Subgroups — C₅×#35325 #11958045

Order 1280.

2370 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₅×#2855	C₂	1	2	yes	maximal, complemented
4	C₅×#2848	C₂	1	2	yes	maximal
5	C₅×#2628	C₂	1	2	yes	maximal, complemented
6	C₅×#2621	C₂	1	2	yes	maximal, complemented
7	C₅×#2611	C₂	1	4	yes	maximal, complemented
8	C₅×#2599	C₂	1	4	yes	maximal, complemented
9	C₅×#2583	C₂	1	2	yes	maximal, complemented
10	C₅×#2561	C₂	1	2	yes	maximal
11	C₅×#2484	C₂	1	2	yes	maximal, complemented
12	C₅×#2482	C₂	1	2	yes	maximal
13	C₅×#2323	C₂	1	4	yes	maximal, complemented
14	C₅×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₅×#533	—	2	8	no	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×#125	C₂²	1	2	yes	complemented
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
25	C₂×C₅×#117	—	2	8	no	—
26	C₂×C₅×#117	C₂²	1	2	yes	—
27	C₂×C₅×#117	C₂²	1	2	yes	—
28	C₂×C₅×#117	C₂²	1	2	yes	—
29	C₂×C₅×#117	C₂²	1	2	yes	—
30	C₂×C₅×#117	C₂²	1	2	yes	—
31	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×#399	C₂²	1	4	yes	—
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×#395	C₂²	1	4	yes	complemented
44	C₅×#393	C₂²	1	4	yes	—
45	C₅×#391	C₂²	1	4	yes	complemented
46	C₅×#389	C₂²	1	8	yes	complemented
47	C₅×#389	C₂²	1	4	yes	complemented
48	C₅×#388	C₂²	1	8	yes	—
49	C₅×#388	C₂²	1	8	yes	—
50	C₅×#387	C₂²	1	8	yes	complemented
51	C₅×#387	C₂²	1	8	yes	complemented
52	C₅×#385	C₂²	1	4	yes	—
53	C₅×#385	C₂²	1	4	yes	—
54	C₅×#385	C₂²	1	8	yes	—
55	C₅×#383	C₂²	1	2	yes	complemented
56	C₅×#382	C₂²	1	2	yes	complemented
57	C₅×#381	C₂²	1	2	yes	—
58	C₅×#381	C₂²	1	4	yes	—
59	C₅×#380	C₂²	1	2	yes	—
60	C₅×#380	C₂²	1	4	yes	—
61	C₅×#379	C₂²	1	4	yes	—
62	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₅×#376	C₂²	1	2	yes	complemented
65	#35325	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁵×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Q₈	C₂³	1	2	yes	—
68	C₂²×C₅×Q₈	C₂³	1	2	yes	—
69	C₂³×C₄×C₅	—	2	4	no	—
70	C₂³×C₄×C₅	—	2	8	no	—
71	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂³	1	2	yes	—
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂³	1	2	yes	—
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	—	2	4	no	—
80	C₅×C₄⋊Q₈	—	2	4	no	—
81	C₅×#125	—	2	8	no	—
82	C₅×C₂²⋊Q₈	—	2	8	no	—
83	C₅×C₂²⋊Q₈	—	2	8	no	—
84	C₅×C₂²⋊Q₈	—	2	16	no	—
85	C₄×C₅×Q₈	—	2	8	no	—
86	C₄×C₅×Q₈	—	2	8	no	—
87	C₅×#117	—	2	8	no	—
88	C₅×#117	—	2	8	no	—
89	C₅×#117	—	2	8	no	—
90	C₅×#117	—	2	8	no	—
91	C₅×#117	—	2	8	no	—
92	C₂×C₅×C₄⋊C₄	—	2	4	no	—
93	C₂×C₅×C₄⋊C₄	—	2	4	no	—
94	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
105	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
107	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
117	C₂×C₄²×C₅	—	2	4	no	—
118	C₂×C₄²×C₅	D₄	1	8	yes	—
119	C₂×C₄²×C₅	C₂³	1	2	yes	—
120	C₂×C₄²×C₅	C₂³	1	4	yes	—
121	C₂×C₄²×C₅	C₂³	1	2	yes	—
122	C₂×C₄²×C₅	C₂³	1	4	yes	—
123	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₅×#95	C₂³	1	4	yes	—
128	C₅×#95	C₂³	1	4	yes	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	4	yes	—
131	C₅×#95	C₂³	1	8	yes	—
132	C₅×#95	C₂³	1	8	yes	—
133	C₅×#95	C₂³	1	8	yes	—
134	C₅×#95	C₂³	1	8	yes	—
135	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂²×#117	C₂×C₅	1	1	yes	characteristic
137	#2855	C₂×C₅	1	2	yes	complemented
138	#2848	C₂×C₅	1	2	yes	—
139	#2628	C₂×C₅	1	2	yes	complemented
140	#2621	C₂×C₅	1	2	yes	complemented
141	#2611	C₂×C₅	1	4	yes	complemented
142	#2599	C₂×C₅	1	4	yes	complemented
143	#2583	C₂×C₅	1	2	yes	complemented
144	#2561	C₂×C₅	1	2	yes	—
145	#2484	C₂×C₅	1	2	yes	complemented
146	#2482	C₂×C₅	1	2	yes	—
147	#2323	C₂×C₅	1	4	yes	complemented
148	#2283	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂⁴×C₅	—	2	2	no	—
150	C₂⁴×C₅	—	2	4	no	—
151	C₂⁴×C₅	—	2	4	no	—
152	C₂⁴×C₅	—	4	2	no	—
153	C₂⁴×C₅	C₂⁴	1	2	yes	—
154	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	4	no	—
157	C₂×C₅×Q₈	—	2	8	no	—
158	C₂×C₅×Q₈	—	4	4	no	—
159	C₂²×C₄×C₅	—	2	32	no	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	2	4	no	—
163	C₂²×C₄×C₅	—	2	4	no	—
164	C₂²×C₄×C₅	—	2	4	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	4	2	no	—
173	C₂²×C₄×C₅	—	4	2	no	—
174	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₅	#41	1	8	yes	—
178	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	—	2	4	no	—
192	C₅×C₄⋊C₄	—	2	4	no	—
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	2	4	no	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	8	no	—
197	C₅×C₄⋊C₄	—	2	8	no	—
198	C₅×C₄⋊C₄	—	2	4	no	—
199	C₅×C₄⋊C₄	—	2	4	no	—
200	C₅×C₄⋊C₄	—	2	8	no	—
201	C₅×C₄⋊C₄	—	2	16	no	—
202	C₅×C₄⋊C₄	—	4	8	no	—
203	C₅×C₂²⋊C₄	—	2	8	no	—
204	C₅×C₂²⋊C₄	—	2	16	no	—
205	C₅×C₂²⋊C₄	—	2	8	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	—	2	4	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	4	8	no	—
211	C₄²×C₅	—	2	4	no	—
212	C₄²×C₅	—	2	4	no	—
213	C₄²×C₅	—	2	8	no	—
214	C₄²×C₅	—	4	4	no	—
215	C₄²×C₅	C₂×D₄	1	4	yes	—
216	C₄²×C₅	C₂×D₄	1	4	yes	—
217	C₄²×C₅	C₂×D₄	1	4	yes	—
218	C₄²×C₅	C₂×D₄	1	4	yes	—
219	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
220	#533	—	2	8	no	—
221	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
222	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
223	C₂×#125	C₂²×C₅	1	2	yes	complemented
224	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
228	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
229	C₂×#117	—	2	8	no	—
230	C₂×#117	C₂²×C₅	1	2	yes	—
231	C₂×#117	C₂²×C₅	1	2	yes	—
232	C₂×#117	C₂²×C₅	1	2	yes	—
233	C₂×#117	C₂²×C₅	1	2	yes	—
234	C₂×#117	C₂²×C₅	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
241	#400	C₂²×C₅	1	4	yes	complemented
242	#399	C₂²×C₅	1	4	yes	—
243	#398	C₂²×C₅	1	4	yes	complemented
244	#398	C₂²×C₅	1	4	yes	complemented
245	#397	C₂²×C₅	1	4	yes	—
246	#397	C₂²×C₅	1	4	yes	—
247	#395	C₂²×C₅	1	4	yes	complemented
248	#393	C₂²×C₅	1	4	yes	—
249	#391	C₂²×C₅	1	4	yes	complemented
250	#389	C₂²×C₅	1	8	yes	complemented
251	#389	C₂²×C₅	1	4	yes	complemented
252	#388	C₂²×C₅	1	8	yes	—
253	#388	C₂²×C₅	1	8	yes	—
254	#387	C₂²×C₅	1	8	yes	complemented
255	#387	C₂²×C₅	1	8	yes	complemented
256	#385	C₂²×C₅	1	4	yes	—
257	#385	C₂²×C₅	1	4	yes	—
258	#385	C₂²×C₅	1	8	yes	—
259	#383	C₂²×C₅	1	2	yes	complemented
260	#382	C₂²×C₅	1	2	yes	complemented
261	#381	C₂²×C₅	1	4	yes	—
262	#381	C₂²×C₅	1	2	yes	—
263	#380	C₂²×C₅	1	4	yes	—
264	#380	C₂²×C₅	1	2	yes	—
265	#379	C₂²×C₅	1	4	yes	—
266	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
267	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
268	#376	C₂²×C₅	1	2	yes	complemented
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	8	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	—	2	4	no	—
275	C₂³×C₅	—	2	4	no	—
276	C₂³×C₅	—	4	16	no	—
277	C₂³×C₅	—	4	4	no	—
278	C₂³×C₅	—	4	4	no	—
279	C₂³×C₅	C₂²×D₄	1	2	yes	—
280	C₂³×C₅	C₂×#41	1	4	yes	—
281	C₂³×C₅	2₋¹⁺⁴	1	4	yes	—
282	C₂³×C₅	C₂⁵	1	1	yes	characteristic
283	C₅×Q₈	—	4	8	no	—
284	C₅×Q₈	—	4	8	no	—
285	C₂×C₄×C₅	—	2	16	no	—
286	C₂×C₄×C₅	—	2	8	no	—
287	C₂×C₄×C₅	—	2	8	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	8	no	—
296	C₂×C₄×C₅	—	2	16	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	8	no	—
302	C₂×C₄×C₅	—	2	8	no	—
303	C₂×C₄×C₅	—	2	8	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	2	8	no	—
306	C₂×C₄×C₅	—	2	8	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	4	4	no	—
309	C₂×C₄×C₅	—	4	4	no	—
310	C₂×C₄×C₅	—	4	4	no	—
311	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₅	C₂×#41	1	4	yes	—
318	C₂×C₄×C₅	C₂×#41	1	4	yes	—
319	C₂⁵	C₂³×C₅	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₅	1	2	yes	—
321	C₂²×Q₈	C₂³×C₅	1	2	yes	—
322	C₂³×C₄	—	2	4	no	—
323	C₂³×C₄	—	2	8	no	—
324	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₅	1	2	yes	—
327	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₅	1	2	yes	—
330	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
332	C₄⋊Q₈	—	2	4	no	—
333	C₄⋊Q₈	—	2	4	no	—
334	#125	—	2	8	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	—	2	16	no	—
338	C₄×Q₈	—	2	8	no	—
339	C₄×Q₈	—	2	8	no	—
340	#117	—	2	8	no	—
341	#117	—	2	8	no	—
342	#117	—	2	8	no	—
343	#117	—	2	8	no	—
344	#117	—	2	8	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
360	C₂×C₂²⋊C₄	—	2	4	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	C₅×D₄	1	8	yes	—
372	C₂×C₄²	C₂³×C₅	1	2	yes	—
373	C₂×C₄²	C₂³×C₅	1	2	yes	—
374	C₂×C₄²	C₂³×C₅	1	4	yes	—
375	C₂×C₄²	C₂³×C₅	1	4	yes	—
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	#95	C₂³×C₅	1	4	yes	—
381	#95	C₂³×C₅	1	4	yes	—
382	#95	C₂³×C₅	1	4	yes	—
383	#95	C₂³×C₅	1	4	yes	—
384	#95	C₂³×C₅	1	8	yes	—
385	#95	C₂³×C₅	1	8	yes	—
386	#95	C₂³×C₅	1	8	yes	—
387	#95	C₂³×C₅	1	8	yes	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	2	8	no	—
391	C₂²×C₅	—	2	4	no	—
392	C₂²×C₅	—	2	8	no	—
393	C₂²×C₅	—	4	16	no	—
394	C₂²×C₅	—	4	2	no	—
395	C₂²×C₅	—	4	2	no	—
396	C₂²×C₅	—	4	4	no	—
397	C₂²×C₅	#536	1	4	yes	—
398	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
399	C₂²×C₅	C₂²×#41	1	2	yes	—
400	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
401	C₂²×C₅	#585	1	2	yes	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	4	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	2	2	no	—
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	4	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	—	4	2	no	—
411	C₄×C₅	—	4	4	no	—
412	C₄×C₅	—	4	8	no	—
413	C₄×C₅	#525	1	4	yes	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	4	2	no	—
418	C₂⁴	C₂⁴×C₅	1	2	yes	—
419	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	4	4	no	—
424	C₂²×C₄	—	2	32	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
440	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
441	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
442	C₂²×C₄	C₅×#41	1	8	yes	—
443	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
445	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	16	no	—
467	C₄⋊C₄	—	4	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	16	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	4	8	no	—
476	C₄²	—	2	4	no	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	8	no	—
479	C₄²	—	4	4	no	—
480	C₄²	C₂×C₅×D₄	1	4	yes	—
481	C₄²	C₂×C₅×D₄	1	4	yes	—
482	C₄²	C₂×C₅×D₄	1	4	yes	—
483	C₄²	C₂×C₅×D₄	1	4	yes	—
484	C₂×C₅	—	2	4	no	—
485	C₂×C₅	—	4	4	no	—
486	C₂×C₅	C₂×#525	1	1	yes	characteristic
487	C₂×C₅	C₂×#536	1	1	yes	characteristic
488	C₂×C₅	#3449	1	1	yes	characteristic
489	C₂×C₅	#3495	1	4	yes	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	8	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	16	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	C₂²×C₅×D₄	1	2	yes	—
501	C₂³	C₂×C₅×#41	1	4	yes	—
502	C₂³	C₅×2₋¹⁺⁴	1	4	yes	—
503	C₂³	C₂⁵×C₅	1	1	yes	characteristic
504	Q₈	—	4	8	no	—
505	Q₈	—	4	8	no	—
506	C₂×C₄	—	2	16	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	16	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
533	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
534	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
535	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
536	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
537	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
538	C₂×C₄	C₂×C₅×#41	1	4	yes	—
539	C₂×C₄	C₂×C₅×#41	1	4	yes	—
540	C₅	#35325	1	1	yes	characteristic, direct product factor, Sylow
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	4	16	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	C₅×#536	1	4	yes	—
551	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
552	C₂²	C₂²×C₅×#41	1	2	yes	—
553	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
554	C₂²	C₅×#585	1	2	yes	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	8	no	—
566	C₄	C₅×#525	1	4	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	4	4	no	—
569	C₂	C₂×C₅×#525	1	1	yes	characteristic
570	C₂	C₂×C₅×#536	1	1	yes	characteristic
571	C₂	C₅×#3449	1	1	yes	characteristic
572	C₂	C₅×#3495	1	4	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×#533	C₂	semidirect
3. C₅×#2855	C₂	semidirect
5. C₅×#2628	C₂	semidirect
6. C₅×#2621	C₂	semidirect
7. C₅×#2611	C₂	semidirect
8. C₅×#2599	C₂	semidirect
9. C₅×#2583	C₂	semidirect
11. C₅×#2484	C₂	semidirect
13. C₅×#2323	C₂	semidirect
14. C₅×#2283	C₂	semidirect
17. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₅×#125	C₂²	semidirect
23. C₂×C₄×C₅×Q₈	C₂²	semidirect
24. C₂×C₄×C₅×Q₈	C₂²	semidirect
37. C₅×#400	C₂²	semidirect
39. C₅×#398	C₂²	semidirect
40. C₅×#398	C₂²	semidirect
43. C₅×#395	C₂²	semidirect
45. C₅×#391	C₂²	semidirect
46. C₅×#389	C₂²	semidirect
47. C₅×#389	C₂²	semidirect
50. C₅×#387	C₂²	semidirect
51. C₅×#387	C₂²	semidirect
55. C₅×#383	C₂²	semidirect
56. C₅×#382	C₂²	semidirect
62. C₄×C₅×C₄⋊C₄	C₂²	semidirect
64. C₅×#376	C₂²	semidirect
65. #35325	C₅	direct (N × H)
135. C₂×#533	C₂×C₅	semidirect
137. #2855	C₂×C₅	semidirect
139. #2628	C₂×C₅	semidirect
140. #2621	C₂×C₅	semidirect
141. #2611	C₂×C₅	semidirect
142. #2599	C₂×C₅	semidirect
143. #2583	C₂×C₅	semidirect
145. #2484	C₂×C₅	semidirect
147. #2323	C₂×C₅	semidirect
148. #2283	C₂×C₅	semidirect
221. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
222. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
223. C₂×#125	C₂²×C₅	semidirect
227. C₂×C₄×Q₈	C₂²×C₅	semidirect
228. C₂×C₄×Q₈	C₂²×C₅	semidirect
241. #400	C₂²×C₅	semidirect
243. #398	C₂²×C₅	semidirect
244. #398	C₂²×C₅	semidirect
247. #395	C₂²×C₅	semidirect
249. #391	C₂²×C₅	semidirect
250. #389	C₂²×C₅	semidirect
251. #389	C₂²×C₅	semidirect
254. #387	C₂²×C₅	semidirect
255. #387	C₂²×C₅	semidirect
259. #383	C₂²×C₅	semidirect
260. #382	C₂²×C₅	semidirect
266. C₄×C₄⋊C₄	C₂²×C₅	semidirect
268. #376	C₂²×C₅	semidirect
540. C₅	#35325	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×#533	2
C₂²×C₅×#117	2
C₅×#2855	2
C₅×#2848	2
C₅×#2628	2
C₅×#2621	2
C₅×#2611	2
C₅×#2599	2
C₅×#2583	2
C₅×#2561	2
C₅×#2484	2
C₅×#2482	2
C₅×#2323	2
C₅×#2283	2
#35325	5

Subgroups — C5×#35325 #11958045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35325 #11958045