—	2	2	no	—
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	2	2	no	—
263	C₂×C₅×Q₈	—	2	2	no	—
264	C₂×C₅×Q₈	—	2	2	no	—
265	C₂×C₅×Q₈	#41	1	4	yes	—
266	C₂²×C₄×C₅	—	2	2	no	—
267	C₂²×C₄×C₅	—	2	2	no	—
268	C₂²×C₄×C₅	—	2	2	no	—
269	C₂²×C₄×C₅	—	2	2	no	—
270	C₂²×C₄×C₅	—	2	2	no	—
271	C₂²×C₄×C₅	—	2	2	no	—
272	C₂²×C₄×C₅	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	2	no	—
274	C₂²×C₄×C₅	—	2	2	no	—
275	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₅×C₄⋊C₄	—	2	2	no	—
298	C₅×C₄⋊C₄	—	2	2	no	—
299	C₅×C₄⋊C₄	—	2	2	no	—
300	C₅×C₄⋊C₄	—	2	4	no	—
301	C₅×C₄⋊C₄	—	2	4	no	—
302	C₅×C₄⋊C₄	—	2	4	no	—
303	C₅×C₄⋊C₄	—	2	2	no	—
304	C₅×C₄⋊C₄	—	2	2	no	—
305	C₅×C₄⋊C₄	—	2	2	no	—
306	C₅×C₄⋊C₄	—	2	4	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	4	no	—
309	C₅×C₄⋊C₄	—	2	4	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	4	no	—
313	C₅×C₄⋊C₄	—	2	4	no	—
314	C₅×C₄⋊C₄	—	2	4	no	—
315	C₅×C₄⋊C₄	—	2	4	no	—
316	C₅×C₄⋊C₄	—	2	4	no	—
317	C₅×C₄⋊C₄	—	2	2	no	—
318	C₅×C₄⋊C₄	—	2	4	no	—
319	C₅×C₄⋊C₄	—	2	4	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	#41	1	4	yes	—
324	C₅×C₄⋊C₄	#41	1	4	yes	—
325	C₅×C₂²⋊C₄	—	2	2	no	—
326	C₅×C₂²⋊C₄	—	2	4	no	—
327	C₅×C₂²⋊C₄	—	2	4	no	—
328	C₅×C₂²⋊C₄	—	2	2	no	—
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	2	4	no	—
331	C₅×C₂²⋊C₄	—	2	4	no	—
332	C₅×C₂²⋊C₄	#41	1	4	yes	—
333	C₄²×C₅	—	2	2	no	—
334	C₄²×C₅	—	2	2	no	—
335	C₄²×C₅	—	2	2	no	—
336	C₄²×C₅	—	2	2	no	—
337	C₄²×C₅	—	2	2	no	—
338	C₄²×C₅	—	2	2	no	—
339	C₄²×C₅	—	2	2	no	—
340	C₄²×C₅	—	2	4	no	—
341	C₄²×C₅	—	2	4	no	—
342	C₄²×C₅	—	2	2	no	—
343	C₄²×C₅	—	2	2	no	—
344	C₄²×C₅	—	2	4	no	—
345	C₄²×C₅	—	2	4	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	2	2	no	—
348	C₄²×C₅	—	2	4	no	—
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	2	2	no	—
352	C₄²×C₅	—	2	2	no	—
353	C₄²×C₅	—	2	4	no	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	4	no	—
356	C₄²×C₅	#41	1	4	yes	—
357	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
358	C₂×#126	C₂²×C₅	1	2	yes	—
359	C₂×#125	C₂²×C₅	1	1	yes	characteristic
360	C₂×#125	C₂²×C₅	1	2	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
362	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
367	C₂×#117	C₂²×C₅	1	1	yes	characteristic
368	C₂×#117	C₂²×C₅	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
370	#401	C₂²×C₅	1	2	yes	—
371	#400	C₂²×C₅	1	2	yes	—
372	#400	C₂²×C₅	1	2	yes	—
373	#400	C₂²×C₅	1	2	yes	—
374	#400	C₂²×C₅	1	2	yes	—
375	#400	C₂²×C₅	1	2	yes	—
376	#400	C₂²×C₅	1	2	yes	—
377	#400	C₂²×C₅	1	2	yes	—
378	#398	C₂²×C₅	1	2	yes	—
379	#398	C₂²×C₅	1	2	yes	—
380	#398	C₂²×C₅	1	2	yes	—
381	#398	C₂²×C₅	1	2	yes	—
382	#397	C₂²×C₅	1	2	yes	—
383	#397	C₂²×C₅	1	2	yes	—
384	#397	C₂²×C₅	1	2	yes	—
385	#396	C₂²×C₅	1	2	yes	—
386	#391	C₂²×C₅	1	1	yes	characteristic
387	#391	C₂²×C₅	1	1	yes	characteristic
388	#391	C₂²×C₅	1	1	yes	characteristic
389	#391	C₂²×C₅	1	1	yes	characteristic
390	#391	C₂²×C₅	1	1	yes	characteristic
391	#391	C₂²×C₅	1	1	yes	characteristic
392	#389	C₂²×C₅	1	1	yes	characteristic
393	#389	C₂²×C₅	1	2	yes	—
394	#389	C₂²×C₅	1	1	yes	characteristic
395	#389	C₂²×C₅	1	2	yes	—
396	#389	C₂²×C₅	1	2	yes	—
397	#389	C₂²×C₅	1	2	yes	—
398	#389	C₂²×C₅	1	1	yes	characteristic
399	#389	C₂²×C₅	1	1	yes	characteristic
400	#389	C₂²×C₅	1	1	yes	characteristic
401	#389	C₂²×C₅	1	1	yes	characteristic
402	#388	C₂²×C₅	1	2	yes	—
403	#388	C₂²×C₅	1	2	yes	—
404	#388	C₂²×C₅	1	2	yes	—
405	#387	C₂²×C₅	1	2	yes	—
406	#387	C₂²×C₅	1	2	yes	—
407	#387	C₂²×C₅	1	2	yes	—
408	#387	C₂²×C₅	1	2	yes	—
409	#387	C₂²×C₅	1	2	yes	—
410	#387	C₂²×C₅	1	2	yes	—
411	#387	C₂²×C₅	1	2	yes	—
412	#387	C₂²×C₅	1	2	yes	—
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	#385	C₂²×C₅	1	2	yes	—
419	#385	C₂²×C₅	1	2	yes	—
420	#384	C₂²×C₅	1	1	yes	characteristic
421	#383	C₂²×C₅	1	2	yes	—
422	#382	C₂²×C₅	1	1	yes	characteristic
423	#382	C₂²×C₅	1	2	yes	—
424	#380	C₂²×C₅	1	1	yes	characteristic
425	#380	C₂²×C₅	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
446	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
447	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	#376	C₂²×C₅	1	2	yes	—
451	#376	C₂²×C₅	1	1	yes	characteristic
452	#376	C₂²×C₅	1	1	yes	characteristic
453	C₄³	C₂²×C₅	1	2	yes	—
454	C₄³	C₂²×C₅	1	1	yes	characteristic
455	C₄³	C₂²×C₅	1	1	yes	characteristic
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	2	1	no	—
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	1	no	—
461	C₂³×C₅	—	2	1	no	—
462	C₂³×C₅	C₂×#41	1	2	yes	—
463	C₂³×C₅	C₂⁵	1	1	yes	characteristic
464	C₅×Q₈	—	2	8	no	—
465	C₅×Q₈	—	4	4	no	—
466	C₂×C₄×C₅	—	2	8	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	2	no	—
475	C₂×C₄×C₅	—	2	2	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	2	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	2	no	—
496	C₂×C₄×C₅	—	2	1	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	2	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	2	no	—
503	C₂×C₄×C₅	—	2	2	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	2	no	—
506	C₂×C₄×C₅	—	2	2	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	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	2	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	4	4	no	—
520	C₂×C₄×C₅	—	4	4	no	—
521	C₂×C₄×C₅	C₂×#41	1	2	yes	—
522	C₂×C₄×C₅	C₂×#41	1	2	yes	—
523	C₂×C₄×C₅	C₂×#41	1	2	yes	—
524	C₂×C₄×C₅	C₂×#41	1	4	yes	—
525	C₂×C₄×C₅	C₂×#41	1	2	yes	—
526	C₂×C₄×C₅	C₂×#41	1	4	yes	—
527	C₂×C₄×C₅	C₂×#41	1	2	yes	—
528	C₂×C₄×C₅	C₂×#41	1	2	yes	—
529	C₂×C₄×C₅	C₂×#41	1	2	yes	—
530	C₂×C₄×C₅	C₂×#41	1	2	yes	—
531	C₂×C₄×C₅	C₂×#41	1	2	yes	—
532	C₂×C₄×C₅	C₂×#41	1	2	yes	—
533	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
534	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
535	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
540	C₄⋊Q₈	—	2	4	no	—
541	#126	—	2	8	no	—
542	#125	—	2	8	no	—
543	#125	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	C₄×Q₈	—	2	4	no	—
547	C₄×Q₈	—	2	4	no	—
548	C₄×Q₈	—	2	4	no	—
549	C₄×Q₈	—	2	4	no	—
550	#117	—	2	4	no	—
551	#117	—	2	4	no	—
552	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂×C₄²	—	2	4	no	—
589	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₅	1	2	yes	—
594	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₅	1	2	yes	—
597	C₂×C₄²	C₂³×C₅	1	2	yes	—
598	C₂×C₄²	C₂³×C₅	1	2	yes	—
599	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₅	1	2	yes	—
601	C₂×C₄²	C₂³×C₅	1	2	yes	—
602	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₅	1	2	yes	—
606	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₅	1	2	yes	—
610	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
613	#95	C₂³×C₅	1	1	yes	characteristic
614	#95	C₂³×C₅	1	1	yes	characteristic
615	#95	C₂³×C₅	1	1	yes	characteristic
616	#95	C₂³×C₅	1	1	yes	characteristic
617	#95	C₂³×C₅	1	1	yes	characteristic
618	#95	C₂³×C₅	1	1	yes	characteristic
619	#95	C₂³×C₅	1	1	yes	characteristic
620	#95	C₂³×C₅	1	1	yes	characteristic
621	#95	C₂³×C₅	1	2	yes	—
622	#95	C₂³×C₅	1	2	yes	—
623	#95	C₂³×C₅	1	2	yes	—
624	#95	C₂³×C₅	1	2	yes	—
625	#95	C₂³×C₅	1	2	yes	—
626	#95	C₂³×C₅	1	2	yes	—
627	#95	C₂³×C₅	1	2	yes	—
628	#95	C₂³×C₅	1	2	yes	—
629	#95	C₂³×C₅	1	2	yes	—
630	#95	C₂³×C₅	1	2	yes	—
631	#95	C₂³×C₅	1	2	yes	—
632	#95	C₂³×C₅	1	2	yes	—
633	#95	C₂³×C₅	1	2	yes	—
634	#95	C₂³×C₅	1	2	yes	—
635	#95	C₂³×C₅	1	2	yes	—
636	#95	C₂³×C₅	1	2	yes	—
637	#95	C₂³×C₅	1	2	yes	—
638	#95	C₂³×C₅	1	2	yes	—
639	#95	C₂³×C₅	1	2	yes	—
640	#95	C₂³×C₅	1	2	yes	—
641	#95	C₂³×C₅	1	2	yes	—
642	#95	C₂³×C₅	1	2	yes	—
643	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	2	yes	—
645	#95	C₂³×C₅	1	2	yes	—
646	#95	C₂³×C₅	1	2	yes	—
647	C₂²×C₅	—	2	2	no	—
648	C₂²×C₅	—	2	2	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	4	1	no	—
652	C₂²×C₅	—	4	1	no	—
653	C₂²×C₅	—	4	1	no	—
654	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
655	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
656	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
657	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
658	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
659	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
661	C₄×C₅	—	2	4	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	2	2	no	—
664	C₄×C₅	—	2	2	no	—
665	C₄×C₅	—	2	2	no	—
666	C₄×C₅	—	2	4	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	2	2	no	—
669	C₄×C₅	—	4	1	no	—
670	C₄×C₅	—	4	2	no	—
671	C₄×C₅	—	4	2	no	—
672	C₄×C₅	—	4	2	no	—
673	C₄×C₅	—	4	1	no	—
674	C₄×C₅	—	4	1	no	—
675	C₄×C₅	—	4	1	no	—
676	C₄×C₅	—	4	2	no	—
677	C₄×C₅	—	4	1	no	—
678	C₄×C₅	—	4	1	no	—
679	C₄×C₅	—	4	2	no	—
680	C₄×C₅	—	4	2	no	—
681	C₄×C₅	#529	1	4	yes	—
682	C₄×C₅	#541	1	4	yes	—
683	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	C₅×#41	1	4	yes	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₅×#41	1	4	yes	—
748	C₄⋊C₄	C₅×#41	1	4	yes	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	C₅×#41	1	4	yes	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	4	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	4	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	C₅×#41	1	4	yes	—
781	C₂×C₅	—	4	2	no	—
782	C₂×C₅	C₂×#529	1	1	yes	characteristic
783	C₂×C₅	#3444	1	1	yes	characteristic
784	C₂×C₅	C₂×#541	1	1	yes	characteristic
785	C₂×C₅	#3482	1	1	yes	characteristic
786	C₂×C₅	#3482	1	1	yes	characteristic
787	C₂×C₅	#3482	1	1	yes	characteristic
788	C₂×C₅	#3482	1	1	yes	characteristic
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	C₂×C₅×#41	1	2	yes	—
796	C₂³	C₂⁵×C₅	1	1	yes	characteristic
797	Q₈	—	2	8	no	—
798	Q₈	—	4	4	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	C₂×C₅×#41	1	2	yes	—
855	C₂×C₄	C₂×C₅×#41	1	2	yes	—
856	C₂×C₄	C₂×C₅×#41	1	2	yes	—
857	C₂×C₄	C₂×C₅×#41	1	4	yes	—
858	C₂×C₄	C₂×C₅×#41	1	2	yes	—
859	C₂×C₄	C₂×C₅×#41	1	4	yes	—
860	C₂×C₄	C₂×C₅×#41	1	2	yes	—
861	C₂×C₄	C₂×C₅×#41	1	2	yes	—
862	C₂×C₄	C₂×C₅×#41	1	2	yes	—
863	C₂×C₄	C₂×C₅×#41	1	2	yes	—
864	C₂×C₄	C₂×C₅×#41	1	2	yes	—
865	C₂×C₄	C₂×C₅×#41	1	2	yes	—
866	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
867	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
868	C₅	#34975	1	1	yes	characteristic, direct product factor, Sylow
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
877	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
878	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
879	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
880	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
881	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	C₅×#529	1	4	yes	—
904	C₄	C₅×#541	1	4	yes	—
905	C₂	—	4	2	no	—
906	C₂	C₂×C₅×#529	1	1	yes	characteristic
907	C₂	C₅×#3444	1	1	yes	characteristic
908	C₂	C₂×C₅×#541	1	1	yes	characteristic
909	C₂	C₅×#3482	1	1	yes	characteristic
910	C₂	C₅×#3482	1	1	yes	characteristic
911	C₂	C₅×#3482	1	1	yes	characteristic
912	C₂	C₅×#3482	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#2533	C₂	semidirect
2. C₅×#2528	C₂	semidirect
3. C₅×#2514	C₂	semidirect
4. C₅×#2506	C₂	semidirect
9. C₅×#2453	C₂	semidirect
10. C₅×#2446	C₂	semidirect
13. C₅×#2402	C₂	semidirect
15. C₄×C₅×C₄⋊Q₈	C₂	semidirect
16. C₄×C₅×#125	C₂	semidirect
17. C₄×C₅×#125	C₂	semidirect
21. C₅×#2295	C₂	semidirect
22. C₄²×C₅×Q₈	C₂	semidirect
123. #34975	C₅	direct (N × H)
236. #2533	C₂×C₅	semidirect
237. #2528	C₂×C₅	semidirect
238. #2514	C₂×C₅	semidirect
239. #2506	C₂×C₅	semidirect
244. #2453	C₂×C₅	semidirect
245. #2446	C₂×C₅	semidirect
248. #2402	C₂×C₅	semidirect
250. C₄×C₄⋊Q₈	C₂×C₅	semidirect
251. C₄×#125	C₂×C₅	semidirect
252. C₄×#125	C₂×C₅	semidirect
256. #2295	C₂×C₅	semidirect
257. C₄²×Q₈	C₂×C₅	semidirect
868. C₅	#34975	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#2533	2
C₅×#2528	2
C₅×#2514	2
C₅×#2506	2
C₅×#2496	2
C₅×#2489	2
C₅×#2478	2
C₅×#2475	2
C₅×#2453	2
C₅×#2446	2
C₅×#2429	2
C₅×#2421	2
C₅×#2402	2
C₅×#2401	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₄×C₅×#126	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₄²×C₅×Q₈	2
C₄×C₅×#117	2
#34975	5

Subgroups — C5×#34975 #11957695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34975 #11957695