Subgroups — C₅×#35310 #11958030

Order 1280.

2346 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2848	C₂	1	2	yes	maximal
6	C₅×#2629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2625	C₂	1	2	yes	maximal, complemented
8	C₅×#2621	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2480	C₂	1	4	yes	maximal
10	C₅×#2478	C₂	1	4	yes	maximal, complemented
11	C₅×#2475	C₂	1	4	yes	maximal, complemented
12	C₅×#2473	C₂	1	4	yes	maximal, complemented
13	C₅×#2323	C₂	1	2	yes	maximal, complemented
14	C₅×#2314	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₅×#541	—	2	8	no	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×#126	C₂²	1	4	yes	—
20	C₂×C₅×#125	C₂²	1	4	yes	complemented
21	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×C₂²⋊Q₈	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	complemented
26	C₂×C₅×#117	—	2	8	no	—
27	C₂×C₅×#117	C₂²	1	2	yes	—
28	C₂×C₅×#117	C₂²	1	2	yes	—
29	C₂×C₅×#117	C₂²	1	1	yes	characteristic
30	C₂×C₅×#117	C₂²	1	1	yes	characteristic
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₅×#400	C₂²	1	4	yes	complemented
38	C₅×#398	C₂²	1	4	yes	complemented
39	C₅×#398	C₂²	1	4	yes	complemented
40	C₅×#398	C₂²	1	4	yes	complemented
41	C₅×#397	C₂²	1	4	yes	—
42	C₅×#397	C₂²	1	4	yes	—
43	C₅×#397	C₂²	1	4	yes	—
44	C₅×#396	C₂²	1	4	yes	—
45	C₅×#391	C₂²	1	2	yes	complemented
46	C₅×#391	C₂²	1	2	yes	complemented
47	C₅×#389	C₂²	1	4	yes	complemented
48	C₅×#389	C₂²	1	4	yes	complemented
49	C₅×#389	C₂²	1	2	yes	complemented
50	C₅×#389	C₂²	1	2	yes	complemented
51	C₅×#388	C₂²	1	4	yes	—
52	C₅×#388	C₂²	1	4	yes	—
53	C₅×#388	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	complemented
55	C₅×#387	C₂²	1	4	yes	complemented
56	C₅×#387	C₂²	1	4	yes	complemented
57	C₅×#387	C₂²	1	4	yes	complemented
58	C₅×#385	C₂²	1	4	yes	—
59	C₅×#385	C₂²	1	4	yes	—
60	C₅×#385	C₂²	1	4	yes	—
61	C₅×#385	C₂²	1	4	yes	—
62	C₅×#385	C₂²	1	4	yes	—
63	C₅×#384	C₂²	1	1	yes	characteristic, complemented
64	C₅×#382	C₂²	1	1	yes	characteristic, complemented
65	C₅×#380	C₂²	1	4	yes	—
66	C₅×#380	C₂²	1	2	yes	—
67	C₅×#380	C₂²	1	2	yes	—
68	C₅×#380	C₂²	1	2	yes	—
69	C₅×#379	C₂²	1	4	yes	—
70	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
72	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
73	#35310	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁵×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₅×Q₈	C₂³	1	2	yes	—
76	C₂³×C₄×C₅	—	2	4	no	—
77	C₂³×C₄×C₅	—	2	4	no	—
78	C₂³×C₄×C₅	—	2	4	no	—
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₅	C₂³	1	2	yes	—
83	C₂³×C₄×C₅	C₂³	1	2	yes	—
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	—	2	4	no	—
88	C₅×#126	—	2	16	no	—
89	C₅×#125	—	2	16	no	—
90	C₅×#125	—	2	4	no	—
91	C₅×C₂²⋊Q₈	—	2	8	no	—
92	C₅×C₂²⋊Q₈	—	2	8	no	—
93	C₅×C₂²⋊Q₈	—	2	8	no	—
94	C₄×C₅×Q₈	—	2	8	no	—
95	C₅×#117	—	2	4	no	—
96	C₅×#117	—	2	8	no	—
97	C₅×#117	—	2	8	no	—
98	C₅×#117	—	2	4	no	—
99	C₅×#117	—	2	4	no	—
100	C₅×#117	D₄	1	8	yes	—
101	C₂×C₅×C₄⋊C₄	—	2	8	no	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	4	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₄²×C₅	—	2	4	no	—
130	C₂×C₄²×C₅	—	2	4	no	—
131	C₂×C₄²×C₅	C₂³	1	4	yes	—
132	C₂×C₄²×C₅	C₂³	1	2	yes	—
133	C₂×C₄²×C₅	C₂³	1	2	yes	—
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂³	1	4	yes	—
137	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	4	yes	—
144	C₅×#95	C₂³	1	4	yes	—
145	C₅×#95	C₂³	1	4	yes	—
146	C₅×#95	C₂³	1	4	yes	—
147	C₅×#95	C₂³	1	4	yes	—
148	C₅×#95	C₂³	1	4	yes	—
149	C₅×#95	C₂³	1	4	yes	—
150	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂²×#117	C₂×C₅	1	1	yes	characteristic
152	#2857	C₂×C₅	1	1	yes	characteristic, complemented
153	#2851	C₂×C₅	1	1	yes	characteristic, complemented
154	#2848	C₂×C₅	1	2	yes	—
155	#2629	C₂×C₅	1	1	yes	characteristic, complemented
156	#2625	C₂×C₅	1	2	yes	complemented
157	#2621	C₂×C₅	1	1	yes	characteristic, complemented
158	#2480	C₂×C₅	1	4	yes	—
159	#2478	C₂×C₅	1	4	yes	complemented
160	#2475	C₂×C₅	1	4	yes	complemented
161	#2473	C₂×C₅	1	4	yes	complemented
162	#2323	C₂×C₅	1	2	yes	complemented
163	#2314	C₂×C₅	1	1	yes	characteristic, complemented
164	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
165	C₂⁴×C₅	—	2	2	no	—
166	C₂⁴×C₅	—	2	2	no	—
167	C₂⁴×C₅	—	2	2	no	—
168	C₂⁴×C₅	—	2	4	no	—
169	C₂⁴×C₅	—	4	2	no	—
170	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
171	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
172	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₅×Q₈	—	2	4	no	—
174	C₂×C₅×Q₈	—	2	4	no	—
175	C₂×C₅×Q₈	—	2	4	no	—
176	C₂²×C₄×C₅	—	2	32	no	—
177	C₂²×C₄×C₅	—	2	2	no	—
178	C₂²×C₄×C₅	—	2	2	no	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	2	2	no	—
184	C₂²×C₄×C₅	—	2	2	no	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	—	2	2	no	—
188	C₂²×C₄×C₅	—	2	2	no	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	—	2	4	no	—
193	C₂²×C₄×C₅	—	2	4	no	—
194	C₂²×C₄×C₅	—	2	4	no	—
195	C₂²×C₄×C₅	—	2	4	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₅	#41	1	4	yes	—
200	C₂²×C₄×C₅	#41	1	4	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	4	no	—
215	C₅×C₄⋊C₄	—	2	4	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	8	no	—
218	C₅×C₄⋊C₄	—	2	8	no	—
219	C₅×C₄⋊C₄	—	2	8	no	—
220	C₅×C₄⋊C₄	—	2	8	no	—
221	C₅×C₄⋊C₄	—	2	4	no	—
222	C₅×C₄⋊C₄	—	2	4	no	—
223	C₅×C₄⋊C₄	—	2	8	no	—
224	C₅×C₄⋊C₄	—	2	8	no	—
225	C₅×C₄⋊C₄	—	4	4	no	—
226	C₅×C₄⋊C₄	—	4	4	no	—
227	C₅×C₄⋊C₄	—	4	4	no	—
228	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
229	C₅×C₂²⋊C₄	—	2	4	no	—
230	C₅×C₂²⋊C₄	—	2	8	no	—
231	C₅×C₂²⋊C₄	—	2	8	no	—
232	C₅×C₂²⋊C₄	—	2	8	no	—
233	C₅×C₂²⋊C₄	—	2	8	no	—
234	C₅×C₂²⋊C₄	—	2	4	no	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	—	4	4	no	—
237	C₅×C₂²⋊C₄	—	4	4	no	—
238	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
239	C₄²×C₅	—	2	4	no	—
240	C₄²×C₅	—	2	4	no	—
241	C₄²×C₅	—	2	2	no	—
242	C₄²×C₅	—	2	2	no	—
243	C₄²×C₅	—	2	8	no	—
244	C₄²×C₅	—	4	4	no	—
245	C₄²×C₅	C₂×D₄	1	4	yes	—
246	C₄²×C₅	C₂×D₄	1	4	yes	—
247	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
248	#541	—	2	8	no	—
249	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₂×#126	C₂²×C₅	1	4	yes	—
251	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂×#125	C₂²×C₅	1	4	yes	complemented
253	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
254	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
256	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
257	C₂×#117	—	2	8	no	—
258	C₂×#117	C₂²×C₅	1	1	yes	characteristic
259	C₂×#117	C₂²×C₅	1	1	yes	characteristic
260	C₂×#117	C₂²×C₅	1	1	yes	characteristic
261	C₂×#117	C₂²×C₅	1	2	yes	—
262	C₂×#117	C₂²×C₅	1	2	yes	—
263	C₂×#117	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
266	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
268	#400	C₂²×C₅	1	4	yes	complemented
269	#398	C₂²×C₅	1	4	yes	complemented
270	#398	C₂²×C₅	1	4	yes	complemented
271	#398	C₂²×C₅	1	4	yes	complemented
272	#397	C₂²×C₅	1	4	yes	—
273	#397	C₂²×C₅	1	4	yes	—
274	#397	C₂²×C₅	1	4	yes	—
275	#396	C₂²×C₅	1	4	yes	—
276	#391	C₂²×C₅	1	2	yes	complemented
277	#391	C₂²×C₅	1	2	yes	complemented
278	#389	C₂²×C₅	1	2	yes	complemented
279	#389	C₂²×C₅	1	4	yes	complemented
280	#389	C₂²×C₅	1	4	yes	complemented
281	#389	C₂²×C₅	1	2	yes	complemented
282	#388	C₂²×C₅	1	4	yes	—
283	#388	C₂²×C₅	1	4	yes	—
284	#388	C₂²×C₅	1	4	yes	—
285	#387	C₂²×C₅	1	4	yes	complemented
286	#387	C₂²×C₅	1	4	yes	complemented
287	#387	C₂²×C₅	1	4	yes	complemented
288	#387	C₂²×C₅	1	4	yes	complemented
289	#385	C₂²×C₅	1	4	yes	—
290	#385	C₂²×C₅	1	4	yes	—
291	#385	C₂²×C₅	1	4	yes	—
292	#385	C₂²×C₅	1	4	yes	—
293	#385	C₂²×C₅	1	4	yes	—
294	#384	C₂²×C₅	1	1	yes	characteristic, complemented
295	#382	C₂²×C₅	1	1	yes	characteristic, complemented
296	#380	C₂²×C₅	1	2	yes	—
297	#380	C₂²×C₅	1	2	yes	—
298	#380	C₂²×C₅	1	2	yes	—
299	#380	C₂²×C₅	1	4	yes	—
300	#379	C₂²×C₅	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
303	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	2	8	no	—
308	C₂³×C₅	—	2	1	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	2	2	no	—
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	4	8	no	—
317	C₂³×C₅	—	4	8	no	—
318	C₂³×C₅	—	4	4	no	—
319	C₂³×C₅	—	4	4	no	—
320	C₂³×C₅	C₂²×D₄	1	2	yes	—
321	C₂³×C₅	C₂×#41	1	2	yes	—
322	C₂³×C₅	C₂×#41	1	2	yes	—
323	C₂³×C₅	2₋¹⁺⁴	1	4	yes	—
324	C₂³×C₅	C₂⁵	1	1	yes	characteristic
325	C₅×Q₈	—	4	8	no	—
326	C₂×C₄×C₅	—	2	8	no	—
327	C₂×C₄×C₅	—	2	8	no	—
328	C₂×C₄×C₅	—	2	8	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	8	no	—
340	C₂×C₄×C₅	—	2	8	no	—
341	C₂×C₄×C₅	—	2	8	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	4	no	—
345	C₂×C₄×C₅	—	2	4	no	—
346	C₂×C₄×C₅	—	2	4	no	—
347	C₂×C₄×C₅	—	2	4	no	—
348	C₂×C₄×C₅	—	2	4	no	—
349	C₂×C₄×C₅	—	2	4	no	—
350	C₂×C₄×C₅	—	2	4	no	—
351	C₂×C₄×C₅	—	2	4	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	4	no	—
355	C₂×C₄×C₅	—	2	4	no	—
356	C₂×C₄×C₅	—	2	4	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	4	8	no	—
361	C₂×C₄×C₅	—	4	8	no	—
362	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₅	C₂×#41	1	2	yes	—
367	C₂×C₄×C₅	C₂×#41	1	2	yes	—
368	C₂×C₄×C₅	C₂×#41	1	2	yes	—
369	C₂×C₄×C₅	C₂×#41	1	2	yes	—
370	C₂⁵	C₂³×C₅	1	1	yes	characteristic
371	C₂²×Q₈	C₂³×C₅	1	2	yes	—
372	C₂³×C₄	—	2	4	no	—
373	C₂³×C₄	—	2	4	no	—
374	C₂³×C₄	—	2	4	no	—
375	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₅	1	2	yes	—
379	C₂³×C₄	C₂³×C₅	1	2	yes	—
380	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
383	C₄⋊Q₈	—	2	4	no	—
384	#126	—	2	16	no	—
385	#125	—	2	16	no	—
386	#125	—	2	4	no	—
387	C₂²⋊Q₈	—	2	8	no	—
388	C₂²⋊Q₈	—	2	8	no	—
389	C₂²⋊Q₈	—	2	8	no	—
390	C₄×Q₈	—	2	8	no	—
391	#117	—	2	4	no	—
392	#117	—	2	8	no	—
393	#117	—	2	8	no	—
394	#117	—	2	4	no	—
395	#117	—	2	4	no	—
396	#117	C₅×D₄	1	8	yes	—
397	C₂×C₄⋊C₄	—	2	8	no	—
398	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
414	C₂×C₂²⋊C₄	—	2	8	no	—
415	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
425	C₂×C₄²	—	2	4	no	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	C₂³×C₅	1	2	yes	—
428	C₂×C₄²	C₂³×C₅	1	2	yes	—
429	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₅	1	4	yes	—
432	C₂×C₄²	C₂³×C₅	1	4	yes	—
433	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	#95	C₂³×C₅	1	4	yes	—
436	#95	C₂³×C₅	1	4	yes	—
437	#95	C₂³×C₅	1	4	yes	—
438	#95	C₂³×C₅	1	4	yes	—
439	#95	C₂³×C₅	1	4	yes	—
440	#95	C₂³×C₅	1	4	yes	—
441	#95	C₂³×C₅	1	4	yes	—
442	#95	C₂³×C₅	1	4	yes	—
443	#95	C₂³×C₅	1	4	yes	—
444	#95	C₂³×C₅	1	4	yes	—
445	#95	C₂³×C₅	1	4	yes	—
446	C₂²×C₅	—	2	2	no	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	2	4	no	—
449	C₂²×C₅	—	2	4	no	—
450	C₂²×C₅	—	2	2	no	—
451	C₂²×C₅	—	2	2	no	—
452	C₂²×C₅	—	2	4	no	—
453	C₂²×C₅	—	2	4	no	—
454	C₂²×C₅	—	4	16	no	—
455	C₂²×C₅	—	4	1	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	#541	1	4	yes	complemented
462	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
463	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
464	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
465	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
466	C₂²×C₅	#585	1	2	yes	—
467	C₄×C₅	—	2	2	no	—
468	C₄×C₅	—	2	2	no	—
469	C₄×C₅	—	2	2	no	—
470	C₄×C₅	—	2	4	no	—
471	C₄×C₅	—	2	4	no	—
472	C₄×C₅	—	4	4	no	—
473	C₄×C₅	—	4	4	no	—
474	C₄×C₅	—	4	4	no	—
475	C₄×C₅	—	4	2	no	—
476	C₄×C₅	—	4	2	no	—
477	C₄×C₅	—	4	4	no	—
478	C₄×C₅	#525	1	4	yes	—
479	C₂⁴	—	2	2	no	—
480	C₂⁴	—	2	2	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	—	2	4	no	—
483	C₂⁴	—	4	2	no	—
484	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
485	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
486	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
487	C₂×Q₈	—	2	4	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂²×C₄	—	2	32	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
513	C₂²×C₄	C₅×#41	1	4	yes	—
514	C₂²×C₄	C₅×#41	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
519	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
520	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
522	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	8	no	—
532	C₄⋊C₄	—	2	8	no	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	8	no	—
558	C₄²	—	4	4	no	—
559	C₄²	C₂×C₅×D₄	1	4	yes	—
560	C₄²	C₂×C₅×D₄	1	4	yes	—
561	C₂×C₅	—	2	4	no	—
562	C₂×C₅	—	4	2	no	—
563	C₂×C₅	—	4	2	no	—
564	C₂×C₅	C₂×#525	1	1	yes	characteristic
565	C₂×C₅	C₂×#541	1	1	yes	characteristic
566	C₂×C₅	#3455	1	1	yes	characteristic
567	C₂×C₅	#3489	1	2	yes	—
568	C₂×C₅	#3495	1	2	yes	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	8	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	4	no	—
585	C₂³	C₂²×C₅×D₄	1	2	yes	—
586	C₂³	C₂×C₅×#41	1	2	yes	—
587	C₂³	C₂×C₅×#41	1	2	yes	—
588	C₂³	C₅×2₋¹⁺⁴	1	4	yes	—
589	C₂³	C₂⁵×C₅	1	1	yes	characteristic
590	Q₈	—	4	8	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	4	8	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
628	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
629	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
630	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
631	C₂×C₄	C₂×C₅×#41	1	2	yes	—
632	C₂×C₄	C₂×C₅×#41	1	2	yes	—
633	C₂×C₄	C₂×C₅×#41	1	2	yes	—
634	C₂×C₄	C₂×C₅×#41	1	2	yes	—
635	C₅	#35310	1	1	yes	characteristic, direct product factor, Sylow
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	4	no	—
644	C₂²	—	4	16	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	C₅×#541	1	4	yes	complemented
652	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
653	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
654	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
655	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
656	C₂²	C₅×#585	1	2	yes	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	4	no	—
667	C₄	—	4	4	no	—
668	C₄	C₅×#525	1	4	yes	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	2	no	—
672	C₂	C₂×C₅×#525	1	1	yes	characteristic
673	C₂	C₂×C₅×#541	1	1	yes	characteristic
674	C₂	C₅×#3455	1	1	yes	characteristic
675	C₂	C₅×#3489	1	2	yes	—
676	C₂	C₅×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁵×C₅	C₂³
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. C₂×C₅×#541	C₂	semidirect
3. C₅×#2857	C₂	semidirect
4. C₅×#2851	C₂	semidirect
6. C₅×#2629	C₂	semidirect
7. C₅×#2625	C₂	semidirect
8. C₅×#2621	C₂	semidirect
10. C₅×#2478	C₂	semidirect
11. C₅×#2475	C₂	semidirect
12. C₅×#2473	C₂	semidirect
13. C₅×#2323	C₂	semidirect
14. C₅×#2314	C₂	semidirect
15. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
18. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₅×#125	C₂²	semidirect
21. C₂×C₅×#125	C₂²	semidirect
25. C₂×C₄×C₅×Q₈	C₂²	semidirect
37. C₅×#400	C₂²	semidirect
38. C₅×#398	C₂²	semidirect
39. C₅×#398	C₂²	semidirect
40. C₅×#398	C₂²	semidirect
45. C₅×#391	C₂²	semidirect
46. C₅×#391	C₂²	semidirect
47. C₅×#389	C₂²	semidirect
48. C₅×#389	C₂²	semidirect
49. C₅×#389	C₂²	semidirect
50. C₅×#389	C₂²	semidirect
54. C₅×#387	C₂²	semidirect
55. C₅×#387	C₂²	semidirect
56. C₅×#387	C₂²	semidirect
57. C₅×#387	C₂²	semidirect
63. C₅×#384	C₂²	semidirect
64. C₅×#382	C₂²	semidirect
70. C₄×C₅×C₄⋊C₄	C₂²	semidirect
71. C₄×C₅×C₄⋊C₄	C₂²	semidirect
73. #35310	C₅	direct (N × H)
150. C₂×#541	C₂×C₅	semidirect
152. #2857	C₂×C₅	semidirect
153. #2851	C₂×C₅	semidirect
155. #2629	C₂×C₅	semidirect
156. #2625	C₂×C₅	semidirect
157. #2621	C₂×C₅	semidirect
159. #2478	C₂×C₅	semidirect
160. #2475	C₂×C₅	semidirect
161. #2473	C₂×C₅	semidirect
162. #2323	C₂×C₅	semidirect
163. #2314	C₂×C₅	semidirect
164. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
249. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
251. C₂×#125	C₂²×C₅	semidirect
252. C₂×#125	C₂²×C₅	semidirect
256. C₂×C₄×Q₈	C₂²×C₅	semidirect
268. #400	C₂²×C₅	semidirect
269. #398	C₂²×C₅	semidirect
270. #398	C₂²×C₅	semidirect
271. #398	C₂²×C₅	semidirect
276. #391	C₂²×C₅	semidirect
277. #391	C₂²×C₅	semidirect
278. #389	C₂²×C₅	semidirect
279. #389	C₂²×C₅	semidirect
280. #389	C₂²×C₅	semidirect
281. #389	C₂²×C₅	semidirect
285. #387	C₂²×C₅	semidirect
286. #387	C₂²×C₅	semidirect
287. #387	C₂²×C₅	semidirect
288. #387	C₂²×C₅	semidirect
294. #384	C₂²×C₅	semidirect
295. #382	C₂²×C₅	semidirect
301. C₄×C₄⋊C₄	C₂²×C₅	semidirect
302. C₄×C₄⋊C₄	C₂²×C₅	semidirect
461. C₂²×C₅	#541	semidirect
635. C₅	#35310	direct (N × H)
651. C₂²	C₅×#541	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#541	2
C₂²×C₅×#117	2
C₅×#2857	2
C₅×#2851	2
C₅×#2848	2
C₅×#2629	2
C₅×#2625	2
C₅×#2621	2
C₅×#2480	2
C₅×#2478	2
C₅×#2475	2
C₅×#2473	2
C₅×#2323	2
C₅×#2314	2
C₄×C₅×C₂²⋊Q₈	2
#35310	5

Subgroups — C5×#35310 #11958030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35310 #11958030