Subgroups — C₅×#60292 #11983012

Order 1280.

1806 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3444	C₂	1	1	yes	maximal, characteristic
2	C₅×#2991	C₂	1	2	yes	maximal, complemented
3	C₅×#2990	C₂	1	2	yes	maximal, complemented
4	C₅×#2989	C₂	1	2	yes	maximal, complemented
5	C₅×#2988	C₂	1	2	yes	maximal, complemented
6	C₅×#2986	C₂	1	2	yes	maximal, complemented
7	C₅×#2979	C₂	1	2	yes	maximal, complemented
8	C₅×#2976	C₂	1	4	yes	maximal, complemented
9	C₅×#2969	C₂	1	4	yes	maximal, complemented
10	C₅×#2966	C₂	1	4	yes	maximal, complemented
11	C₅×#2925	C₂	1	4	yes	maximal, complemented
12	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#533	C₄	1	1	yes	characteristic
15	C₅×#533	C₄	1	1	yes	characteristic
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₅×#532	C₄	1	1	yes	characteristic
18	C₅×#532	C₄	1	1	yes	characteristic
19	C₅×#532	C₂²	1	1	yes	characteristic
20	C₅×#529	C₄	1	2	yes	—
21	C₅×#529	C₄	1	2	yes	—
22	C₅×#529	C₄	1	2	yes	—
23	C₅×#529	C₄	1	2	yes	—
24	C₅×#529	C₂²	1	2	yes	—
25	C₅×#529	C₂²	1	2	yes	—
26	C₅×#525	C₄	1	2	yes	—
27	C₅×#525	C₄	1	2	yes	—
28	C₅×#525	C₂²	1	2	yes	—
29	C₄×C₅×#41	C₂²	1	2	yes	—
30	C₄×C₅×#41	C₂²	1	2	yes	—
31	C₄×C₅×#41	C₂²	1	2	yes	—
32	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₅×#446	C₂²	1	4	yes	complemented
34	C₅×#446	C₂²	1	4	yes	complemented
35	C₅×C₈×Q₈	C₂²	1	4	yes	complemented
36	C₅×C₈×Q₈	C₂²	1	4	yes	complemented
37	C₅×#436	C₂²	1	8	yes	—
38	C₅×#436	C₂²	1	4	yes	complemented
39	C₅×#436	C₂²	1	4	yes	complemented
40	C₅×#435	C₂²	1	8	yes	—
41	C₅×#435	C₂²	1	8	yes	—
42	C₅×C₈×D₄	C₂²	1	8	yes	—
43	C₅×C₈×D₄	C₂²	1	4	yes	complemented
44	C₅×C₈×D₄	C₂²	1	4	yes	complemented
45	C₅×#433	C₂²	1	8	yes	—
46	C₅×#433	C₂²	1	8	yes	complemented
47	C₅×#432	C₂²	1	2	yes	—
48	C₅×#432	C₂²	1	2	yes	—
49	C₅×#432	C₂²	1	4	yes	complemented
50	C₅×#431	C₂²	1	2	yes	—
51	C₅×#431	C₂²	1	2	yes	—
52	C₅×#431	C₂²	1	2	yes	—
53	C₅×#431	C₂²	1	2	yes	—
54	C₅×#431	C₂²	1	2	yes	—
55	C₅×#431	C₂²	1	2	yes	—
56	C₅×#431	C₂²	1	4	yes	complemented
57	C₅×#423	C₂²	1	1	yes	characteristic
58	C₅×#423	C₂²	1	1	yes	characteristic
59	C₅×#423	C₂²	1	4	yes	complemented
60	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
63	C₅×#408	C₂²	1	8	yes	—
64	C₅×#407	C₂²	1	2	yes	—
65	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
66	C₅×#405	C₂²	1	8	yes	complemented
67	C₄×C₅×M₁₆	C₂²	1	2	yes	—
68	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
69	#60292	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₅×#41	C₂×C₄	1	2	yes	—
71	C₂×C₅×#41	C₂×C₄	1	2	yes	—
72	C₂×C₅×#41	C₂³	1	2	yes	—
73	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₅×M₁₆	C₂³	1	2	yes	—
77	C₂×C₅×M₁₆	C₂³	1	2	yes	—
78	C₂×C₅×M₁₆	C₂³	1	8	yes	—
79	C₂²×C₅×C₈	C₂³	1	2	yes	—
80	C₂²×C₅×C₈	C₂³	1	2	yes	—
81	C₂²×C₅×C₈	C₂³	1	8	yes	—
82	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₅×#127	C₂×C₄	1	1	yes	characteristic
86	C₅×#126	C₂×C₄	1	4	yes	—
87	C₅×#126	C₂×C₄	1	4	yes	—
88	C₅×#125	C₂×C₄	1	2	yes	—
89	C₅×#125	C₂×C₄	1	2	yes	—
90	C₅×#125	C₂×C₄	1	2	yes	—
91	C₅×#124	C₂×C₄	1	2	yes	—
92	C₅×#124	C₂×C₄	1	2	yes	—
93	C₅×#124	C₂×C₄	1	2	yes	—
94	C₅×#123	C₂×C₄	1	4	yes	—
95	C₅×#123	C₂×C₄	1	4	yes	—
96	C₅×#123	C₂×C₄	1	4	yes	—
97	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
98	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
99	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
100	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
101	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
102	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
103	C₅×#121	C₂×C₄	1	2	yes	—
104	C₅×#121	C₂×C₄	1	2	yes	—
105	C₅×#121	C₂×C₄	1	2	yes	—
106	C₅×#121	C₂×C₄	1	2	yes	—
107	C₅×#121	C₂×C₄	1	2	yes	—
108	C₅×#121	C₂×C₄	1	2	yes	—
109	C₅×#120	C₂×C₄	1	4	yes	—
110	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
111	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
112	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
113	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
114	C₄×C₅×Q₈	C₂³	1	2	yes	—
115	C₄×C₅×Q₈	C₂³	1	2	yes	—
116	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
117	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
118	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
119	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
120	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
121	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
122	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
123	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
124	C₄×C₅×D₄	C₂³	1	4	yes	—
125	C₄×C₅×D₄	C₂³	1	2	yes	—
126	C₄×C₅×D₄	C₂³	1	2	yes	—
127	C₄×C₅×D₄	C₂³	1	4	yes	—
128	C₅×#117	C₂×C₄	1	2	yes	—
129	C₅×#117	C₂×C₄	1	2	yes	—
130	C₅×#117	C₂×C₄	1	4	yes	—
131	C₅×#117	C₂×C₄	1	4	yes	—
132	C₅×#117	C₂³	1	4	yes	—
133	C₅×#117	C₂³	1	2	yes	—
134	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂×C₄	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	4	yes	—
144	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₅×C₄⋊C₈	C₂³	1	2	yes	—
148	C₅×C₄⋊C₈	C₂³	1	2	yes	—
149	C₅×C₄⋊C₈	C₂³	1	2	yes	—
150	C₅×C₄⋊C₈	C₂³	1	2	yes	—
151	C₅×C₄⋊C₈	C₂³	1	2	yes	—
152	C₅×C₄⋊C₈	C₂³	1	8	yes	—
153	C₅×C₄⋊C₈	C₂³	1	2	yes	—
154	C₅×C₄⋊C₈	C₂³	1	2	yes	—
155	C₅×C₄⋊C₈	C₂³	1	2	yes	—
156	C₅×C₄⋊C₈	C₂³	1	8	yes	—
157	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
161	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
162	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
163	C₅×#97	C₂³	1	4	yes	—
164	C₅×#97	C₂³	1	8	yes	—
165	C₄×C₅×C₈	C₂³	1	4	yes	—
166	C₄×C₅×C₈	C₂³	1	4	yes	—
167	C₄×C₅×C₈	C₂³	1	4	yes	—
168	C₄×C₅×C₈	C₂³	1	8	yes	—
169	#3444	C₂×C₅	1	1	yes	characteristic
170	#2991	C₂×C₅	1	2	yes	complemented
171	#2990	C₂×C₅	1	2	yes	complemented
172	#2989	C₂×C₅	1	2	yes	complemented
173	#2988	C₂×C₅	1	2	yes	complemented
174	#2986	C₂×C₅	1	2	yes	complemented
175	#2979	C₂×C₅	1	2	yes	complemented
176	#2976	C₂×C₅	1	4	yes	complemented
177	#2969	C₂×C₅	1	4	yes	complemented
178	#2966	C₂×C₅	1	4	yes	complemented
179	#2925	C₂×C₅	1	4	yes	complemented
180	#2920	C₂×C₅	1	1	yes	characteristic, complemented
181	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
182	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₅×#41	—	2	8	no	—
184	C₅×#41	—	4	2	no	—
185	C₅×#41	—	4	2	no	—
186	C₅×#41	—	4	4	no	—
187	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
188	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
189	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
190	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
191	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
192	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
193	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
194	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
195	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₅	—	2	4	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	—	4	1	no	—
199	C₂²×C₄×C₅	—	4	1	no	—
200	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
209	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
216	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
221	C₅×M₁₆	—	4	2	no	—
222	C₅×M₁₆	—	4	8	no	—
223	C₅×M₁₆	—	4	2	no	—
224	C₂×C₅×C₈	—	4	2	no	—
225	C₂×C₅×C₈	—	4	8	no	—
226	C₂×C₅×C₈	—	4	2	no	—
227	C₂×C₅×C₈	C₂⁴	1	4	yes	—
228	C₂×C₅×C₈	C₂⁴	1	4	yes	—
229	C₂×C₅×C₈	C₂⁴	1	4	yes	—
230	C₂×C₅×C₈	C₂⁴	1	4	yes	—
231	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
232	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
233	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
234	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
235	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
236	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
237	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
238	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
240	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
241	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
242	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
243	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
244	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
245	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
246	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
247	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
248	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
249	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
250	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
251	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
252	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
253	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
254	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
257	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
259	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
260	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
261	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
262	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
263	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
264	C₄²×C₅	C₂²×C₄	1	4	yes	—
265	C₄²×C₅	C₂²×C₄	1	4	yes	—
266	C₄²×C₅	C₂⁴	1	1	yes	characteristic
267	C₄²×C₅	C₂⁴	1	1	yes	characteristic
268	C₄²×C₅	C₂⁴	1	1	yes	characteristic
269	C₄²×C₅	C₂⁴	1	1	yes	characteristic
270	C₄²×C₅	C₂⁴	1	4	yes	—
271	#533	C₄×C₅	1	1	yes	characteristic
272	#533	C₄×C₅	1	1	yes	characteristic
273	#533	C₂²×C₅	1	1	yes	characteristic
274	#532	C₄×C₅	1	1	yes	characteristic
275	#532	C₄×C₅	1	1	yes	characteristic
276	#532	C₂²×C₅	1	1	yes	characteristic
277	#529	C₄×C₅	1	2	yes	—
278	#529	C₄×C₅	1	2	yes	—
279	#529	C₄×C₅	1	2	yes	—
280	#529	C₄×C₅	1	2	yes	—
281	#529	C₂²×C₅	1	2	yes	—
282	#529	C₂²×C₅	1	2	yes	—
283	#525	C₄×C₅	1	2	yes	—
284	#525	C₄×C₅	1	2	yes	—
285	#525	C₂²×C₅	1	2	yes	—
286	C₄×#41	C₂²×C₅	1	2	yes	—
287	C₄×#41	C₂²×C₅	1	2	yes	—
288	C₄×#41	C₂²×C₅	1	2	yes	—
289	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
290	#446	C₂²×C₅	1	4	yes	complemented
291	#446	C₂²×C₅	1	4	yes	complemented
292	C₈×Q₈	C₂²×C₅	1	4	yes	complemented
293	C₈×Q₈	C₂²×C₅	1	4	yes	complemented
294	#436	C₂²×C₅	1	8	yes	—
295	#436	C₂²×C₅	1	4	yes	complemented
296	#436	C₂²×C₅	1	4	yes	complemented
297	#435	C₂²×C₅	1	8	yes	—
298	#435	C₂²×C₅	1	8	yes	—
299	C₈×D₄	C₂²×C₅	1	8	yes	—
300	C₈×D₄	C₂²×C₅	1	4	yes	complemented
301	C₈×D₄	C₂²×C₅	1	4	yes	complemented
302	#433	C₂²×C₅	1	8	yes	—
303	#433	C₂²×C₅	1	8	yes	complemented
304	#432	C₂²×C₅	1	2	yes	—
305	#432	C₂²×C₅	1	2	yes	—
306	#432	C₂²×C₅	1	4	yes	complemented
307	#431	C₂²×C₅	1	2	yes	—
308	#431	C₂²×C₅	1	2	yes	—
309	#431	C₂²×C₅	1	2	yes	—
310	#431	C₂²×C₅	1	2	yes	—
311	#431	C₂²×C₅	1	2	yes	—
312	#431	C₂²×C₅	1	2	yes	—
313	#431	C₂²×C₅	1	4	yes	complemented
314	#423	C₂²×C₅	1	1	yes	characteristic
315	#423	C₂²×C₅	1	1	yes	characteristic
316	#423	C₂²×C₅	1	4	yes	complemented
317	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
320	#408	C₂²×C₅	1	8	yes	—
321	#407	C₂²×C₅	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
323	#405	C₂²×C₅	1	8	yes	complemented
324	C₄×M₁₆	C₂²×C₅	1	2	yes	—
325	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
326	C₂³×C₅	—	2	2	no	—
327	C₂³×C₅	—	4	1	no	—
328	C₂³×C₅	—	4	1	no	—
329	C₂³×C₅	C₂³×C₄	1	4	yes	—
330	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
331	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
332	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₅×Q₈	—	2	4	no	—
334	C₅×Q₈	—	2	4	no	—
335	C₅×Q₈	—	4	2	no	—
336	C₅×D₄	—	2	8	no	—
337	C₅×D₄	—	2	4	no	—
338	C₅×D₄	—	2	4	no	—
339	C₅×D₄	—	4	2	no	—
340	C₅×D₄	—	4	4	no	—
341	C₅×D₄	—	4	4	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	8	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	4	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	4	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	4	no	—
366	C₂×C₄×C₅	#131	1	4	yes	—
367	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
376	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
377	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
378	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
380	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
382	C₅×C₈	—	2	4	no	—
383	C₅×C₈	—	2	4	no	—
384	C₅×C₈	—	2	4	no	—
385	C₅×C₈	—	2	4	no	—
386	C₂×#41	C₂×C₄×C₅	1	2	yes	—
387	C₂×#41	C₂×C₄×C₅	1	2	yes	—
388	C₂×#41	C₂³×C₅	1	2	yes	—
389	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
390	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂×M₁₆	C₂³×C₅	1	2	yes	—
393	C₂×M₁₆	C₂³×C₅	1	2	yes	—
394	C₂×M₁₆	C₂³×C₅	1	8	yes	—
395	C₂²×C₈	C₂³×C₅	1	2	yes	—
396	C₂²×C₈	C₂³×C₅	1	2	yes	—
397	C₂²×C₈	C₂³×C₅	1	8	yes	—
398	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
399	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
400	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
401	#127	C₂×C₄×C₅	1	1	yes	characteristic
402	#126	C₂×C₄×C₅	1	4	yes	—
403	#126	C₂×C₄×C₅	1	4	yes	—
404	#125	C₂×C₄×C₅	1	2	yes	—
405	#125	C₂×C₄×C₅	1	2	yes	—
406	#125	C₂×C₄×C₅	1	2	yes	—
407	#124	C₂×C₄×C₅	1	2	yes	—
408	#124	C₂×C₄×C₅	1	2	yes	—
409	#124	C₂×C₄×C₅	1	2	yes	—
410	#123	C₂×C₄×C₅	1	4	yes	—
411	#123	C₂×C₄×C₅	1	4	yes	—
412	#123	C₂×C₄×C₅	1	4	yes	—
413	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
414	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
415	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
416	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
417	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
418	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
419	#121	C₂×C₄×C₅	1	2	yes	—
420	#121	C₂×C₄×C₅	1	2	yes	—
421	#121	C₂×C₄×C₅	1	2	yes	—
422	#121	C₂×C₄×C₅	1	2	yes	—
423	#121	C₂×C₄×C₅	1	2	yes	—
424	#121	C₂×C₄×C₅	1	2	yes	—
425	#120	C₂×C₄×C₅	1	4	yes	—
426	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
427	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
428	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
429	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
430	C₄×Q₈	C₂³×C₅	1	2	yes	—
431	C₄×Q₈	C₂³×C₅	1	2	yes	—
432	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
433	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
434	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
435	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
436	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
437	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
438	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
439	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
440	C₄×D₄	C₂³×C₅	1	4	yes	—
441	C₄×D₄	C₂³×C₅	1	4	yes	—
442	C₄×D₄	C₂³×C₅	1	2	yes	—
443	C₄×D₄	C₂³×C₅	1	2	yes	—
444	#117	C₂×C₄×C₅	1	2	yes	—
445	#117	C₂×C₄×C₅	1	2	yes	—
446	#117	C₂×C₄×C₅	1	4	yes	—
447	#117	C₂×C₄×C₅	1	4	yes	—
448	#117	C₂³×C₅	1	2	yes	—
449	#117	C₂³×C₅	1	4	yes	—
450	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
451	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
452	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
454	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
455	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅	1	4	yes	—
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	C₄⋊C₈	C₂³×C₅	1	2	yes	—
464	C₄⋊C₈	C₂³×C₅	1	2	yes	—
465	C₄⋊C₈	C₂³×C₅	1	2	yes	—
466	C₄⋊C₈	C₂³×C₅	1	2	yes	—
467	C₄⋊C₈	C₂³×C₅	1	2	yes	—
468	C₄⋊C₈	C₂³×C₅	1	8	yes	—
469	C₄⋊C₈	C₂³×C₅	1	2	yes	—
470	C₄⋊C₈	C₂³×C₅	1	2	yes	—
471	C₄⋊C₈	C₂³×C₅	1	2	yes	—
472	C₄⋊C₈	C₂³×C₅	1	8	yes	—
473	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
474	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
475	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
476	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
477	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
478	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
479	#97	C₂³×C₅	1	4	yes	—
480	#97	C₂³×C₅	1	8	yes	—
481	C₄×C₈	C₂³×C₅	1	4	yes	—
482	C₄×C₈	C₂³×C₅	1	4	yes	—
483	C₄×C₈	C₂³×C₅	1	4	yes	—
484	C₄×C₈	C₂³×C₅	1	8	yes	—
485	C₂²×C₅	—	2	1	no	—
486	C₂²×C₅	—	2	1	no	—
487	C₂²×C₅	—	2	1	no	—
488	C₂²×C₅	—	2	1	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	2	1	no	—
491	C₂²×C₅	—	2	1	no	—
492	C₂²×C₅	—	2	4	no	—
493	C₂²×C₅	—	2	1	no	—
494	C₂²×C₅	—	2	1	no	—
495	C₂²×C₅	—	2	4	no	—
496	C₂²×C₅	—	4	4	no	—
497	C₂²×C₅	C₂×#131	1	2	yes	—
498	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	4	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	4	no	—
506	C₄×C₅	—	2	1	no	—
507	C₄×C₅	—	2	1	no	—
508	C₄×C₅	—	2	1	no	—
509	C₄×C₅	—	2	4	no	—
510	C₄×C₅	C₂×#131	1	2	yes	—
511	C₄×C₅	C₂×#131	1	2	yes	—
512	C₄×C₅	#568	1	2	yes	—
513	C₄×C₅	#585	1	1	yes	characteristic
514	C₄×C₅	#585	1	1	yes	characteristic
515	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
516	#41	—	2	8	no	—
517	#41	—	4	2	no	—
518	#41	—	4	2	no	—
519	#41	—	4	4	no	—
520	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
521	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
522	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
523	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
524	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
525	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
526	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
527	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
528	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
542	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
549	C₂²×C₄	C₂²×C₄×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	4	yes	—
554	M₁₆	—	4	2	no	—
555	M₁₆	—	4	8	no	—
556	M₁₆	—	4	2	no	—
557	C₂×C₈	—	4	2	no	—
558	C₂×C₈	—	4	8	no	—
559	C₂×C₈	—	4	2	no	—
560	C₂×C₈	C₂⁴×C₅	1	4	yes	—
561	C₂×C₈	C₂⁴×C₅	1	4	yes	—
562	C₂×C₈	C₂⁴×C₅	1	4	yes	—
563	C₂×C₈	C₂⁴×C₅	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
565	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
566	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
567	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
571	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
573	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
585	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
586	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
587	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
588	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
589	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
590	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
593	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₅	1	4	yes	—
598	C₄²	C₂²×C₄×C₅	1	4	yes	—
599	C₄²	C₂⁴×C₅	1	1	yes	characteristic
600	C₄²	C₂⁴×C₅	1	1	yes	characteristic
601	C₄²	C₂⁴×C₅	1	1	yes	characteristic
602	C₄²	C₂⁴×C₅	1	4	yes	—
603	C₄²	C₂⁴×C₅	1	1	yes	characteristic
604	C₂×C₅	—	2	2	no	—
605	C₂×C₅	—	4	4	no	—
606	C₂×C₅	—	4	1	no	—
607	C₂×C₅	—	4	1	no	—
608	C₂×C₅	#3428	1	1	yes	characteristic
609	C₂×C₅	C₂²×#131	1	1	yes	characteristic
610	C₂×C₅	C₂×#568	1	1	yes	characteristic
611	C₂³	—	2	2	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	C₂³×C₄×C₅	1	4	yes	—
615	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
616	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
617	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
618	Q₈	—	2	4	no	—
619	Q₈	—	2	4	no	—
620	Q₈	—	4	2	no	—
621	D₄	—	2	8	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	2	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	C₅×#131	1	4	yes	—
652	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
653	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
654	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
658	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
661	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
662	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
663	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
664	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
666	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
667	C₈	—	2	4	no	—
668	C₈	—	2	4	no	—
669	C₈	—	2	4	no	—
670	C₈	—	2	4	no	—
671	C₅	#60292	1	1	yes	characteristic, direct product factor, Sylow
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	C₂×C₅×#131	1	2	yes	—
685	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	4	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	4	no	—
697	C₄	C₂×C₅×#131	1	2	yes	—
698	C₄	C₂×C₅×#131	1	2	yes	—
699	C₄	C₅×#568	1	2	yes	—
700	C₄	C₅×#585	1	1	yes	characteristic
701	C₄	C₅×#585	1	1	yes	characteristic
702	C₂	—	2	2	no	—
703	C₂	—	4	1	no	—
704	C₂	—	4	1	no	—
705	C₂	—	4	4	no	—
706	C₂	C₅×#3428	1	1	yes	characteristic
707	C₂	C₂²×C₅×#131	1	1	yes	characteristic
708	C₂	C₂×C₅×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂⁴×C₄
prime radical	C₅×#3444	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2991	C₂	semidirect
3. C₅×#2990	C₂	semidirect
4. C₅×#2989	C₂	semidirect
5. C₅×#2988	C₂	semidirect
6. C₅×#2986	C₂	semidirect
7. C₅×#2979	C₂	semidirect
8. C₅×#2976	C₂	semidirect
9. C₅×#2969	C₂	semidirect
10. C₅×#2966	C₂	semidirect
11. C₅×#2925	C₂	semidirect
12. C₅×#2920	C₂	semidirect
13. C₂×C₅×#431	C₂	semidirect
33. C₅×#446	C₂²	semidirect
34. C₅×#446	C₂²	semidirect
35. C₅×C₈×Q₈	C₂²	semidirect
36. C₅×C₈×Q₈	C₂²	semidirect
38. C₅×#436	C₂²	semidirect
39. C₅×#436	C₂²	semidirect
43. C₅×C₈×D₄	C₂²	semidirect
44. C₅×C₈×D₄	C₂²	semidirect
46. C₅×#433	C₂²	semidirect
49. C₅×#432	C₂²	semidirect
56. C₅×#431	C₂²	semidirect
59. C₅×#423	C₂²	semidirect
62. C₂×C₅×C₄⋊C₈	C₂²	semidirect
66. C₅×#405	C₂²	semidirect
69. #60292	C₅	direct (N × H)
170. #2991	C₂×C₅	semidirect
171. #2990	C₂×C₅	semidirect
172. #2989	C₂×C₅	semidirect
173. #2988	C₂×C₅	semidirect
174. #2986	C₂×C₅	semidirect
175. #2979	C₂×C₅	semidirect
176. #2976	C₂×C₅	semidirect
177. #2969	C₂×C₅	semidirect
178. #2966	C₂×C₅	semidirect
179. #2925	C₂×C₅	semidirect
180. #2920	C₂×C₅	semidirect
181. C₂×#431	C₂×C₅	semidirect
290. #446	C₂²×C₅	semidirect
291. #446	C₂²×C₅	semidirect
292. C₈×Q₈	C₂²×C₅	semidirect
293. C₈×Q₈	C₂²×C₅	semidirect
295. #436	C₂²×C₅	semidirect
296. #436	C₂²×C₅	semidirect
300. C₈×D₄	C₂²×C₅	semidirect
301. C₈×D₄	C₂²×C₅	semidirect
303. #433	C₂²×C₅	semidirect
306. #432	C₂²×C₅	semidirect
313. #431	C₂²×C₅	semidirect
316. #423	C₂²×C₅	semidirect
319. C₂×C₄⋊C₈	C₂²×C₅	semidirect
323. #405	C₂²×C₅	semidirect
671. C₅	#60292	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×#3444	2
C₅×#2991	2
C₅×#2990	2
C₅×#2989	2
C₅×#2988	2
C₅×#2986	2
C₅×#2979	2
C₅×#2976	2
C₅×#2969	2
C₅×#2966	2
C₅×#2925	2
C₅×#2920	2
C₂×C₅×#431	2
#60292	5

Subgroups — C5×#60292 #11983012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60292 #11983012