Subgroups — C₅×#34877 #11957597

Order 1280.

2646 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2611	C₂	1	2	yes	maximal, complemented
4	C₅×#2610	C₂	1	2	yes	maximal, complemented
5	C₅×#2601	C₂	1	4	yes	maximal, complemented
6	C₅×#2591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2539	C₂	1	1	yes	maximal, characteristic
10	C₅×#2413	C₂	1	2	yes	maximal, complemented
11	C₅×#2411	C₂	1	2	yes	maximal, complemented
12	C₅×#2396	C₂	1	2	yes	maximal, complemented
13	C₅×#2392	C₂	1	2	yes	maximal, complemented
14	C₄×C₅×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×#120	C₂	1	2	yes	maximal, complemented
16	C₅×#2293	C₂	1	4	yes	maximal, complemented
17	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₅×#529	—	2	8	no	—
20	C₂×C₅×#126	C₂²	1	2	yes	complemented
21	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×#123	C₂²	1	2	yes	—
24	C₂×C₅×#123	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#121	C₂²	1	1	yes	characteristic
27	C₂×C₅×#120	C₂²	1	2	yes	—
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#117	—	2	8	no	—
33	C₂×C₅×#117	C₂²	1	2	yes	—
34	C₂×C₅×#117	C₂²	1	2	yes	—
35	C₂×C₅×#117	C₂²	1	2	yes	—
36	C₂×C₅×#117	C₂²	1	2	yes	—
37	C₂×C₅×#117	C₂²	1	2	yes	—
38	C₂×C₅×#117	C₂²	1	2	yes	complemented
39	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
45	C₅×#400	C₂²	1	2	yes	complemented
46	C₅×#399	C₂²	1	2	yes	—
47	C₅×#398	C₂²	1	2	yes	complemented
48	C₅×#398	C₂²	1	4	yes	complemented
49	C₅×#397	C₂²	1	2	yes	—
50	C₅×#396	C₂²	1	4	yes	—
51	C₅×#396	C₂²	1	4	yes	complemented
52	C₅×#395	C₂²	1	2	yes	complemented
53	C₅×#394	C₂²	1	4	yes	—
54	C₅×#394	C₂²	1	2	yes	complemented
55	C₅×#393	C₂²	1	2	yes	—
56	C₅×#392	C₂²	1	2	yes	—
57	C₅×#390	C₂²	1	4	yes	—
58	C₅×#390	C₂²	1	4	yes	—
59	C₅×#389	C₂²	1	4	yes	complemented
60	C₅×#389	C₂²	1	4	yes	complemented
61	C₅×#388	C₂²	1	4	yes	—
62	C₅×#388	C₂²	1	4	yes	—
63	C₅×#388	C₂²	1	4	yes	complemented
64	C₅×#388	C₂²	1	4	yes	complemented
65	C₅×#388	C₂²	1	4	yes	complemented
66	C₅×#387	C₂²	1	4	yes	complemented
67	C₅×#386	C₂²	1	2	yes	—
68	C₅×#386	C₂²	1	4	yes	—
69	C₅×#386	C₂²	1	2	yes	—
70	C₅×#385	C₂²	1	2	yes	—
71	C₅×#385	C₂²	1	4	yes	—
72	C₅×#385	C₂²	1	2	yes	—
73	C₅×#381	C₂²	1	2	yes	—
74	C₅×#379	C₂²	1	2	yes	—
75	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
76	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
77	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
78	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₅×#376	C₂²	1	2	yes	complemented
84	C₄³×C₅	C₂²	1	2	yes	complemented
85	#34877	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁵×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₅×D₄	C₂³	1	2	yes	—
89	C₂²×C₅×D₄	C₂³	1	4	yes	—
90	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₅	—	2	4	no	—
92	C₂³×C₄×C₅	—	2	8	no	—
93	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₅	C₂³	1	2	yes	—
96	C₂³×C₄×C₅	C₂³	1	2	yes	—
97	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₅×#126	—	2	8	no	—
103	C₅×#125	—	2	4	no	—
104	C₅×#124	—	2	4	no	—
105	C₅×#123	—	2	8	no	—
106	C₅×#123	—	2	8	no	—
107	C₅×C₂²⋊Q₈	—	2	4	no	—
108	C₅×#121	—	2	4	no	—
109	C₅×#120	—	2	8	no	—
110	C₄×C₅×Q₈	—	2	4	no	—
111	C₄×C₅×D₄	—	2	8	no	—
112	C₄×C₅×D₄	—	2	16	no	—
113	C₄×C₅×D₄	—	2	4	no	—
114	C₅×#117	—	2	8	no	—
115	C₅×#117	—	2	8	no	—
116	C₅×#117	—	2	8	no	—
117	C₅×#117	—	2	8	no	—
118	C₅×#117	—	2	8	no	—
119	C₅×#117	—	2	8	no	—
120	C₂×C₅×C₄⋊C₄	—	2	4	no	—
121	C₂×C₅×C₄⋊C₄	—	2	4	no	—
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	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
137	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₄²×C₅	—	2	4	no	—
156	C₂×C₄²×C₅	D₄	1	8	yes	complemented
157	C₂×C₄²×C₅	C₂³	1	4	yes	—
158	C₂×C₄²×C₅	C₂³	1	2	yes	—
159	C₂×C₄²×C₅	C₂³	1	4	yes	—
160	C₂×C₄²×C₅	C₂³	1	2	yes	—
161	C₂×C₄²×C₅	C₂³	1	2	yes	—
162	C₂×C₄²×C₅	C₂³	1	2	yes	—
163	C₂×C₄²×C₅	C₂³	1	2	yes	—
164	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₅×#95	C₂³	1	4	yes	—
169	C₅×#95	C₂³	1	2	yes	—
170	C₅×#95	C₂³	1	2	yes	—
171	C₅×#95	C₂³	1	4	yes	—
172	C₅×#95	C₂³	1	4	yes	—
173	C₅×#95	C₂³	1	4	yes	—
174	C₅×#95	C₂³	1	4	yes	—
175	C₅×#95	C₂³	1	4	yes	—
176	C₅×#95	C₂³	1	4	yes	—
177	C₂×#529	C₂×C₅	1	1	yes	characteristic, complemented
178	C₂²×#117	C₂×C₅	1	1	yes	characteristic, complemented
179	#2611	C₂×C₅	1	2	yes	complemented
180	#2610	C₂×C₅	1	2	yes	complemented
181	#2601	C₂×C₅	1	4	yes	complemented
182	#2591	C₂×C₅	1	1	yes	characteristic, complemented
183	#2583	C₂×C₅	1	1	yes	characteristic, complemented
184	#2561	C₂×C₅	1	1	yes	characteristic, complemented
185	#2539	C₂×C₅	1	1	yes	characteristic
186	#2413	C₂×C₅	1	2	yes	complemented
187	#2411	C₂×C₅	1	2	yes	complemented
188	#2396	C₂×C₅	1	2	yes	complemented
189	#2392	C₂×C₅	1	2	yes	complemented
190	C₄×#123	C₂×C₅	1	2	yes	complemented
191	C₄×#120	C₂×C₅	1	2	yes	complemented
192	#2293	C₂×C₅	1	4	yes	complemented
193	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
194	C₂⁴×C₅	—	2	2	no	—
195	C₂⁴×C₅	—	2	4	no	—
196	C₂⁴×C₅	—	2	4	no	—
197	C₂⁴×C₅	—	4	2	no	—
198	C₂⁴×C₅	C₂⁴	1	2	yes	—
199	C₂⁴×C₅	C₂⁴	1	2	yes	—
200	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
201	C₂×C₅×Q₈	—	2	2	no	—
202	C₂×C₅×Q₈	—	4	2	no	—
203	C₂×C₅×D₄	—	2	4	no	—
204	C₂×C₅×D₄	—	2	8	no	—
205	C₂×C₅×D₄	—	2	4	no	—
206	C₂×C₅×D₄	—	2	4	no	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	2	8	no	—
209	C₂×C₅×D₄	—	4	4	no	—
210	C₂×C₅×D₄	—	4	2	no	—
211	C₂²×C₄×C₅	—	2	32	no	—
212	C₂²×C₄×C₅	—	2	2	no	—
213	C₂²×C₄×C₅	—	2	4	no	—
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	2	4	no	—
216	C₂²×C₄×C₅	—	2	4	no	—
217	C₂²×C₄×C₅	—	2	4	no	—
218	C₂²×C₄×C₅	—	2	4	no	—
219	C₂²×C₄×C₅	—	2	4	no	—
220	C₂²×C₄×C₅	—	2	4	no	—
221	C₂²×C₄×C₅	—	2	2	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	4	no	—
224	C₂²×C₄×C₅	—	2	4	no	—
225	C₂²×C₄×C₅	—	2	8	no	—
226	C₂²×C₄×C₅	—	4	2	no	—
227	C₂²×C₄×C₅	—	4	2	no	—
228	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₅	#41	1	8	yes	—
232	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₅×C₄⋊C₄	—	2	4	no	—
247	C₅×C₄⋊C₄	—	2	4	no	—
248	C₅×C₄⋊C₄	—	2	4	no	—
249	C₅×C₄⋊C₄	—	2	4	no	—
250	C₅×C₄⋊C₄	—	2	4	no	—
251	C₅×C₄⋊C₄	—	2	4	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	—	2	4	no	—
254	C₅×C₄⋊C₄	—	2	2	no	—
255	C₅×C₄⋊C₄	—	2	4	no	—
256	C₅×C₄⋊C₄	—	2	8	no	—
257	C₅×C₄⋊C₄	—	2	8	no	—
258	C₅×C₄⋊C₄	—	2	8	no	—
259	C₅×C₄⋊C₄	—	4	4	no	—
260	C₅×C₂²⋊C₄	—	2	4	no	—
261	C₅×C₂²⋊C₄	—	2	4	no	—
262	C₅×C₂²⋊C₄	—	2	8	no	—
263	C₅×C₂²⋊C₄	—	2	4	no	—
264	C₅×C₂²⋊C₄	—	2	4	no	—
265	C₅×C₂²⋊C₄	—	2	4	no	—
266	C₅×C₂²⋊C₄	—	2	4	no	—
267	C₅×C₂²⋊C₄	—	2	4	no	—
268	C₅×C₂²⋊C₄	—	2	4	no	—
269	C₅×C₂²⋊C₄	—	2	4	no	—
270	C₅×C₂²⋊C₄	—	2	4	no	—
271	C₅×C₂²⋊C₄	—	2	8	no	—
272	C₅×C₂²⋊C₄	—	2	8	no	—
273	C₅×C₂²⋊C₄	—	2	8	no	—
274	C₅×C₂²⋊C₄	—	4	4	no	—
275	C₅×C₂²⋊C₄	—	4	4	no	—
276	C₅×C₂²⋊C₄	#41	1	8	yes	—
277	C₄²×C₅	—	2	4	no	—
278	C₄²×C₅	—	2	4	no	—
279	C₄²×C₅	—	2	4	no	—
280	C₄²×C₅	—	2	8	no	—
281	C₄²×C₅	—	2	8	no	—
282	C₄²×C₅	—	4	2	no	—
283	C₄²×C₅	—	4	2	no	—
284	C₄²×C₅	C₂×D₄	1	4	yes	—
285	C₄²×C₅	C₂×D₄	1	4	yes	—
286	C₄²×C₅	C₂×D₄	1	4	yes	—
287	C₄²×C₅	C₂×D₄	1	4	yes	—
288	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
289	#529	—	2	8	no	—
290	C₂×#126	C₂²×C₅	1	2	yes	complemented
291	C₂×#125	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₂×#124	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×#123	C₂²×C₅	1	2	yes	—
294	C₂×#123	C₂²×C₅	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
296	C₂×#121	C₂²×C₅	1	1	yes	characteristic
297	C₂×#120	C₂²×C₅	1	2	yes	—
298	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
300	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
301	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×#117	—	2	8	no	—
303	C₂×#117	C₂²×C₅	1	2	yes	—
304	C₂×#117	C₂²×C₅	1	2	yes	—
305	C₂×#117	C₂²×C₅	1	2	yes	—
306	C₂×#117	C₂²×C₅	1	2	yes	—
307	C₂×#117	C₂²×C₅	1	2	yes	—
308	C₂×#117	C₂²×C₅	1	2	yes	complemented
309	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
313	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
314	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
315	#400	C₂²×C₅	1	2	yes	complemented
316	#399	C₂²×C₅	1	2	yes	—
317	#398	C₂²×C₅	1	2	yes	complemented
318	#398	C₂²×C₅	1	4	yes	complemented
319	#397	C₂²×C₅	1	2	yes	—
320	#396	C₂²×C₅	1	4	yes	—
321	#396	C₂²×C₅	1	4	yes	complemented
322	#395	C₂²×C₅	1	2	yes	complemented
323	#394	C₂²×C₅	1	4	yes	—
324	#394	C₂²×C₅	1	2	yes	complemented
325	#393	C₂²×C₅	1	2	yes	—
326	#392	C₂²×C₅	1	2	yes	—
327	#390	C₂²×C₅	1	4	yes	—
328	#390	C₂²×C₅	1	4	yes	—
329	#389	C₂²×C₅	1	4	yes	complemented
330	#389	C₂²×C₅	1	4	yes	complemented
331	#388	C₂²×C₅	1	4	yes	—
332	#388	C₂²×C₅	1	4	yes	—
333	#388	C₂²×C₅	1	4	yes	complemented
334	#388	C₂²×C₅	1	4	yes	complemented
335	#388	C₂²×C₅	1	4	yes	complemented
336	#387	C₂²×C₅	1	4	yes	complemented
337	#386	C₂²×C₅	1	2	yes	—
338	#386	C₂²×C₅	1	2	yes	—
339	#386	C₂²×C₅	1	4	yes	—
340	#385	C₂²×C₅	1	2	yes	—
341	#385	C₂²×C₅	1	2	yes	—
342	#385	C₂²×C₅	1	4	yes	—
343	#381	C₂²×C₅	1	2	yes	—
344	#379	C₂²×C₅	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
346	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
347	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
348	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
349	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
353	#376	C₂²×C₅	1	2	yes	complemented
354	C₄³	C₂²×C₅	1	2	yes	complemented
355	C₂³×C₅	—	2	2	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	8	no	—
358	C₂³×C₅	—	2	2	no	—
359	C₂³×C₅	—	2	4	no	—
360	C₂³×C₅	—	2	2	no	—
361	C₂³×C₅	—	2	4	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	4	no	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	2	4	no	—
367	C₂³×C₅	—	4	16	no	—
368	C₂³×C₅	—	4	4	no	—
369	C₂³×C₅	—	4	4	no	—
370	C₂³×C₅	C₂²×D₄	1	2	yes	—
371	C₂³×C₅	C₂×#41	1	4	yes	—
372	C₂³×C₅	C₂×#41	1	4	yes	—
373	C₂³×C₅	C₂⁵	1	1	yes	characteristic
374	C₅×Q₈	—	4	4	no	—
375	C₅×D₄	—	4	16	no	—
376	C₅×D₄	—	4	4	no	—
377	C₅×D₄	—	4	8	no	—
378	C₂×C₄×C₅	—	2	16	no	—
379	C₂×C₄×C₅	—	2	8	no	—
380	C₂×C₄×C₅	—	2	8	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	4	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	4	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	8	no	—
391	C₂×C₄×C₅	—	2	16	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	2	2	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	4	no	—
398	C₂×C₄×C₅	—	2	4	no	—
399	C₂×C₄×C₅	—	2	2	no	—
400	C₂×C₄×C₅	—	2	4	no	—
401	C₂×C₄×C₅	—	2	4	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	2	4	no	—
404	C₂×C₄×C₅	—	2	4	no	—
405	C₂×C₄×C₅	—	2	4	no	—
406	C₂×C₄×C₅	—	4	4	no	—
407	C₂×C₄×C₅	—	4	4	no	—
408	C₂×C₄×C₅	—	4	4	no	—
409	C₂×C₄×C₅	—	4	8	no	—
410	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₅	C₂×#41	1	8	yes	—
417	C₂×C₄×C₅	C₂×#41	1	4	yes	—
418	C₂×C₄×C₅	C₂×#41	1	4	yes	—
419	C₂⁵	C₂³×C₅	1	1	yes	characteristic
420	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₅	1	2	yes	—
422	C₂²×D₄	C₂³×C₅	1	4	yes	—
423	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
424	C₂³×C₄	—	2	4	no	—
425	C₂³×C₄	—	2	8	no	—
426	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₅	1	2	yes	—
429	C₂³×C₄	C₂³×C₅	1	2	yes	—
430	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₅	1	2	yes	—
433	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
435	#126	—	2	8	no	—
436	#125	—	2	4	no	—
437	#124	—	2	4	no	—
438	#123	—	2	8	no	—
439	#123	—	2	8	no	—
440	C₂²⋊Q₈	—	2	4	no	—
441	#121	—	2	4	no	—
442	#120	—	2	8	no	—
443	C₄×Q₈	—	2	4	no	—
444	C₄×D₄	—	2	8	no	—
445	C₄×D₄	—	2	16	no	—
446	C₄×D₄	—	2	4	no	—
447	#117	—	2	8	no	—
448	#117	—	2	8	no	—
449	#117	—	2	8	no	—
450	#117	—	2	8	no	—
451	#117	—	2	8	no	—
452	#117	—	2	8	no	—
453	C₂×C₄⋊C₄	—	2	4	no	—
454	C₂×C₄⋊C₄	—	2	4	no	—
455	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	—	2	4	no	—
471	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
488	C₂×C₄²	—	2	4	no	—
489	C₂×C₄²	C₅×D₄	1	8	yes	complemented
490	C₂×C₄²	C₂³×C₅	1	2	yes	—
491	C₂×C₄²	C₂³×C₅	1	2	yes	—
492	C₂×C₄²	C₂³×C₅	1	4	yes	—
493	C₂×C₄²	C₂³×C₅	1	2	yes	—
494	C₂×C₄²	C₂³×C₅	1	4	yes	—
495	C₂×C₄²	C₂³×C₅	1	2	yes	—
496	C₂×C₄²	C₂³×C₅	1	2	yes	—
497	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
501	#95	C₂³×C₅	1	4	yes	—
502	#95	C₂³×C₅	1	2	yes	—
503	#95	C₂³×C₅	1	2	yes	—
504	#95	C₂³×C₅	1	4	yes	—
505	#95	C₂³×C₅	1	4	yes	—
506	#95	C₂³×C₅	1	4	yes	—
507	#95	C₂³×C₅	1	4	yes	—
508	#95	C₂³×C₅	1	4	yes	—
509	#95	C₂³×C₅	1	4	yes	—
510	C₂²×C₅	—	2	2	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	2	8	no	—
513	C₂²×C₅	—	2	4	no	—
514	C₂²×C₅	—	2	8	no	—
515	C₂²×C₅	—	4	16	no	—
516	C₂²×C₅	—	4	2	no	—
517	C₂²×C₅	—	4	2	no	—
518	C₂²×C₅	—	4	4	no	—
519	C₂²×C₅	—	4	2	no	—
520	C₂²×C₅	—	4	2	no	—
521	C₂²×C₅	—	4	2	no	—
522	C₂²×C₅	—	4	4	no	—
523	C₂²×C₅	—	4	4	no	—
524	C₂²×C₅	#532	1	4	yes	—
525	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
526	C₂²×C₅	C₂²×#41	1	2	yes	—
527	C₂²×C₅	C₂²×#41	1	2	yes	—
528	C₂²×C₅	#585	1	2	yes	—
529	C₄×C₅	—	2	2	no	—
530	C₄×C₅	—	2	4	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	2	2	no	—
534	C₄×C₅	—	2	2	no	—
535	C₄×C₅	—	2	8	no	—
536	C₄×C₅	—	4	2	no	—
537	C₄×C₅	—	4	2	no	—
538	C₄×C₅	—	4	2	no	—
539	C₄×C₅	—	4	2	no	—
540	C₄×C₅	—	4	2	no	—
541	C₄×C₅	—	4	4	no	—
542	C₄×C₅	#525	1	4	yes	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	4	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	4	2	no	—
547	C₂⁴	C₂⁴×C₅	1	2	yes	—
548	C₂⁴	C₂⁴×C₅	1	2	yes	—
549	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	4	2	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂²×C₄	—	2	32	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
578	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
579	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
580	C₂²×C₄	C₅×#41	1	8	yes	—
581	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	8	no	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	2	8	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	C₅×#41	1	8	yes	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	8	no	—
630	C₄²	—	2	8	no	—
631	C₄²	—	4	2	no	—
632	C₄²	—	4	2	no	—
633	C₄²	C₂×C₅×D₄	1	4	yes	—
634	C₄²	C₂×C₅×D₄	1	4	yes	—
635	C₄²	C₂×C₅×D₄	1	4	yes	—
636	C₄²	C₂×C₅×D₄	1	4	yes	—
637	C₂×C₅	—	2	4	no	—
638	C₂×C₅	—	4	4	no	—
639	C₂×C₅	—	8	2	no	—
640	C₂×C₅	C₂×#525	1	1	yes	characteristic
641	C₂×C₅	C₂×#532	1	1	yes	characteristic
642	C₂×C₅	#3449	1	1	yes	characteristic
643	C₂×C₅	#3475	1	4	yes	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	4	16	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	4	4	no	—
659	C₂³	C₂²×C₅×D₄	1	2	yes	—
660	C₂³	C₂×C₅×#41	1	4	yes	—
661	C₂³	C₂×C₅×#41	1	4	yes	—
662	C₂³	C₂⁵×C₅	1	1	yes	characteristic
663	Q₈	—	4	4	no	—
664	D₄	—	4	16	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	8	no	—
667	C₂×C₄	—	2	16	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	8	no	—
680	C₂×C₄	—	2	16	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
700	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
701	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
702	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
703	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
704	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
705	C₂×C₄	C₂×C₅×#41	1	8	yes	—
706	C₂×C₄	C₂×C₅×#41	1	4	yes	—
707	C₂×C₄	C₂×C₅×#41	1	4	yes	—
708	C₅	#34877	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	8	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	4	16	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	C₅×#532	1	4	yes	—
724	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
725	C₂²	C₂²×C₅×#41	1	2	yes	—
726	C₂²	C₂²×C₅×#41	1	2	yes	—
727	C₂²	C₅×#585	1	2	yes	—
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	4	no	—
741	C₄	C₅×#525	1	4	yes	—
742	C₂	—	2	4	no	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	C₂×C₅×#525	1	1	yes	characteristic
746	C₂	C₂×C₅×#532	1	1	yes	characteristic
747	C₂	C₅×#3449	1	1	yes	characteristic
748	C₂	C₅×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle	C₂³×C₅	C₂⁵
prime radical	C₅×#2539	C₂
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. C₂×C₅×#529	C₂	semidirect
2. C₂²×C₅×#117	C₂	semidirect
3. C₅×#2611	C₂	semidirect
4. C₅×#2610	C₂	semidirect
5. C₅×#2601	C₂	semidirect
6. C₅×#2591	C₂	semidirect
7. C₅×#2583	C₂	semidirect
8. C₅×#2561	C₂	semidirect
10. C₅×#2413	C₂	semidirect
11. C₅×#2411	C₂	semidirect
12. C₅×#2396	C₂	semidirect
13. C₅×#2392	C₂	semidirect
14. C₄×C₅×#123	C₂	semidirect
15. C₄×C₅×#120	C₂	semidirect
16. C₅×#2293	C₂	semidirect
17. C₄×C₅×#117	C₂	semidirect
20. C₂×C₅×#126	C₂²	semidirect
21. C₂×C₅×#125	C₂²	semidirect
22. C₂×C₅×#124	C₂²	semidirect
28. C₂×C₄×C₅×Q₈	C₂²	semidirect
31. C₂×C₄×C₅×D₄	C₂²	semidirect
38. C₂×C₅×#117	C₂²	semidirect
45. C₅×#400	C₂²	semidirect
47. C₅×#398	C₂²	semidirect
48. C₅×#398	C₂²	semidirect
51. C₅×#396	C₂²	semidirect
52. C₅×#395	C₂²	semidirect
54. C₅×#394	C₂²	semidirect
59. C₅×#389	C₂²	semidirect
60. C₅×#389	C₂²	semidirect
63. C₅×#388	C₂²	semidirect
64. C₅×#388	C₂²	semidirect
65. C₅×#388	C₂²	semidirect
66. C₅×#387	C₂²	semidirect
75. C₄×C₅×C₄⋊C₄	C₂²	semidirect
76. C₄×C₅×C₄⋊C₄	C₂²	semidirect
77. C₄×C₅×C₄⋊C₄	C₂²	semidirect
82. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
83. C₅×#376	C₂²	semidirect
84. C₄³×C₅	C₂²	semidirect
85. #34877	C₅	direct (N × H)
156. C₂×C₄²×C₅	D₄	semidirect
177. C₂×#529	C₂×C₅	semidirect
178. C₂²×#117	C₂×C₅	semidirect
179. #2611	C₂×C₅	semidirect
180. #2610	C₂×C₅	semidirect
181. #2601	C₂×C₅	semidirect
182. #2591	C₂×C₅	semidirect
183. #2583	C₂×C₅	semidirect
184. #2561	C₂×C₅	semidirect
186. #2413	C₂×C₅	semidirect
187. #2411	C₂×C₅	semidirect
188. #2396	C₂×C₅	semidirect
189. #2392	C₂×C₅	semidirect
190. C₄×#123	C₂×C₅	semidirect
191. C₄×#120	C₂×C₅	semidirect
192. #2293	C₂×C₅	semidirect
193. C₄×#117	C₂×C₅	semidirect
290. C₂×#126	C₂²×C₅	semidirect
291. C₂×#125	C₂²×C₅	semidirect
292. C₂×#124	C₂²×C₅	semidirect
298. C₂×C₄×Q₈	C₂²×C₅	semidirect
301. C₂×C₄×D₄	C₂²×C₅	semidirect
308. C₂×#117	C₂²×C₅	semidirect
315. #400	C₂²×C₅	semidirect
317. #398	C₂²×C₅	semidirect
318. #398	C₂²×C₅	semidirect
321. #396	C₂²×C₅	semidirect
322. #395	C₂²×C₅	semidirect
324. #394	C₂²×C₅	semidirect
329. #389	C₂²×C₅	semidirect
330. #389	C₂²×C₅	semidirect
333. #388	C₂²×C₅	semidirect
334. #388	C₂²×C₅	semidirect
335. #388	C₂²×C₅	semidirect
336. #387	C₂²×C₅	semidirect
345. C₄×C₄⋊C₄	C₂²×C₅	semidirect
346. C₄×C₄⋊C₄	C₂²×C₅	semidirect
347. C₄×C₄⋊C₄	C₂²×C₅	semidirect
352. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
353. #376	C₂²×C₅	semidirect
354. C₄³	C₂²×C₅	semidirect
489. C₂×C₄²	C₅×D₄	semidirect
708. C₅	#34877	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×#529	2
C₂²×C₅×#117	2
C₅×#2611	2
C₅×#2610	2
C₅×#2601	2
C₅×#2591	2
C₅×#2583	2
C₅×#2561	2
C₅×#2539	2
C₅×#2413	2
C₅×#2411	2
C₅×#2396	2
C₅×#2392	2
C₄×C₅×#123	2
C₄×C₅×#120	2
C₅×#2293	2
C₄×C₅×#117	2
#34877	5

Subgroups — C5×#34877 #11957597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34877 #11957597