Subgroups — C₅×#60310 #11983030

Order 1280.

1914 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3459	C₂	1	1	yes	maximal, characteristic
2	C₅×#2994	C₂	1	4	yes	maximal, complemented
3	C₅×#2992	C₂	1	2	yes	maximal, complemented
4	C₅×#2977	C₂	1	4	yes	maximal, complemented
5	C₅×#2976	C₂	1	2	yes	maximal, complemented
6	C₅×#2973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2972	C₂	1	2	yes	maximal, complemented
8	C₅×#2968	C₂	1	4	yes	maximal, complemented
9	C₅×#2966	C₂	1	2	yes	maximal, complemented
10	C₅×#2933	C₂	1	4	yes	maximal, complemented
11	C₅×#2929	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#435	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#131	C₂²	1	2	yes	complemented
15	C₂²×C₅×M₁₆	C₂²	1	2	yes	complemented
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₅×#543	C₄	1	1	yes	characteristic
19	C₅×#539	C₄	1	2	yes	—
20	C₅×#539	C₄	1	4	yes	—
21	C₅×#538	C₄	1	2	yes	—
22	C₅×#538	C₄	1	4	yes	—
23	C₅×#534	C₄	1	1	yes	characteristic
24	C₅×#534	C₄	1	2	yes	—
25	C₅×#529	C₂²	1	2	yes	—
26	C₅×#529	C₂²	1	4	yes	—
27	C₅×#525	C₂²	1	2	yes	—
28	C₅×#525	C₂²	1	4	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₅×#446	C₂²	1	4	yes	complemented
32	C₅×#446	C₂²	1	2	yes	complemented
33	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
34	C₅×#436	C₂²	1	4	yes	complemented
35	C₅×#436	C₂²	1	2	yes	complemented
36	C₅×#435	C₂²	1	4	yes	complemented
37	C₅×#435	C₂²	1	4	yes	complemented
38	C₅×#435	C₂²	1	4	yes	complemented
39	C₅×#435	C₂²	1	4	yes	complemented
40	C₅×#435	C₂²	1	4	yes	complemented
41	C₅×#435	C₂²	1	4	yes	complemented
42	C₅×#435	C₂²	1	4	yes	complemented
43	C₅×#435	C₂²	1	4	yes	complemented
44	C₅×#435	C₂²	1	4	yes	complemented
45	C₅×C₈×D₄	C₂²	1	4	yes	complemented
46	C₅×C₈×D₄	C₂²	1	4	yes	complemented
47	C₅×C₈×D₄	C₂²	1	4	yes	complemented
48	C₅×C₈×D₄	C₂²	1	4	yes	complemented
49	C₅×C₈×D₄	C₂²	1	4	yes	complemented
50	C₅×C₈×D₄	C₂²	1	4	yes	complemented
51	C₅×C₈×D₄	C₂²	1	2	yes	complemented
52	C₅×C₈×D₄	C₂²	1	4	yes	complemented
53	C₅×#433	C₂²	1	4	yes	complemented
54	C₅×#433	C₂²	1	4	yes	complemented
55	C₅×#433	C₂²	1	4	yes	complemented
56	C₅×#432	C₂²	1	2	yes	complemented
57	C₅×#431	C₂²	1	4	yes	complemented
58	C₅×#424	C₂²	1	4	yes	complemented
59	C₅×#424	C₂²	1	2	yes	complemented
60	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
62	C₅×#408	C₂²	1	2	yes	complemented
63	C₅×#408	C₂²	1	4	yes	complemented
64	C₅×#407	C₂²	1	2	yes	complemented
65	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
67	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
69	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
70	C₅×#405	C₂²	1	2	yes	complemented
71	C₅×#405	C₂²	1	4	yes	complemented
72	C₂×C₅×#97	C₂²	1	2	yes	complemented
73	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
74	#60310	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂×C₅×#41	C₂³	1	2	yes	—
76	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂³	1	2	yes	—
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₅×#131	—	4	4	no	—
82	C₂×C₅×M₁₆	—	4	4	no	—
83	C₂×C₅×M₁₆	C₂³	1	4	yes	—
84	C₂×C₅×M₁₆	C₂³	1	2	yes	—
85	C₂×C₅×M₁₆	C₂³	1	2	yes	—
86	C₂×C₅×M₁₆	C₂³	1	4	yes	—
87	C₂²×C₅×C₈	—	4	2	no	—
88	C₂²×C₅×C₈	—	4	2	no	—
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	2	yes	—
91	C₂²×C₅×C₈	C₂³	1	2	yes	—
92	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₅×C₈	C₂³	1	2	yes	—
94	C₂²×C₅×C₈	C₂³	1	4	yes	—
95	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₂²×C₅×C₈	C₂³	1	2	yes	—
97	C₂²×C₅×C₈	C₂³	1	2	yes	—
98	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂²×C₅×C₈	C₂³	1	4	yes	—
100	C₂²×C₅×C₈	C₂³	1	2	yes	—
101	C₅×#126	C₂×C₄	1	4	yes	—
102	C₅×#126	C₂×C₄	1	4	yes	—
103	C₅×#126	C₂×C₄	1	4	yes	—
104	C₅×#125	C₂×C₄	1	2	yes	—
105	C₅×#125	C₂×C₄	1	4	yes	—
106	C₅×#124	C₂×C₄	1	2	yes	—
107	C₅×#124	C₂×C₄	1	4	yes	—
108	C₅×#123	C₂×C₄	1	4	yes	—
109	C₅×#123	C₂×C₄	1	4	yes	—
110	C₅×#123	C₂×C₄	1	4	yes	—
111	C₅×#123	C₂×C₄	1	4	yes	—
112	C₅×#123	C₂×C₄	1	4	yes	—
113	C₅×#123	C₂×C₄	1	4	yes	—
114	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
115	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
116	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
117	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
118	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
119	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
120	C₅×#121	C₂×C₄	1	2	yes	—
121	C₅×#121	C₂×C₄	1	4	yes	—
122	C₅×#121	C₂×C₄	1	2	yes	—
123	C₅×#121	C₂×C₄	1	4	yes	—
124	C₅×#121	C₂×C₄	1	2	yes	—
125	C₅×#121	C₂×C₄	1	4	yes	—
126	C₅×#120	C₂×C₄	1	4	yes	—
127	C₅×#120	C₂×C₄	1	4	yes	—
128	C₅×#120	C₂×C₄	1	4	yes	—
129	C₄×C₅×Q₈	C₂³	1	2	yes	—
130	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
131	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
132	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
133	C₄×C₅×D₄	C₂³	1	4	yes	—
134	C₄×C₅×D₄	C₂³	1	4	yes	—
135	C₄×C₅×D₄	C₂³	1	4	yes	—
136	C₄×C₅×D₄	C₂³	1	4	yes	—
137	C₄×C₅×D₄	C₂³	1	2	yes	—
138	C₅×#117	C₂³	1	2	yes	—
139	C₅×#117	C₂³	1	4	yes	—
140	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
142	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
145	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	2	yes	—
148	C₅×C₄⋊C₈	C₂³	1	4	yes	—
149	C₅×C₄⋊C₈	C₂³	1	4	yes	—
150	C₅×C₄⋊C₈	C₂³	1	4	yes	—
151	C₅×C₄⋊C₈	C₂³	1	4	yes	—
152	C₅×C₄⋊C₈	C₂³	1	2	yes	—
153	C₅×C₄⋊C₈	C₂³	1	4	yes	—
154	C₅×C₄⋊C₈	C₂³	1	2	yes	—
155	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
156	C₅×C₂²⋊C₈	C₂³	1	4	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	4	yes	—
162	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₅×#97	C₂³	1	4	yes	—
165	C₅×#97	C₂³	1	4	yes	—
166	C₅×#97	C₂³	1	4	yes	—
167	C₄×C₅×C₈	C₂³	1	2	yes	—
168	C₄×C₅×C₈	C₂³	1	2	yes	—
169	C₄×C₅×C₈	C₂³	1	4	yes	—
170	C₄×C₅×C₈	C₂³	1	4	yes	—
171	#3459	C₂×C₅	1	1	yes	characteristic
172	#2994	C₂×C₅	1	4	yes	complemented
173	#2992	C₂×C₅	1	2	yes	complemented
174	#2977	C₂×C₅	1	4	yes	complemented
175	#2976	C₂×C₅	1	2	yes	complemented
176	#2973	C₂×C₅	1	1	yes	characteristic, complemented
177	#2972	C₂×C₅	1	2	yes	complemented
178	#2968	C₂×C₅	1	4	yes	complemented
179	#2966	C₂×C₅	1	2	yes	complemented
180	#2933	C₂×C₅	1	4	yes	complemented
181	#2929	C₂×C₅	1	2	yes	complemented
182	C₂×#435	C₂×C₅	1	2	yes	complemented
183	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
184	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
186	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₅×#41	—	4	2	no	—
188	C₅×#41	—	4	2	no	—
189	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
190	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
191	C₂×C₅×D₄	—	2	4	no	—
192	C₂×C₅×D₄	—	2	8	no	—
193	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
194	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
195	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
196	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
197	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
198	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
199	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₅	—	4	1	no	—
201	C₂²×C₄×C₅	—	4	1	no	—
202	C₂²×C₄×C₅	—	4	2	no	—
203	C₂²×C₄×C₅	—	4	1	no	—
204	C₂²×C₄×C₅	—	4	2	no	—
205	C₂²×C₄×C₅	—	4	1	no	—
206	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
208	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
210	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
212	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
213	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
215	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
220	C₅×M₁₆	—	2	8	no	—
221	C₅×M₁₆	—	4	4	no	—
222	C₅×M₁₆	—	4	2	no	—
223	C₅×M₁₆	—	4	2	no	—
224	C₂×C₅×C₈	—	2	2	no	—
225	C₂×C₅×C₈	—	2	4	no	—
226	C₂×C₅×C₈	—	2	4	no	—
227	C₂×C₅×C₈	—	4	1	no	—
228	C₂×C₅×C₈	—	4	2	no	—
229	C₂×C₅×C₈	—	4	2	no	—
230	C₂×C₅×C₈	—	4	1	no	—
231	C₂×C₅×C₈	—	4	1	no	—
232	C₂×C₅×C₈	—	4	4	no	—
233	C₂×C₅×C₈	—	4	2	no	—
234	C₂×C₅×C₈	—	4	2	no	—
235	C₂×C₅×C₈	—	4	4	no	—
236	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
237	C₂×C₅×C₈	C₂⁴	1	2	yes	—
238	C₂×C₅×C₈	C₂⁴	1	2	yes	—
239	C₂×C₅×C₈	C₂⁴	1	2	yes	—
240	C₂×C₅×C₈	C₂⁴	1	4	yes	—
241	C₂×C₅×C₈	C₂⁴	1	4	yes	—
242	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
243	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
244	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
245	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
246	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
247	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
248	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
249	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
250	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
251	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
252	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
253	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
254	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
255	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
256	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
257	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
258	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
259	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
260	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
261	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
262	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
263	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
264	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
265	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
266	C₄²×C₅	C₂²×C₄	1	2	yes	—
267	C₄²×C₅	C₂²×C₄	1	4	yes	—
268	C₄²×C₅	C₂⁴	1	2	yes	—
269	C₄²×C₅	C₂⁴	1	4	yes	—
270	C₂×#131	C₂²×C₅	1	2	yes	complemented
271	C₂²×M₁₆	C₂²×C₅	1	2	yes	complemented
272	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	#543	C₄×C₅	1	1	yes	characteristic
275	#539	C₄×C₅	1	2	yes	—
276	#539	C₄×C₅	1	4	yes	—
277	#538	C₄×C₅	1	2	yes	—
278	#538	C₄×C₅	1	4	yes	—
279	#534	C₄×C₅	1	1	yes	characteristic
280	#534	C₄×C₅	1	2	yes	—
281	#529	C₂²×C₅	1	2	yes	—
282	#529	C₂²×C₅	1	4	yes	—
283	#525	C₂²×C₅	1	2	yes	—
284	#525	C₂²×C₅	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
287	#446	C₂²×C₅	1	2	yes	complemented
288	#446	C₂²×C₅	1	4	yes	complemented
289	C₈×Q₈	C₂²×C₅	1	2	yes	complemented
290	#436	C₂²×C₅	1	2	yes	complemented
291	#436	C₂²×C₅	1	4	yes	complemented
292	#435	C₂²×C₅	1	4	yes	complemented
293	#435	C₂²×C₅	1	4	yes	complemented
294	#435	C₂²×C₅	1	4	yes	complemented
295	#435	C₂²×C₅	1	4	yes	complemented
296	#435	C₂²×C₅	1	4	yes	complemented
297	#435	C₂²×C₅	1	4	yes	complemented
298	#435	C₂²×C₅	1	4	yes	complemented
299	#435	C₂²×C₅	1	4	yes	complemented
300	#435	C₂²×C₅	1	4	yes	complemented
301	C₈×D₄	C₂²×C₅	1	4	yes	complemented
302	C₈×D₄	C₂²×C₅	1	4	yes	complemented
303	C₈×D₄	C₂²×C₅	1	4	yes	complemented
304	C₈×D₄	C₂²×C₅	1	4	yes	complemented
305	C₈×D₄	C₂²×C₅	1	4	yes	complemented
306	C₈×D₄	C₂²×C₅	1	4	yes	complemented
307	C₈×D₄	C₂²×C₅	1	2	yes	complemented
308	C₈×D₄	C₂²×C₅	1	4	yes	complemented
309	#433	C₂²×C₅	1	4	yes	complemented
310	#433	C₂²×C₅	1	4	yes	complemented
311	#433	C₂²×C₅	1	4	yes	complemented
312	#432	C₂²×C₅	1	2	yes	complemented
313	#431	C₂²×C₅	1	4	yes	complemented
314	#424	C₂²×C₅	1	2	yes	complemented
315	#424	C₂²×C₅	1	4	yes	complemented
316	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
317	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
318	#408	C₂²×C₅	1	2	yes	complemented
319	#408	C₂²×C₅	1	4	yes	complemented
320	#407	C₂²×C₅	1	2	yes	complemented
321	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
323	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
325	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
326	#405	C₂²×C₅	1	2	yes	complemented
327	#405	C₂²×C₅	1	4	yes	complemented
328	C₂×#97	C₂²×C₅	1	2	yes	complemented
329	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
330	C₂³×C₅	—	2	2	no	—
331	C₂³×C₅	—	2	4	no	—
332	C₂³×C₅	—	4	1	no	—
333	C₂³×C₅	—	4	1	no	—
334	C₂³×C₅	—	4	1	no	—
335	C₂³×C₅	—	4	1	no	—
336	C₂³×C₅	—	4	2	no	—
337	C₂³×C₅	—	4	2	no	—
338	C₂³×C₅	#131	1	4	yes	complemented
339	C₂³×C₅	C₂³×C₄	1	2	yes	—
340	C₂³×C₅	C₂³×C₄	1	4	yes	—
341	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
342	C₂³×C₅	C₂³×C₄	1	2	yes	—
343	C₅×Q₈	—	4	2	no	—
344	C₅×Q₈	—	4	2	no	—
345	C₅×D₄	—	2	8	no	—
346	C₅×D₄	—	2	8	no	—
347	C₅×D₄	—	2	8	no	—
348	C₅×D₄	—	4	4	no	—
349	C₅×D₄	—	4	2	no	—
350	C₅×D₄	—	4	2	no	—
351	C₅×D₄	—	4	4	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	4	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	4	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	2	no	—
364	C₂×C₄×C₅	—	4	2	no	—
365	C₂×C₄×C₅	—	4	4	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	2	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	2	no	—
370	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
372	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
373	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
374	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
375	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
376	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
377	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
378	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
379	C₅×C₈	—	2	1	no	—
380	C₅×C₈	—	2	2	no	—
381	C₅×C₈	—	2	2	no	—
382	C₅×C₈	—	2	4	no	—
383	C₅×C₈	—	2	2	no	—
384	C₅×C₈	—	2	4	no	—
385	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
386	C₂×#41	C₂³×C₅	1	2	yes	—
387	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
388	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
389	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅	1	2	yes	—
392	#131	—	4	4	no	—
393	C₂×M₁₆	—	4	4	no	—
394	C₂×M₁₆	C₂³×C₅	1	4	yes	—
395	C₂×M₁₆	C₂³×C₅	1	4	yes	—
396	C₂×M₁₆	C₂³×C₅	1	2	yes	—
397	C₂×M₁₆	C₂³×C₅	1	2	yes	—
398	C₂²×C₈	—	4	2	no	—
399	C₂²×C₈	—	4	2	no	—
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	2	yes	—
402	C₂²×C₈	C₂³×C₅	1	2	yes	—
403	C₂²×C₈	C₂³×C₅	1	2	yes	—
404	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₅	1	2	yes	—
407	C₂²×C₈	C₂³×C₅	1	2	yes	—
408	C₂²×C₈	C₂³×C₅	1	4	yes	—
409	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₅	1	2	yes	—
411	C₂²×C₈	C₂³×C₅	1	4	yes	—
412	#126	C₂×C₄×C₅	1	4	yes	—
413	#126	C₂×C₄×C₅	1	4	yes	—
414	#126	C₂×C₄×C₅	1	4	yes	—
415	#125	C₂×C₄×C₅	1	2	yes	—
416	#125	C₂×C₄×C₅	1	4	yes	—
417	#124	C₂×C₄×C₅	1	2	yes	—
418	#124	C₂×C₄×C₅	1	4	yes	—
419	#123	C₂×C₄×C₅	1	4	yes	—
420	#123	C₂×C₄×C₅	1	4	yes	—
421	#123	C₂×C₄×C₅	1	4	yes	—
422	#123	C₂×C₄×C₅	1	4	yes	—
423	#123	C₂×C₄×C₅	1	4	yes	—
424	#123	C₂×C₄×C₅	1	4	yes	—
425	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
426	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
427	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
428	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
429	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
430	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
431	#121	C₂×C₄×C₅	1	2	yes	—
432	#121	C₂×C₄×C₅	1	4	yes	—
433	#121	C₂×C₄×C₅	1	2	yes	—
434	#121	C₂×C₄×C₅	1	4	yes	—
435	#121	C₂×C₄×C₅	1	2	yes	—
436	#121	C₂×C₄×C₅	1	4	yes	—
437	#120	C₂×C₄×C₅	1	4	yes	—
438	#120	C₂×C₄×C₅	1	4	yes	—
439	#120	C₂×C₄×C₅	1	4	yes	—
440	C₄×Q₈	C₂³×C₅	1	2	yes	—
441	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
442	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
443	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
444	C₄×D₄	C₂³×C₅	1	4	yes	—
445	C₄×D₄	C₂³×C₅	1	4	yes	—
446	C₄×D₄	C₂³×C₅	1	4	yes	—
447	C₄×D₄	C₂³×C₅	1	4	yes	—
448	C₄×D₄	C₂³×C₅	1	2	yes	—
449	#117	C₂³×C₅	1	2	yes	—
450	#117	C₂³×C₅	1	4	yes	—
451	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
457	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₅	1	2	yes	—
459	C₄⋊C₈	C₂³×C₅	1	4	yes	—
460	C₄⋊C₈	C₂³×C₅	1	4	yes	—
461	C₄⋊C₈	C₂³×C₅	1	4	yes	—
462	C₄⋊C₈	C₂³×C₅	1	4	yes	—
463	C₄⋊C₈	C₂³×C₅	1	2	yes	—
464	C₄⋊C₈	C₂³×C₅	1	4	yes	—
465	C₄⋊C₈	C₂³×C₅	1	2	yes	—
466	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
467	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
469	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
470	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
471	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
472	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
474	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
475	#97	C₂³×C₅	1	4	yes	—
476	#97	C₂³×C₅	1	4	yes	—
477	#97	C₂³×C₅	1	4	yes	—
478	C₄×C₈	C₂³×C₅	1	2	yes	—
479	C₄×C₈	C₂³×C₅	1	2	yes	—
480	C₄×C₈	C₂³×C₅	1	4	yes	—
481	C₄×C₈	C₂³×C₅	1	4	yes	—
482	C₂²×C₅	—	2	1	no	—
483	C₂²×C₅	—	2	2	no	—
484	C₂²×C₅	—	2	1	no	—
485	C₂²×C₅	—	2	2	no	—
486	C₂²×C₅	—	2	2	no	—
487	C₂²×C₅	—	2	4	no	—
488	C₂²×C₅	—	2	2	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	2	4	no	—
492	C₂²×C₅	—	4	4	no	—
493	C₂²×C₅	—	4	4	no	—
494	C₂²×C₅	—	8	4	no	—
495	C₂²×C₅	C₂×#131	1	2	yes	—
496	C₂²×C₅	C₂×#131	1	4	yes	—
497	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	2	2	no	—
500	C₄×C₅	—	2	2	no	—
501	C₄×C₅	—	2	4	no	—
502	C₄×C₅	—	2	2	no	—
503	C₄×C₅	—	2	4	no	—
504	C₄×C₅	—	2	2	no	—
505	C₄×C₅	—	2	4	no	—
506	C₄×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄×C₅	#585	1	1	yes	characteristic
508	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
510	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
511	#41	—	4	2	no	—
512	#41	—	4	2	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	—	2	8	no	—
517	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
518	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
519	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
520	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
521	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
523	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
532	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
534	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
536	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
538	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
539	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
544	M₁₆	—	2	8	no	—
545	M₁₆	—	4	4	no	—
546	M₁₆	—	4	2	no	—
547	M₁₆	—	4	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	2	4	no	—
550	C₂×C₈	—	2	4	no	—
551	C₂×C₈	—	4	1	no	—
552	C₂×C₈	—	4	2	no	—
553	C₂×C₈	—	4	2	no	—
554	C₂×C₈	—	4	1	no	—
555	C₂×C₈	—	4	2	no	—
556	C₂×C₈	—	4	4	no	—
557	C₂×C₈	—	4	1	no	—
558	C₂×C₈	—	4	4	no	—
559	C₂×C₈	—	4	2	no	—
560	C₂×C₈	C₂⁴×C₅	1	2	yes	—
561	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
562	C₂×C₈	C₂⁴×C₅	1	2	yes	—
563	C₂×C₈	C₂⁴×C₅	1	4	yes	—
564	C₂×C₈	C₂⁴×C₅	1	4	yes	—
565	C₂×C₈	C₂⁴×C₅	1	2	yes	—
566	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
567	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
570	C₄⋊C₄	C₂²×C₄×C₅	1	2	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	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
576	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
577	C₄⋊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	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
590	C₄²	C₂²×C₄×C₅	1	2	yes	—
591	C₄²	C₂²×C₄×C₅	1	4	yes	—
592	C₄²	C₂⁴×C₅	1	2	yes	—
593	C₄²	C₂⁴×C₅	1	4	yes	—
594	C₂×C₅	—	2	2	no	—
595	C₂×C₅	—	2	4	no	—
596	C₂×C₅	—	4	2	no	—
597	C₂×C₅	—	4	4	no	—
598	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂×C₅	C₂²×#131	1	1	yes	characteristic
600	C₂×C₅	#3573	1	1	yes	characteristic
601	C₂³	—	2	2	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	C₅×#131	1	4	yes	complemented
610	C₂³	C₂³×C₄×C₅	1	2	yes	—
611	C₂³	C₂³×C₄×C₅	1	4	yes	—
612	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
613	C₂³	C₂³×C₄×C₅	1	2	yes	—
614	Q₈	—	4	2	no	—
615	Q₈	—	4	2	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	8	no	—
618	D₄	—	2	8	no	—
619	D₄	—	4	2	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
642	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
643	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
644	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
645	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
646	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
648	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
649	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
650	C₈	—	2	1	no	—
651	C₈	—	2	2	no	—
652	C₈	—	2	2	no	—
653	C₈	—	2	4	no	—
654	C₈	—	2	2	no	—
655	C₈	—	2	4	no	—
656	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
657	C₅	#60310	1	1	yes	characteristic, direct product factor, Sylow
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	C₂×C₅×#131	1	2	yes	—
672	C₂²	C₂×C₅×#131	1	4	yes	—
673	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
683	C₄	C₅×#585	1	1	yes	characteristic
684	C₂	—	2	2	no	—
685	C₂	—	2	4	no	—
686	C₂	—	4	2	no	—
687	C₂	—	4	4	no	—
688	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂	C₂²×C₅×#131	1	1	yes	characteristic
690	C₂	C₅×#3573	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×#3459	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×#2994	C₂	semidirect
3. C₅×#2992	C₂	semidirect
4. C₅×#2977	C₂	semidirect
5. C₅×#2976	C₂	semidirect
6. C₅×#2973	C₂	semidirect
7. C₅×#2972	C₂	semidirect
8. C₅×#2968	C₂	semidirect
9. C₅×#2966	C₂	semidirect
10. C₅×#2933	C₂	semidirect
11. C₅×#2929	C₂	semidirect
12. C₂×C₅×#435	C₂	semidirect
13. C₂×C₅×C₈×D₄	C₂	semidirect
14. C₂×C₅×#131	C₂²	semidirect
15. C₂²×C₅×M₁₆	C₂²	semidirect
17. C₂³×C₅×C₈	C₂²	semidirect
31. C₅×#446	C₂²	semidirect
32. C₅×#446	C₂²	semidirect
33. C₅×C₈×Q₈	C₂²	semidirect
34. C₅×#436	C₂²	semidirect
35. C₅×#436	C₂²	semidirect
36. C₅×#435	C₂²	semidirect
37. C₅×#435	C₂²	semidirect
38. C₅×#435	C₂²	semidirect
39. C₅×#435	C₂²	semidirect
40. C₅×#435	C₂²	semidirect
41. C₅×#435	C₂²	semidirect
42. C₅×#435	C₂²	semidirect
43. C₅×#435	C₂²	semidirect
44. C₅×#435	C₂²	semidirect
45. C₅×C₈×D₄	C₂²	semidirect
46. C₅×C₈×D₄	C₂²	semidirect
47. C₅×C₈×D₄	C₂²	semidirect
48. C₅×C₈×D₄	C₂²	semidirect
49. C₅×C₈×D₄	C₂²	semidirect
50. C₅×C₈×D₄	C₂²	semidirect
51. C₅×C₈×D₄	C₂²	semidirect
52. C₅×C₈×D₄	C₂²	semidirect
53. C₅×#433	C₂²	semidirect
54. C₅×#433	C₂²	semidirect
55. C₅×#433	C₂²	semidirect
56. C₅×#432	C₂²	semidirect
57. C₅×#431	C₂²	semidirect
58. C₅×#424	C₂²	semidirect
59. C₅×#424	C₂²	semidirect
60. C₂×C₅×C₄⋊C₈	C₂²	semidirect
61. C₂×C₅×C₄⋊C₈	C₂²	semidirect
62. C₅×#408	C₂²	semidirect
63. C₅×#408	C₂²	semidirect
64. C₅×#407	C₂²	semidirect
67. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
68. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
69. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
70. C₅×#405	C₂²	semidirect
71. C₅×#405	C₂²	semidirect
72. C₂×C₅×#97	C₂²	semidirect
73. C₂×C₄×C₅×C₈	C₂²	semidirect
74. #60310	C₅	direct (N × H)
172. #2994	C₂×C₅	semidirect
173. #2992	C₂×C₅	semidirect
174. #2977	C₂×C₅	semidirect
175. #2976	C₂×C₅	semidirect
176. #2973	C₂×C₅	semidirect
177. #2972	C₂×C₅	semidirect
178. #2968	C₂×C₅	semidirect
179. #2966	C₂×C₅	semidirect
180. #2933	C₂×C₅	semidirect
181. #2929	C₂×C₅	semidirect
182. C₂×#435	C₂×C₅	semidirect
183. C₂×C₈×D₄	C₂×C₅	semidirect
270. C₂×#131	C₂²×C₅	semidirect
271. C₂²×M₁₆	C₂²×C₅	semidirect
273. C₂³×C₈	C₂²×C₅	semidirect
287. #446	C₂²×C₅	semidirect
288. #446	C₂²×C₅	semidirect
289. C₈×Q₈	C₂²×C₅	semidirect
290. #436	C₂²×C₅	semidirect
291. #436	C₂²×C₅	semidirect
292. #435	C₂²×C₅	semidirect
293. #435	C₂²×C₅	semidirect
294. #435	C₂²×C₅	semidirect
295. #435	C₂²×C₅	semidirect
296. #435	C₂²×C₅	semidirect
297. #435	C₂²×C₅	semidirect
298. #435	C₂²×C₅	semidirect
299. #435	C₂²×C₅	semidirect
300. #435	C₂²×C₅	semidirect
301. C₈×D₄	C₂²×C₅	semidirect
302. C₈×D₄	C₂²×C₅	semidirect
303. C₈×D₄	C₂²×C₅	semidirect
304. C₈×D₄	C₂²×C₅	semidirect
305. C₈×D₄	C₂²×C₅	semidirect
306. C₈×D₄	C₂²×C₅	semidirect
307. C₈×D₄	C₂²×C₅	semidirect
308. C₈×D₄	C₂²×C₅	semidirect
309. #433	C₂²×C₅	semidirect
310. #433	C₂²×C₅	semidirect
311. #433	C₂²×C₅	semidirect
312. #432	C₂²×C₅	semidirect
313. #431	C₂²×C₅	semidirect
314. #424	C₂²×C₅	semidirect
315. #424	C₂²×C₅	semidirect
316. C₂×C₄⋊C₈	C₂²×C₅	semidirect
317. C₂×C₄⋊C₈	C₂²×C₅	semidirect
318. #408	C₂²×C₅	semidirect
319. #408	C₂²×C₅	semidirect
320. #407	C₂²×C₅	semidirect
323. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
324. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
325. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
326. #405	C₂²×C₅	semidirect
327. #405	C₂²×C₅	semidirect
328. C₂×#97	C₂²×C₅	semidirect
329. C₂×C₄×C₈	C₂²×C₅	semidirect
338. C₂³×C₅	#131	semidirect
609. C₂³	C₅×#131	semidirect
657. C₅	#60310	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×#3459	2
C₅×#2994	2
C₅×#2992	2
C₅×#2977	2
C₅×#2976	2
C₅×#2973	2
C₅×#2972	2
C₅×#2968	2
C₅×#2966	2
C₅×#2933	2
C₅×#2929	2
C₂×C₅×#435	2
C₂×C₅×C₈×D₄	2
#60310	5

Subgroups — C5×#60310 #11983030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60310 #11983030