Subgroups — C₅×#35291 #11958011

Order 1280.

1650 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2857	C₂	1	1	yes	maximal, characteristic
4	C₅×#2857	C₂	1	1	yes	maximal, characteristic
5	C₅×#2645	C₂	1	2	yes	maximal, complemented
6	C₅×#2625	C₂	1	2	yes	maximal
7	C₅×#2514	C₂	1	2	yes	maximal, complemented
8	C₅×#2509	C₂	1	2	yes	maximal, complemented
9	C₅×#2508	C₂	1	2	yes	maximal, complemented
10	C₅×#2495	C₂	1	2	yes	maximal
11	C₅×#2494	C₂	1	2	yes	maximal
12	C₅×#2489	C₂	1	2	yes	maximal
13	C₅×#2453	C₂	1	2	yes	maximal, complemented
14	C₅×#2421	C₂	1	2	yes	maximal
15	C₅×#2323	C₂	1	2	yes	maximal
16	C₅×#2320	C₂	1	2	yes	maximal, complemented
17	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#125	C₂²	1	2	yes	—
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₂×C₅×#117	C₂²	1	1	yes	characteristic
28	C₂×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₅×#401	C₂²	1	4	yes	—
31	C₅×#400	C₂²	1	4	yes	—
32	C₅×#400	C₂²	1	4	yes	—
33	C₅×#400	C₂²	1	4	yes	—
34	C₅×#400	C₂²	1	4	yes	—
35	C₅×#398	C₂²	1	4	yes	—
36	C₅×#397	C₂²	1	4	yes	—
37	C₅×#397	C₂²	1	4	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#391	C₂²	1	2	yes	—
41	C₅×#391	C₂²	1	2	yes	—
42	C₅×#391	C₂²	1	2	yes	—
43	C₅×#391	C₂²	1	2	yes	—
44	C₅×#391	C₂²	1	2	yes	—
45	C₅×#391	C₂²	1	2	yes	—
46	C₅×#389	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#389	C₂²	1	2	yes	—
51	C₅×#389	C₂²	1	2	yes	—
52	C₅×#389	C₂²	1	4	yes	—
53	C₅×#389	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	2	yes	—
55	C₅×#389	C₂²	1	2	yes	—
56	C₅×#389	C₂²	1	2	yes	—
57	C₅×#389	C₂²	1	2	yes	—
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#388	C₂²	1	4	yes	—
60	C₅×#388	C₂²	1	4	yes	—
61	C₅×#387	C₂²	1	4	yes	—
62	C₅×#387	C₂²	1	4	yes	—
63	C₅×#387	C₂²	1	4	yes	—
64	C₅×#384	C₂²	1	1	yes	characteristic
65	C₅×#384	C₂²	1	1	yes	characteristic
66	C₅×#383	C₂²	1	4	yes	—
67	C₅×#382	C₂²	1	4	yes	—
68	C₅×#382	C₂²	1	2	yes	—
69	C₅×#382	C₂²	1	2	yes	—
70	C₅×#382	C₂²	1	2	yes	—
71	C₅×#380	C₂²	1	2	yes	—
72	C₅×#380	C₂²	1	2	yes	—
73	C₅×#380	C₂²	1	2	yes	—
74	C₅×#380	C₂²	1	2	yes	—
75	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
83	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
84	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
85	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₅×#376	C₂²	1	1	yes	characteristic
88	C₅×#376	C₂²	1	1	yes	characteristic
89	C₄³×C₅	C₂²	1	1	yes	characteristic
90	C₄³×C₅	C₂²	1	1	yes	characteristic
91	#35291	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂²×C₅×Q₈	C₂³	1	2	yes	—
93	C₂²×C₅×Q₈	C₂³	1	2	yes	—
94	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊Q₈	—	2	4	no	—
98	C₅×C₄⋊Q₈	—	2	4	no	—
99	C₅×#125	—	4	4	no	—
100	C₅×C₂²⋊Q₈	—	2	8	no	—
101	C₅×C₂²⋊Q₈	—	4	4	no	—
102	C₄×C₅×Q₈	—	2	8	no	—
103	C₄×C₅×Q₈	—	4	4	no	—
104	C₅×#117	—	2	4	no	—
105	C₅×#117	—	2	4	no	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₄²×C₅	—	2	4	no	—
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂³	1	4	yes	—
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₅	C₂³	1	4	yes	—
149	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₅×#95	C₂³	1	1	yes	characteristic
152	C₅×#95	C₂³	1	1	yes	characteristic
153	C₅×#95	C₂³	1	1	yes	characteristic
154	C₅×#95	C₂³	1	1	yes	characteristic
155	C₅×#95	C₂³	1	1	yes	characteristic
156	C₅×#95	C₂³	1	1	yes	characteristic
157	C₅×#95	C₂³	1	1	yes	characteristic
158	C₅×#95	C₂³	1	1	yes	characteristic
159	C₅×#95	C₂³	1	4	yes	—
160	C₅×#95	C₂³	1	4	yes	—
161	C₅×#95	C₂³	1	4	yes	—
162	C₅×#95	C₂³	1	4	yes	—
163	C₅×#95	C₂³	1	4	yes	—
164	C₅×#95	C₂³	1	4	yes	—
165	C₅×#95	C₂³	1	4	yes	—
166	C₅×#95	C₂³	1	4	yes	—
167	C₅×#95	C₂³	1	4	yes	—
168	C₅×#95	C₂³	1	4	yes	—
169	C₅×#95	C₂³	1	4	yes	—
170	C₅×#95	C₂³	1	4	yes	—
171	C₅×#95	C₂³	1	4	yes	—
172	C₅×#95	C₂³	1	4	yes	—
173	#2862	C₂×C₅	1	1	yes	characteristic, complemented
174	#2859	C₂×C₅	1	1	yes	characteristic, complemented
175	#2857	C₂×C₅	1	1	yes	characteristic
176	#2857	C₂×C₅	1	1	yes	characteristic
177	#2645	C₂×C₅	1	2	yes	complemented
178	#2625	C₂×C₅	1	2	yes	—
179	#2514	C₂×C₅	1	2	yes	complemented
180	#2509	C₂×C₅	1	2	yes	complemented
181	#2508	C₂×C₅	1	2	yes	complemented
182	#2495	C₂×C₅	1	2	yes	—
183	#2494	C₂×C₅	1	2	yes	—
184	#2489	C₂×C₅	1	2	yes	—
185	#2453	C₂×C₅	1	2	yes	complemented
186	#2421	C₂×C₅	1	2	yes	—
187	#2323	C₂×C₅	1	2	yes	—
188	#2320	C₂×C₅	1	2	yes	complemented
189	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
190	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
191	C₄×#117	C₂×C₅	1	1	yes	characteristic
192	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₅×Q₈	—	2	4	no	—
194	C₂×C₅×Q₈	—	2	4	no	—
195	C₂×C₅×Q₈	—	2	4	no	—
196	C₂×C₅×Q₈	—	2	4	no	—
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	—	2	4	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	#41	1	4	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	2	2	no	—
228	C₅×C₄⋊C₄	—	2	2	no	—
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	8	no	—
232	C₅×C₄⋊C₄	—	2	4	no	—
233	C₅×C₄⋊C₄	—	2	8	no	—
234	C₅×C₄⋊C₄	—	2	4	no	—
235	C₅×C₄⋊C₄	—	2	4	no	—
236	C₅×C₄⋊C₄	—	2	4	no	—
237	C₅×C₄⋊C₄	—	2	4	no	—
238	C₅×C₄⋊C₄	—	2	4	no	—
239	C₅×C₄⋊C₄	—	2	4	no	—
240	C₅×C₄⋊C₄	—	2	4	no	—
241	C₅×C₄⋊C₄	—	2	4	no	—
242	C₅×C₄⋊C₄	—	4	4	no	—
243	C₅×C₄⋊C₄	—	4	4	no	—
244	C₅×C₄⋊C₄	—	4	4	no	—
245	C₅×C₄⋊C₄	—	4	4	no	—
246	C₅×C₂²⋊C₄	—	2	2	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	8	no	—
249	C₅×C₂²⋊C₄	—	2	2	no	—
250	C₅×C₂²⋊C₄	—	2	2	no	—
251	C₅×C₂²⋊C₄	—	4	4	no	—
252	C₄²×C₅	—	2	2	no	—
253	C₄²×C₅	—	2	2	no	—
254	C₄²×C₅	—	2	2	no	—
255	C₄²×C₅	—	2	2	no	—
256	C₄²×C₅	—	2	2	no	—
257	C₄²×C₅	—	2	2	no	—
258	C₄²×C₅	—	2	8	no	—
259	C₄²×C₅	—	2	2	no	—
260	C₄²×C₅	—	2	2	no	—
261	C₄²×C₅	—	2	2	no	—
262	C₄²×C₅	—	2	2	no	—
263	C₄²×C₅	—	2	2	no	—
264	C₄²×C₅	—	2	2	no	—
265	C₄²×C₅	—	2	2	no	—
266	C₄²×C₅	—	2	2	no	—
267	C₄²×C₅	—	4	4	no	—
268	C₄²×C₅	#41	1	4	yes	—
269	C₄²×C₅	#41	1	4	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×#125	C₂²×C₅	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
275	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
277	C₂×#117	C₂²×C₅	1	1	yes	characteristic
278	C₂×#117	C₂²×C₅	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
280	#401	C₂²×C₅	1	4	yes	—
281	#400	C₂²×C₅	1	4	yes	—
282	#400	C₂²×C₅	1	4	yes	—
283	#400	C₂²×C₅	1	4	yes	—
284	#400	C₂²×C₅	1	4	yes	—
285	#398	C₂²×C₅	1	4	yes	—
286	#397	C₂²×C₅	1	4	yes	—
287	#397	C₂²×C₅	1	4	yes	—
288	#391	C₂²×C₅	1	2	yes	—
289	#391	C₂²×C₅	1	2	yes	—
290	#391	C₂²×C₅	1	2	yes	—
291	#391	C₂²×C₅	1	2	yes	—
292	#391	C₂²×C₅	1	2	yes	—
293	#391	C₂²×C₅	1	2	yes	—
294	#391	C₂²×C₅	1	2	yes	—
295	#391	C₂²×C₅	1	2	yes	—
296	#389	C₂²×C₅	1	2	yes	—
297	#389	C₂²×C₅	1	2	yes	—
298	#389	C₂²×C₅	1	2	yes	—
299	#389	C₂²×C₅	1	2	yes	—
300	#389	C₂²×C₅	1	2	yes	—
301	#389	C₂²×C₅	1	2	yes	—
302	#389	C₂²×C₅	1	2	yes	—
303	#389	C₂²×C₅	1	4	yes	—
304	#389	C₂²×C₅	1	2	yes	—
305	#389	C₂²×C₅	1	2	yes	—
306	#389	C₂²×C₅	1	2	yes	—
307	#389	C₂²×C₅	1	2	yes	—
308	#389	C₂²×C₅	1	2	yes	—
309	#388	C₂²×C₅	1	4	yes	—
310	#388	C₂²×C₅	1	4	yes	—
311	#387	C₂²×C₅	1	4	yes	—
312	#387	C₂²×C₅	1	4	yes	—
313	#387	C₂²×C₅	1	4	yes	—
314	#384	C₂²×C₅	1	1	yes	characteristic
315	#384	C₂²×C₅	1	1	yes	characteristic
316	#383	C₂²×C₅	1	4	yes	—
317	#382	C₂²×C₅	1	4	yes	—
318	#382	C₂²×C₅	1	2	yes	—
319	#382	C₂²×C₅	1	2	yes	—
320	#382	C₂²×C₅	1	2	yes	—
321	#380	C₂²×C₅	1	2	yes	—
322	#380	C₂²×C₅	1	2	yes	—
323	#380	C₂²×C₅	1	2	yes	—
324	#380	C₂²×C₅	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
333	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
334	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
336	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
337	#376	C₂²×C₅	1	1	yes	characteristic
338	#376	C₂²×C₅	1	1	yes	characteristic
339	C₄³	C₂²×C₅	1	1	yes	characteristic
340	C₄³	C₂²×C₅	1	1	yes	characteristic
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	—	2	1	no	—
343	C₂³×C₅	—	2	1	no	—
344	C₂³×C₅	—	2	1	no	—
345	C₂³×C₅	—	2	1	no	—
346	C₂³×C₅	—	2	1	no	—
347	C₂³×C₅	C₂×#41	1	2	yes	—
348	C₂³×C₅	C₂⁵	1	1	yes	characteristic
349	C₅×Q₈	—	4	8	no	—
350	C₅×Q₈	—	4	8	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	8	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	4	no	—
367	C₂×C₄×C₅	—	2	4	no	—
368	C₂×C₄×C₅	—	2	4	no	—
369	C₂×C₄×C₅	—	2	4	no	—
370	C₂×C₄×C₅	—	2	4	no	—
371	C₂×C₄×C₅	—	2	4	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	4	no	—
376	C₂×C₄×C₅	—	2	4	no	—
377	C₂×C₄×C₅	—	2	4	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	4	no	—
389	C₂×C₄×C₅	—	2	4	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	4	no	—
394	C₂×C₄×C₅	—	4	4	no	—
395	C₂×C₄×C₅	—	4	4	no	—
396	C₂×C₄×C₅	C₂×#41	1	2	yes	—
397	C₂×C₄×C₅	C₂×#41	1	2	yes	—
398	C₂×C₄×C₅	C₂×#41	1	2	yes	—
399	C₂×C₄×C₅	C₂×#41	1	2	yes	—
400	C₂×C₄×C₅	C₂×#41	1	2	yes	—
401	C₂×C₄×C₅	C₂×#41	1	2	yes	—
402	C₂×C₄×C₅	C₂×#41	1	2	yes	—
403	C₂×C₄×C₅	C₂×#41	1	2	yes	—
404	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
406	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
407	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
408	C₂²×Q₈	C₂³×C₅	1	2	yes	—
409	C₂²×Q₈	C₂³×C₅	1	2	yes	—
410	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
413	C₄⋊Q₈	—	2	4	no	—
414	C₄⋊Q₈	—	2	4	no	—
415	#125	—	4	4	no	—
416	C₂²⋊Q₈	—	2	8	no	—
417	C₂²⋊Q₈	—	4	4	no	—
418	C₄×Q₈	—	2	8	no	—
419	C₄×Q₈	—	4	4	no	—
420	#117	—	2	4	no	—
421	#117	—	2	4	no	—
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
448	C₂×C₄²	—	2	4	no	—
449	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₅	1	4	yes	—
454	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₅	1	4	yes	—
465	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
467	#95	C₂³×C₅	1	1	yes	characteristic
468	#95	C₂³×C₅	1	1	yes	characteristic
469	#95	C₂³×C₅	1	1	yes	characteristic
470	#95	C₂³×C₅	1	1	yes	characteristic
471	#95	C₂³×C₅	1	1	yes	characteristic
472	#95	C₂³×C₅	1	1	yes	characteristic
473	#95	C₂³×C₅	1	1	yes	characteristic
474	#95	C₂³×C₅	1	1	yes	characteristic
475	#95	C₂³×C₅	1	4	yes	—
476	#95	C₂³×C₅	1	4	yes	—
477	#95	C₂³×C₅	1	4	yes	—
478	#95	C₂³×C₅	1	4	yes	—
479	#95	C₂³×C₅	1	4	yes	—
480	#95	C₂³×C₅	1	4	yes	—
481	#95	C₂³×C₅	1	4	yes	—
482	#95	C₂³×C₅	1	4	yes	—
483	#95	C₂³×C₅	1	4	yes	—
484	#95	C₂³×C₅	1	4	yes	—
485	#95	C₂³×C₅	1	4	yes	—
486	#95	C₂³×C₅	1	4	yes	—
487	#95	C₂³×C₅	1	4	yes	—
488	#95	C₂³×C₅	1	4	yes	—
489	C₂²×C₅	—	2	2	no	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	2	2	no	—
492	C₂²×C₅	—	4	1	no	—
493	C₂²×C₅	—	4	1	no	—
494	C₂²×C₅	—	4	1	no	—
495	C₂²×C₅	—	4	1	no	—
496	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
497	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
502	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
503	C₄×C₅	—	2	2	no	—
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	2	no	—
506	C₄×C₅	—	4	4	no	—
507	C₄×C₅	—	4	1	no	—
508	C₄×C₅	—	4	1	no	—
509	C₄×C₅	—	4	4	no	—
510	C₄×C₅	—	4	1	no	—
511	C₄×C₅	—	4	1	no	—
512	C₄×C₅	—	4	1	no	—
513	C₄×C₅	—	4	1	no	—
514	C₄×C₅	—	4	4	no	—
515	C₄×C₅	—	4	1	no	—
516	C₄×C₅	—	4	1	no	—
517	C₄×C₅	—	4	4	no	—
518	C₄×C₅	#529	1	4	yes	—
519	C₄×C₅	#541	1	4	yes	—
520	C₄×C₅	#542	1	4	yes	—
521	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	4	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	C₅×#41	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	4	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	2	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	2	2	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	2	8	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	4	4	no	—
597	C₄²	C₅×#41	1	4	yes	—
598	C₄²	C₅×#41	1	4	yes	—
599	C₂×C₅	—	4	2	no	—
600	C₂×C₅	C₂×#529	1	1	yes	characteristic
601	C₂×C₅	C₂×#541	1	1	yes	characteristic
602	C₂×C₅	C₂×#542	1	1	yes	characteristic
603	C₂×C₅	#3509	1	1	yes	characteristic
604	C₂×C₅	#3509	1	1	yes	characteristic
605	C₂×C₅	#3511	1	1	yes	characteristic
606	C₂×C₅	#3511	1	1	yes	characteristic
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	C₂×C₅×#41	1	2	yes	—
614	C₂³	C₂⁵×C₅	1	1	yes	characteristic
615	Q₈	—	4	8	no	—
616	Q₈	—	4	8	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	C₂×C₅×#41	1	2	yes	—
663	C₂×C₄	C₂×C₅×#41	1	2	yes	—
664	C₂×C₄	C₂×C₅×#41	1	2	yes	—
665	C₂×C₄	C₂×C₅×#41	1	2	yes	—
666	C₂×C₄	C₂×C₅×#41	1	2	yes	—
667	C₂×C₄	C₂×C₅×#41	1	2	yes	—
668	C₂×C₄	C₂×C₅×#41	1	2	yes	—
669	C₂×C₄	C₂×C₅×#41	1	2	yes	—
670	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
671	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
672	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
673	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
674	C₅	#35291	1	1	yes	characteristic, direct product factor, Sylow
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
683	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
684	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
685	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
687	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	4	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	4	no	—
704	C₄	C₅×#529	1	4	yes	—
705	C₄	C₅×#541	1	4	yes	—
706	C₄	C₅×#542	1	4	yes	—
707	C₂	—	4	2	no	—
708	C₂	C₂×C₅×#529	1	1	yes	characteristic
709	C₂	C₂×C₅×#541	1	1	yes	characteristic
710	C₂	C₂×C₅×#542	1	1	yes	characteristic
711	C₂	C₅×#3509	1	1	yes	characteristic
712	C₂	C₅×#3509	1	1	yes	characteristic
713	C₂	C₅×#3511	1	1	yes	characteristic
714	C₂	C₅×#3511	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#2862	C₂	semidirect
2. C₅×#2859	C₂	semidirect
5. C₅×#2645	C₂	semidirect
7. C₅×#2514	C₂	semidirect
8. C₅×#2509	C₂	semidirect
9. C₅×#2508	C₂	semidirect
13. C₅×#2453	C₂	semidirect
16. C₅×#2320	C₂	semidirect
17. C₄×C₅×C₄⋊Q₈	C₂	semidirect
18. C₄×C₅×C₄⋊Q₈	C₂	semidirect
91. #35291	C₅	direct (N × H)
173. #2862	C₂×C₅	semidirect
174. #2859	C₂×C₅	semidirect
177. #2645	C₂×C₅	semidirect
179. #2514	C₂×C₅	semidirect
180. #2509	C₂×C₅	semidirect
181. #2508	C₂×C₅	semidirect
185. #2453	C₂×C₅	semidirect
188. #2320	C₂×C₅	semidirect
189. C₄×C₄⋊Q₈	C₂×C₅	semidirect
190. C₄×C₄⋊Q₈	C₂×C₅	semidirect
674. C₅	#35291	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×#2862	2
C₅×#2859	2
C₅×#2857	2
C₅×#2645	2
C₅×#2625	2
C₅×#2514	2
C₅×#2509	2
C₅×#2508	2
C₅×#2495	2
C₅×#2494	2
C₅×#2489	2
C₅×#2453	2
C₅×#2421	2
C₅×#2323	2
C₅×#2320	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#117	2
#35291	5

Subgroups — C5×#35291 #11958011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35291 #11958011