Subgroups — C₅×#60290 #11983010

Order 1280.

1816 conjugacy classes of subgroups.

The subgroup lattice has 700 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
2	C₅×#2994	C₂	1	4	yes	maximal, complemented
3	C₅×#2993	C₂	1	4	yes	maximal, complemented
4	C₅×#2983	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2974	C₂	1	4	yes	maximal, complemented
8	C₅×#2972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2969	C₂	1	4	yes	maximal, complemented
10	C₅×#2966	C₂	1	4	yes	maximal, complemented
11	C₅×#2924	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×#529	C₄	1	2	yes	—
15	C₅×#529	C₄	1	2	yes	—
16	C₅×#529	C₄	1	2	yes	—
17	C₅×#529	C₄	1	2	yes	—
18	C₅×#529	C₂²	1	2	yes	—
19	C₅×#529	C₂²	1	2	yes	—
20	C₅×#529	C₂²	1	2	yes	—
21	C₅×#529	C₂²	1	2	yes	—
22	C₂×C₅×#126	C₄	1	2	yes	—
23	C₂×C₅×#125	C₄	1	1	yes	characteristic
24	C₂×C₅×#124	C₄	1	1	yes	characteristic
25	C₂×C₅×#123	C₄	1	2	yes	—
26	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
27	C₂×C₅×#121	C₄	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₅×#117	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	4	yes	complemented
38	C₅×#436	C₂²	1	8	yes	complemented
39	C₅×#436	C₂²	1	4	yes	complemented
40	C₅×#435	C₂²	1	8	yes	complemented
41	C₅×#435	C₂²	1	8	yes	complemented
42	C₅×C₈×D₄	C₂²	1	4	yes	complemented
43	C₅×C₈×D₄	C₂²	1	8	yes	complemented
44	C₅×C₈×D₄	C₂²	1	4	yes	complemented
45	C₅×#433	C₂²	1	8	yes	complemented
46	C₅×#433	C₂²	1	8	yes	complemented
47	C₅×#432	C₂²	1	4	yes	—
48	C₅×#432	C₂²	1	2	yes	—
49	C₅×#432	C₂²	1	2	yes	complemented
50	C₅×#431	C₂²	1	1	yes	characteristic
51	C₅×#431	C₂²	1	1	yes	characteristic
52	C₅×#431	C₂²	1	4	yes	—
53	C₅×#431	C₂²	1	1	yes	characteristic
54	C₅×#431	C₂²	1	1	yes	characteristic
55	C₅×#431	C₂²	1	2	yes	—
56	C₅×#431	C₂²	1	2	yes	complemented
57	C₅×#431	C₂²	1	2	yes	complemented
58	C₅×#431	C₂²	1	2	yes	complemented
59	C₅×#424	C₂²	1	8	yes	complemented
60	C₅×#423	C₂²	1	2	yes	complemented
61	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
62	C₅×#407	C₂²	1	2	yes	—
63	C₅×#407	C₂²	1	4	yes	—
64	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
65	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
66	C₅×#405	C₂²	1	8	yes	complemented
67	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
68	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
69	#60290	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₅×D₄	C₂×C₄	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	C₂³×C₄×C₅	C₂³	1	2	yes	—
77	C₂×C₅×M₁₆	C₂³	1	4	yes	—
78	C₂×C₅×M₁₆	C₂³	1	8	yes	—
79	C₂²×C₅×C₈	C₂³	1	4	yes	—
80	C₂²×C₅×C₈	C₂³	1	8	yes	—
81	C₅×#126	C₂×C₄	1	4	yes	—
82	C₅×#126	C₂×C₄	1	4	yes	—
83	C₅×#126	C₂×C₄	1	4	yes	—
84	C₅×#126	C₂×C₄	1	4	yes	—
85	C₅×#125	C₂×C₄	1	2	yes	—
86	C₅×#125	C₂×C₄	1	2	yes	—
87	C₅×#125	C₂×C₄	1	2	yes	—
88	C₅×#125	C₂×C₄	1	2	yes	—
89	C₅×#124	C₂×C₄	1	2	yes	—
90	C₅×#124	C₂×C₄	1	2	yes	—
91	C₅×#124	C₂×C₄	1	2	yes	—
92	C₅×#124	C₂×C₄	1	2	yes	—
93	C₅×#123	C₂×C₄	1	4	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×#121	C₂×C₄	1	2	yes	—
102	C₅×#121	C₂×C₄	1	2	yes	—
103	C₅×#121	C₂×C₄	1	2	yes	—
104	C₅×#121	C₂×C₄	1	2	yes	—
105	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
106	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
107	C₄×C₅×Q₈	C₂³	1	2	yes	—
108	C₄×C₅×Q₈	C₂³	1	2	yes	—
109	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
110	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
111	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
112	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
113	C₄×C₅×D₄	C₂³	1	4	yes	—
114	C₄×C₅×D₄	C₂³	1	2	yes	—
115	C₄×C₅×D₄	C₂³	1	2	yes	—
116	C₄×C₅×D₄	C₂³	1	4	yes	—
117	C₅×#117	C₂×C₄	1	4	yes	—
118	C₅×#117	C₂×C₄	1	4	yes	—
119	C₅×#117	C₂³	1	4	yes	—
120	C₅×#117	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
128	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
132	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
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	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	2	yes	—
145	C₅×C₄⋊C₈	C₂³	1	4	yes	—
146	C₅×C₄⋊C₈	C₂³	1	2	yes	—
147	C₅×C₄⋊C₈	C₂³	1	2	yes	—
148	C₅×C₄⋊C₈	C₂³	1	4	yes	—
149	C₅×C₄⋊C₈	C₂³	1	2	yes	—
150	C₅×C₄⋊C₈	C₂³	1	2	yes	—
151	C₅×C₄⋊C₈	C₂³	1	8	yes	—
152	C₅×C₄⋊C₈	C₂³	1	8	yes	—
153	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
154	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
155	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
156	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
157	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
158	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
161	C₅×#97	C₂³	1	4	yes	—
162	C₅×#97	C₂³	1	8	yes	—
163	C₄×C₅×C₈	C₂³	1	4	yes	—
164	C₄×C₅×C₈	C₂³	1	2	yes	—
165	C₄×C₅×C₈	C₂³	1	2	yes	—
166	C₄×C₅×C₈	C₂³	1	2	yes	—
167	C₄×C₅×C₈	C₂³	1	2	yes	—
168	C₄×C₅×C₈	C₂³	1	8	yes	—
169	C₂×#529	C₂×C₅	1	1	yes	characteristic
170	#2994	C₂×C₅	1	4	yes	complemented
171	#2993	C₂×C₅	1	4	yes	complemented
172	#2983	C₂×C₅	1	1	yes	characteristic, complemented
173	#2982	C₂×C₅	1	1	yes	characteristic, complemented
174	#2975	C₂×C₅	1	1	yes	characteristic, complemented
175	#2974	C₂×C₅	1	4	yes	complemented
176	#2972	C₂×C₅	1	1	yes	characteristic, complemented
177	#2969	C₂×C₅	1	4	yes	complemented
178	#2966	C₂×C₅	1	4	yes	complemented
179	#2924	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	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
184	C₂×C₅×Q₈	—	2	4	no	—
185	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
186	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
187	C₂×C₅×D₄	—	2	4	no	—
188	C₂×C₅×D₄	—	4	4	no	—
189	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
190	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
191	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
192	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₅	—	2	4	no	—
194	C₂²×C₄×C₅	—	4	2	no	—
195	C₂²×C₄×C₅	—	4	4	no	—
196	C₂²×C₄×C₅	—	4	2	no	—
197	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
213	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
214	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
215	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	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	4	yes	—
220	C₅×M₁₆	—	4	4	no	—
221	C₅×M₁₆	—	4	8	no	—
222	C₂×C₅×C₈	—	4	8	no	—
223	C₂×C₅×C₈	—	4	4	no	—
224	C₂×C₅×C₈	C₂⁴	1	4	yes	—
225	C₂×C₅×C₈	C₂⁴	1	4	yes	—
226	C₂×C₅×C₈	C₂⁴	1	4	yes	—
227	C₂×C₅×C₈	C₂⁴	1	4	yes	—
228	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
229	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
230	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
231	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
232	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
233	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
234	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
235	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
236	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
237	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
238	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
240	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
241	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
242	C₅×C₂²⋊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	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
263	C₄²×C₅	C₂⁴	1	1	yes	characteristic
264	C₄²×C₅	C₂⁴	1	1	yes	characteristic
265	C₄²×C₅	C₂⁴	1	1	yes	characteristic
266	C₄²×C₅	C₂⁴	1	1	yes	characteristic
267	C₄²×C₅	C₂⁴	1	4	yes	—
268	#529	C₄×C₅	1	2	yes	—
269	#529	C₄×C₅	1	2	yes	—
270	#529	C₄×C₅	1	2	yes	—
271	#529	C₄×C₅	1	2	yes	—
272	#529	C₂²×C₅	1	2	yes	—
273	#529	C₂²×C₅	1	2	yes	—
274	#529	C₂²×C₅	1	2	yes	—
275	#529	C₂²×C₅	1	2	yes	—
276	C₂×#126	C₄×C₅	1	2	yes	—
277	C₂×#125	C₄×C₅	1	1	yes	characteristic
278	C₂×#124	C₄×C₅	1	1	yes	characteristic
279	C₂×#123	C₄×C₅	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
281	C₂×#121	C₄×C₅	1	1	yes	characteristic
282	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
285	C₂×#117	C₂²×C₅	1	2	yes	—
286	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
287	#446	C₂²×C₅	1	4	yes	complemented
288	#446	C₂²×C₅	1	4	yes	complemented
289	C₈×Q₈	C₂²×C₅	1	4	yes	complemented
290	C₈×Q₈	C₂²×C₅	1	4	yes	complemented
291	#436	C₂²×C₅	1	4	yes	complemented
292	#436	C₂²×C₅	1	8	yes	complemented
293	#436	C₂²×C₅	1	4	yes	complemented
294	#435	C₂²×C₅	1	8	yes	complemented
295	#435	C₂²×C₅	1	8	yes	complemented
296	C₈×D₄	C₂²×C₅	1	4	yes	complemented
297	C₈×D₄	C₂²×C₅	1	8	yes	complemented
298	C₈×D₄	C₂²×C₅	1	4	yes	complemented
299	#433	C₂²×C₅	1	8	yes	complemented
300	#433	C₂²×C₅	1	8	yes	complemented
301	#432	C₂²×C₅	1	2	yes	—
302	#432	C₂²×C₅	1	4	yes	—
303	#432	C₂²×C₅	1	2	yes	complemented
304	#431	C₂²×C₅	1	2	yes	—
305	#431	C₂²×C₅	1	1	yes	characteristic
306	#431	C₂²×C₅	1	1	yes	characteristic
307	#431	C₂²×C₅	1	1	yes	characteristic
308	#431	C₂²×C₅	1	1	yes	characteristic
309	#431	C₂²×C₅	1	4	yes	—
310	#431	C₂²×C₅	1	2	yes	complemented
311	#431	C₂²×C₅	1	2	yes	complemented
312	#431	C₂²×C₅	1	2	yes	complemented
313	#424	C₂²×C₅	1	8	yes	complemented
314	#423	C₂²×C₅	1	2	yes	complemented
315	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
316	#407	C₂²×C₅	1	2	yes	—
317	#407	C₂²×C₅	1	4	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
319	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
320	#405	C₂²×C₅	1	8	yes	complemented
321	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
322	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	2	2	no	—
325	C₂³×C₅	—	2	4	no	—
326	C₂³×C₅	—	4	1	no	—
327	C₂³×C₅	—	4	2	no	—
328	C₂³×C₅	—	4	2	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×D₄	—	2	8	no	—
336	C₅×D₄	—	2	4	no	—
337	C₅×D₄	—	2	4	no	—
338	C₅×D₄	—	4	4	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	4	no	—
341	C₂×C₄×C₅	—	2	2	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	2	no	—
348	C₂×C₄×C₅	—	2	8	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	4	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	2	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	2	no	—
361	C₂×C₄×C₅	#131	1	4	yes	—
362	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
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	4	yes	—
372	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
373	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
374	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
375	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
377	C₅×C₈	—	2	4	no	—
378	C₅×C₈	—	2	4	no	—
379	C₅×C₈	—	2	4	no	—
380	C₅×C₈	—	2	4	no	—
381	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
382	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
384	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
385	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₅	1	2	yes	—
387	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×M₁₆	C₂³×C₅	1	4	yes	—
389	C₂×M₁₆	C₂³×C₅	1	8	yes	—
390	C₂²×C₈	C₂³×C₅	1	4	yes	—
391	C₂²×C₈	C₂³×C₅	1	8	yes	—
392	#126	C₂×C₄×C₅	1	4	yes	—
393	#126	C₂×C₄×C₅	1	4	yes	—
394	#126	C₂×C₄×C₅	1	4	yes	—
395	#126	C₂×C₄×C₅	1	4	yes	—
396	#125	C₂×C₄×C₅	1	2	yes	—
397	#125	C₂×C₄×C₅	1	2	yes	—
398	#125	C₂×C₄×C₅	1	2	yes	—
399	#125	C₂×C₄×C₅	1	2	yes	—
400	#124	C₂×C₄×C₅	1	2	yes	—
401	#124	C₂×C₄×C₅	1	2	yes	—
402	#124	C₂×C₄×C₅	1	2	yes	—
403	#124	C₂×C₄×C₅	1	2	yes	—
404	#123	C₂×C₄×C₅	1	4	yes	—
405	#123	C₂×C₄×C₅	1	4	yes	—
406	#123	C₂×C₄×C₅	1	4	yes	—
407	#123	C₂×C₄×C₅	1	4	yes	—
408	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
409	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
410	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
411	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
412	#121	C₂×C₄×C₅	1	2	yes	—
413	#121	C₂×C₄×C₅	1	2	yes	—
414	#121	C₂×C₄×C₅	1	2	yes	—
415	#121	C₂×C₄×C₅	1	2	yes	—
416	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
417	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
418	C₄×Q₈	C₂³×C₅	1	2	yes	—
419	C₄×Q₈	C₂³×C₅	1	2	yes	—
420	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
421	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
422	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
423	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
424	C₄×D₄	C₂³×C₅	1	4	yes	—
425	C₄×D₄	C₂³×C₅	1	2	yes	—
426	C₄×D₄	C₂³×C₅	1	2	yes	—
427	C₄×D₄	C₂³×C₅	1	4	yes	—
428	#117	C₂×C₄×C₅	1	4	yes	—
429	#117	C₂×C₄×C₅	1	4	yes	—
430	#117	C₂³×C₅	1	4	yes	—
431	#117	C₂³×C₅	1	4	yes	—
432	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
433	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
434	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
436	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
443	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
444	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
445	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
446	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
447	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
448	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅	1	2	yes	—
451	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₄⋊C₈	C₂³×C₅	1	4	yes	—
457	C₄⋊C₈	C₂³×C₅	1	2	yes	—
458	C₄⋊C₈	C₂³×C₅	1	2	yes	—
459	C₄⋊C₈	C₂³×C₅	1	4	yes	—
460	C₄⋊C₈	C₂³×C₅	1	2	yes	—
461	C₄⋊C₈	C₂³×C₅	1	2	yes	—
462	C₄⋊C₈	C₂³×C₅	1	8	yes	—
463	C₄⋊C₈	C₂³×C₅	1	8	yes	—
464	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
465	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
466	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
467	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
469	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
470	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
471	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
472	#97	C₂³×C₅	1	4	yes	—
473	#97	C₂³×C₅	1	8	yes	—
474	C₄×C₈	C₂³×C₅	1	4	yes	—
475	C₄×C₈	C₂³×C₅	1	2	yes	—
476	C₄×C₈	C₂³×C₅	1	2	yes	—
477	C₄×C₈	C₂³×C₅	1	2	yes	—
478	C₄×C₈	C₂³×C₅	1	2	yes	—
479	C₄×C₈	C₂³×C₅	1	8	yes	—
480	C₂²×C₅	—	2	1	no	—
481	C₂²×C₅	—	2	1	no	—
482	C₂²×C₅	—	2	1	no	—
483	C₂²×C₅	—	2	1	no	—
484	C₂²×C₅	—	2	1	no	—
485	C₂²×C₅	—	2	4	no	—
486	C₂²×C₅	—	2	1	no	—
487	C₂²×C₅	—	2	4	no	—
488	C₂²×C₅	—	2	1	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	4	4	no	—
491	C₂²×C₅	—	8	4	no	—
492	C₂²×C₅	C₂×#131	1	2	yes	—
493	C₂²×C₅	#568	1	2	yes	—
494	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
495	C₄×C₅	—	2	1	no	—
496	C₄×C₅	—	2	1	no	—
497	C₄×C₅	—	2	4	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	4	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	1	no	—
506	C₄×C₅	—	2	4	no	—
507	C₄×C₅	C₂×#131	1	2	yes	—
508	C₄×C₅	C₂×#131	1	2	yes	—
509	C₄×C₅	#585	1	2	yes	—
510	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
511	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
512	C₂×Q₈	—	2	4	no	—
513	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
514	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	4	4	no	—
517	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
518	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
519	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
527	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
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	2	yes	—
541	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
542	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
543	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	M₁₆	—	4	4	no	—
549	M₁₆	—	4	8	no	—
550	C₂×C₈	—	4	8	no	—
551	C₂×C₈	—	4	4	no	—
552	C₂×C₈	C₂⁴×C₅	1	4	yes	—
553	C₂×C₈	C₂⁴×C₅	1	4	yes	—
554	C₂×C₈	C₂⁴×C₅	1	4	yes	—
555	C₂×C₈	C₂⁴×C₅	1	4	yes	—
556	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
559	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
560	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
561	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
562	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
563	C₄⋊C₄	C₂²×C₄×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	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
572	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
575	C₂²⋊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	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
579	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
581	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
582	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
583	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
584	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
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	4	yes	—
591	C₄²	C₂⁴×C₅	1	1	yes	characteristic
592	C₄²	C₂⁴×C₅	1	1	yes	characteristic
593	C₄²	C₂⁴×C₅	1	1	yes	characteristic
594	C₄²	C₂⁴×C₅	1	4	yes	—
595	C₄²	C₂⁴×C₅	1	1	yes	characteristic
596	C₂×C₅	—	2	2	no	—
597	C₂×C₅	—	2	2	no	—
598	C₂×C₅	—	4	1	no	—
599	C₂×C₅	—	4	4	no	—
600	C₂×C₅	#3428	1	1	yes	characteristic
601	C₂×C₅	C₂²×#131	1	1	yes	characteristic
602	C₂×C₅	C₂×#568	1	1	yes	characteristic
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	C₂³×C₄×C₅	1	4	yes	—
610	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
611	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
612	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
613	Q₈	—	2	4	no	—
614	Q₈	—	2	4	no	—
615	D₄	—	2	8	no	—
616	D₄	—	2	4	no	—
617	D₄	—	2	4	no	—
618	D₄	—	4	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	C₅×#131	1	4	yes	—
642	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
650	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
651	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
652	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
656	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
657	C₈	—	2	4	no	—
658	C₈	—	2	4	no	—
659	C₈	—	2	4	no	—
660	C₈	—	2	4	no	—
661	C₅	#60290	1	1	yes	characteristic, direct product factor, Sylow
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	8	4	no	—
674	C₂²	C₂×C₅×#131	1	2	yes	—
675	C₂²	C₅×#568	1	2	yes	—
676	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	C₂×C₅×#131	1	2	yes	—
690	C₄	C₂×C₅×#131	1	2	yes	—
691	C₄	C₅×#585	1	2	yes	—
692	C₂	—	2	2	no	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	4	no	—
696	C₂	C₅×#3428	1	1	yes	characteristic
697	C₂	C₂²×C₅×#131	1	1	yes	characteristic
698	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	C₂×C₅×#121	C₄
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×#2994	C₂	semidirect
3. C₅×#2993	C₂	semidirect
4. C₅×#2983	C₂	semidirect
5. C₅×#2982	C₂	semidirect
6. C₅×#2975	C₂	semidirect
7. C₅×#2974	C₂	semidirect
8. C₅×#2972	C₂	semidirect
9. C₅×#2969	C₂	semidirect
10. C₅×#2966	C₂	semidirect
11. C₅×#2924	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
37. C₅×#436	C₂²	semidirect
38. C₅×#436	C₂²	semidirect
39. C₅×#436	C₂²	semidirect
40. C₅×#435	C₂²	semidirect
41. C₅×#435	C₂²	semidirect
42. C₅×C₈×D₄	C₂²	semidirect
43. C₅×C₈×D₄	C₂²	semidirect
44. C₅×C₈×D₄	C₂²	semidirect
45. C₅×#433	C₂²	semidirect
46. C₅×#433	C₂²	semidirect
49. C₅×#432	C₂²	semidirect
56. C₅×#431	C₂²	semidirect
57. C₅×#431	C₂²	semidirect
58. C₅×#431	C₂²	semidirect
59. C₅×#424	C₂²	semidirect
60. C₅×#423	C₂²	semidirect
61. C₂×C₅×C₄⋊C₈	C₂²	semidirect
66. C₅×#405	C₂²	semidirect
67. C₄×C₅×M₁₆	C₂²	semidirect
68. C₂×C₄×C₅×C₈	C₂²	semidirect
69. #60290	C₅	direct (N × H)
170. #2994	C₂×C₅	semidirect
171. #2993	C₂×C₅	semidirect
172. #2983	C₂×C₅	semidirect
173. #2982	C₂×C₅	semidirect
174. #2975	C₂×C₅	semidirect
175. #2974	C₂×C₅	semidirect
176. #2972	C₂×C₅	semidirect
177. #2969	C₂×C₅	semidirect
178. #2966	C₂×C₅	semidirect
179. #2924	C₂×C₅	semidirect
180. #2920	C₂×C₅	semidirect
181. C₂×#431	C₂×C₅	semidirect
287. #446	C₂²×C₅	semidirect
288. #446	C₂²×C₅	semidirect
289. C₈×Q₈	C₂²×C₅	semidirect
290. C₈×Q₈	C₂²×C₅	semidirect
291. #436	C₂²×C₅	semidirect
292. #436	C₂²×C₅	semidirect
293. #436	C₂²×C₅	semidirect
294. #435	C₂²×C₅	semidirect
295. #435	C₂²×C₅	semidirect
296. C₈×D₄	C₂²×C₅	semidirect
297. C₈×D₄	C₂²×C₅	semidirect
298. C₈×D₄	C₂²×C₅	semidirect
299. #433	C₂²×C₅	semidirect
300. #433	C₂²×C₅	semidirect
303. #432	C₂²×C₅	semidirect
310. #431	C₂²×C₅	semidirect
311. #431	C₂²×C₅	semidirect
312. #431	C₂²×C₅	semidirect
313. #424	C₂²×C₅	semidirect
314. #423	C₂²×C₅	semidirect
315. C₂×C₄⋊C₈	C₂²×C₅	semidirect
320. #405	C₂²×C₅	semidirect
321. C₄×M₁₆	C₂²×C₅	semidirect
322. C₂×C₄×C₈	C₂²×C₅	semidirect
661. C₅	#60290	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
C₅×#2994	2
C₅×#2993	2
C₅×#2983	2
C₅×#2982	2
C₅×#2975	2
C₅×#2974	2
C₅×#2972	2
C₅×#2969	2
C₅×#2966	2
C₅×#2924	2
C₅×#2920	2
C₂×C₅×#431	2
#60290	5

Subgroups — C5×#60290 #11983010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60290 #11983010