Subgroups — C₅×#34480 #11957200

Order 1280.

2436 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₅×#2376	C₂	1	4	yes	maximal, complemented
3	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	2	yes	maximal, complemented
5	C₅×#2360	C₂	1	2	yes	maximal, complemented
6	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2345	C₂	1	2	yes	maximal, complemented
9	C₅×#2341	C₂	1	2	yes	maximal, complemented
10	C₅×#2335	C₂	1	4	yes	maximal, complemented
11	C₅×#2324	C₂	1	2	yes	maximal, complemented
12	C₅×#2323	C₂	1	2	yes	maximal, complemented
13	C₅×#2316	C₂	1	2	yes	maximal, complemented
14	C₅×#2311	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	2	yes	—
19	C₅×#547	C₄	1	16	yes	complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#123	C₂²	1	4	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×#121	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×#117	C₂²	1	2	yes	—
30	C₂×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₅×#117	C₂²	1	2	yes	—
32	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₅×#391	C₂²	1	2	yes	—
35	C₅×#391	C₂²	1	2	yes	—
36	C₅×#390	C₂²	1	1	yes	characteristic
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#390	C₂²	1	1	yes	characteristic
39	C₅×#390	C₂²	1	1	yes	characteristic
40	C₅×#390	C₂²	1	2	yes	—
41	C₅×#390	C₂²	1	4	yes	—
42	C₅×#390	C₂²	1	4	yes	—
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	4	yes	—
50	C₅×#389	C₂²	1	2	yes	—
51	C₅×#389	C₂²	1	4	yes	—
52	C₅×#389	C₂²	1	2	yes	—
53	C₅×#388	C₂²	1	2	yes	—
54	C₅×#388	C₂²	1	2	yes	—
55	C₅×#388	C₂²	1	2	yes	—
56	C₅×#388	C₂²	1	2	yes	—
57	C₅×#388	C₂²	1	4	yes	—
58	C₅×#388	C₂²	1	4	yes	—
59	C₅×#388	C₂²	1	4	yes	—
60	C₅×#387	C₂²	1	4	yes	—
61	C₅×#387	C₂²	1	4	yes	—
62	C₅×#387	C₂²	1	4	yes	—
63	C₅×#386	C₂²	1	4	yes	—
64	C₅×#386	C₂²	1	4	yes	—
65	C₅×#385	C₂²	1	4	yes	—
66	C₅×#385	C₂²	1	4	yes	—
67	C₅×#384	C₂²	1	1	yes	characteristic
68	C₅×#380	C₂²	1	4	yes	—
69	C₅×#380	C₂²	1	4	yes	—
70	C₅×#380	C₂²	1	4	yes	—
71	C₅×#380	C₂²	1	2	yes	—
72	C₅×#380	C₂²	1	2	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₄³×C₅	C₂²	1	1	yes	characteristic
84	#34480	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂×C₅×#41	—	4	4	no	—
86	C₂×C₅×#41	—	4	4	no	—
87	C₂×C₅×#41	C₂×C₄	1	16	yes	complemented
88	C₂²×C₅×Q₈	C₂³	1	2	yes	—
89	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂²×C₅×D₄	C₂³	1	4	yes	—
92	C₂³×C₄×C₅	C₂³	1	2	yes	—
93	C₂³×C₄×C₅	C₂³	1	2	yes	—
94	C₂³×C₄×C₅	C₂³	1	4	yes	—
95	C₂³×C₄×C₅	C₂³	1	4	yes	—
96	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₅×#123	C₂×C₄	1	32	yes	complemented
98	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
99	C₅×#121	C₂×C₄	1	16	yes	—
100	C₄×C₅×Q₈	—	4	4	no	—
101	C₄×C₅×Q₈	—	4	4	no	—
102	C₄×C₅×D₄	—	4	4	no	—
103	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
104	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
105	C₅×#117	—	4	4	no	—
106	C₅×#117	—	4	4	no	—
107	C₅×#117	—	4	4	no	—
108	C₂×C₅×C₄⋊C₄	—	4	4	no	—
109	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
143	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₅	C₂³	1	2	yes	—
149	C₂×C₄²×C₅	C₂³	1	2	yes	—
150	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₅	C₂³	1	4	yes	—
152	C₂×C₄²×C₅	C₂³	1	4	yes	—
153	C₂×C₄²×C₅	C₂³	1	4	yes	—
154	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
155	C₅×#95	C₂³	1	2	yes	—
156	C₅×#95	C₂³	1	2	yes	—
157	C₅×#95	C₂³	1	4	yes	—
158	C₅×#95	C₂³	1	2	yes	—
159	C₅×#95	C₂³	1	4	yes	—
160	C₅×#95	C₂³	1	2	yes	—
161	C₅×#95	C₂³	1	4	yes	—
162	C₅×#95	C₂³	1	4	yes	—
163	C₅×#95	C₂³	1	4	yes	—
164	C₅×#95	C₂³	1	4	yes	—
165	C₅×#95	C₂³	1	2	yes	—
166	C₅×#95	C₂³	1	2	yes	—
167	C₂×#547	C₂×C₅	1	1	yes	characteristic
168	#2376	C₂×C₅	1	4	yes	complemented
169	#2365	C₂×C₅	1	1	yes	characteristic, complemented
170	#2363	C₂×C₅	1	2	yes	complemented
171	#2360	C₂×C₅	1	2	yes	complemented
172	#2354	C₂×C₅	1	1	yes	characteristic, complemented
173	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
174	#2345	C₂×C₅	1	2	yes	complemented
175	#2341	C₂×C₅	1	2	yes	complemented
176	#2335	C₂×C₅	1	4	yes	complemented
177	#2324	C₂×C₅	1	2	yes	complemented
178	#2323	C₂×C₅	1	2	yes	complemented
179	#2316	C₂×C₅	1	2	yes	complemented
180	#2311	C₂×C₅	1	2	yes	complemented
181	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
182	#2293	C₂×C₅	1	1	yes	characteristic, complemented
183	#2293	C₂×C₅	1	1	yes	characteristic, complemented
184	C₂⁴×C₅	C₂⁴	1	2	yes	—
185	C₂⁴×C₅	C₂⁴	1	2	yes	—
186	C₅×#41	—	4	32	no	—
187	C₂×C₅×Q₈	—	2	4	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
190	C₂×C₅×D₄	—	2	2	no	—
191	C₂×C₅×D₄	—	2	2	no	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	4	4	no	—
195	C₂×C₅×D₄	—	4	4	no	—
196	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
197	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
198	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	2	4	no	—
201	C₂²×C₄×C₅	—	2	4	no	—
202	C₂²×C₄×C₅	—	2	4	no	—
203	C₂²×C₄×C₅	—	4	4	no	—
204	C₂²×C₄×C₅	—	4	4	no	—
205	C₂²×C₄×C₅	—	4	4	no	—
206	C₂²×C₄×C₅	—	4	4	no	—
207	C₂²×C₄×C₅	—	4	4	no	—
208	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
209	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
210	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	2	4	no	—
228	C₅×C₄⋊C₄	—	2	2	no	—
229	C₅×C₄⋊C₄	—	2	4	no	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	4	4	no	—
233	C₅×C₄⋊C₄	—	4	2	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	4	2	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	4	4	no	—
239	C₅×C₄⋊C₄	—	4	4	no	—
240	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
241	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
242	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
243	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
244	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	4	2	no	—
248	C₅×C₂²⋊C₄	—	4	2	no	—
249	C₅×C₂²⋊C₄	—	4	4	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	—	4	2	no	—
252	C₅×C₂²⋊C₄	—	4	2	no	—
253	C₅×C₂²⋊C₄	—	4	2	no	—
254	C₅×C₂²⋊C₄	—	4	4	no	—
255	C₅×C₂²⋊C₄	—	4	4	no	—
256	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
257	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
258	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
259	C₄²×C₅	—	2	2	no	—
260	C₄²×C₅	—	2	2	no	—
261	C₄²×C₅	—	2	4	no	—
262	C₄²×C₅	—	2	4	no	—
263	C₄²×C₅	—	2	2	no	—
264	C₄²×C₅	—	2	2	no	—
265	C₄²×C₅	—	2	2	no	—
266	C₄²×C₅	—	4	1	no	—
267	C₄²×C₅	—	4	4	no	—
268	C₄²×C₅	—	4	4	no	—
269	C₄²×C₅	—	4	4	no	—
270	C₄²×C₅	C₂²×C₄	1	4	yes	—
271	C₂²×#41	C₂²×C₅	1	2	yes	—
272	#547	C₄×C₅	1	16	yes	complemented
273	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×#123	C₂²×C₅	1	4	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
276	C₂×#121	C₂²×C₅	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
278	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×#117	C₂²×C₅	1	2	yes	—
283	C₂×#117	C₂²×C₅	1	2	yes	—
284	C₂×#117	C₂²×C₅	1	2	yes	—
285	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
286	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
287	#391	C₂²×C₅	1	2	yes	—
288	#391	C₂²×C₅	1	2	yes	—
289	#390	C₂²×C₅	1	1	yes	characteristic
290	#390	C₂²×C₅	1	2	yes	—
291	#390	C₂²×C₅	1	1	yes	characteristic
292	#390	C₂²×C₅	1	4	yes	—
293	#390	C₂²×C₅	1	4	yes	—
294	#390	C₂²×C₅	1	1	yes	characteristic
295	#390	C₂²×C₅	1	1	yes	characteristic
296	#389	C₂²×C₅	1	2	yes	—
297	#389	C₂²×C₅	1	2	yes	—
298	#389	C₂²×C₅	1	1	yes	characteristic
299	#389	C₂²×C₅	1	4	yes	—
300	#389	C₂²×C₅	1	2	yes	—
301	#389	C₂²×C₅	1	4	yes	—
302	#389	C₂²×C₅	1	2	yes	—
303	#389	C₂²×C₅	1	1	yes	characteristic
304	#389	C₂²×C₅	1	1	yes	characteristic
305	#389	C₂²×C₅	1	1	yes	characteristic
306	#388	C₂²×C₅	1	4	yes	—
307	#388	C₂²×C₅	1	4	yes	—
308	#388	C₂²×C₅	1	2	yes	—
309	#388	C₂²×C₅	1	2	yes	—
310	#388	C₂²×C₅	1	4	yes	—
311	#388	C₂²×C₅	1	2	yes	—
312	#388	C₂²×C₅	1	2	yes	—
313	#387	C₂²×C₅	1	4	yes	—
314	#387	C₂²×C₅	1	4	yes	—
315	#387	C₂²×C₅	1	4	yes	—
316	#386	C₂²×C₅	1	4	yes	—
317	#386	C₂²×C₅	1	4	yes	—
318	#385	C₂²×C₅	1	4	yes	—
319	#385	C₂²×C₅	1	4	yes	—
320	#384	C₂²×C₅	1	1	yes	characteristic
321	#380	C₂²×C₅	1	4	yes	—
322	#380	C₂²×C₅	1	4	yes	—
323	#380	C₂²×C₅	1	4	yes	—
324	#380	C₂²×C₅	1	2	yes	—
325	#380	C₂²×C₅	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
336	C₄³	C₂²×C₅	1	1	yes	characteristic
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	—	2	2	no	—
340	C₂³×C₅	—	2	2	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	—	2	2	no	—
347	C₂³×C₅	—	2	2	no	—
348	C₂³×C₅	—	2	2	no	—
349	C₂³×C₅	C₂³×C₄	1	4	yes	—
350	C₂³×C₅	C₂³×C₄	1	4	yes	—
351	C₂³×C₅	C₂⁵	1	1	yes	characteristic
352	C₅×Q₈	—	2	16	no	—
353	C₅×D₄	—	2	8	no	—
354	C₅×D₄	—	2	8	no	—
355	C₅×D₄	—	4	16	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	4	no	—
359	C₂×C₄×C₅	—	2	4	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	16	no	—
367	C₂×C₄×C₅	—	2	16	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	4	no	—
380	C₂×C₄×C₅	—	2	4	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	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	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	4	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	4	16	no	—
393	C₂×C₄×C₅	—	8	8	no	—
394	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
395	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
396	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
397	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
398	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
399	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
400	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
401	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
404	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
405	C₂×#41	—	4	4	no	—
406	C₂×#41	—	4	4	no	—
407	C₂×#41	C₂×C₄×C₅	1	16	yes	complemented
408	C₂²×Q₈	C₂³×C₅	1	2	yes	—
409	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₅	1	4	yes	—
412	C₂³×C₄	C₂³×C₅	1	2	yes	—
413	C₂³×C₄	C₂³×C₅	1	2	yes	—
414	C₂³×C₄	C₂³×C₅	1	4	yes	—
415	C₂³×C₄	C₂³×C₅	1	4	yes	—
416	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
417	#123	C₂×C₄×C₅	1	32	yes	complemented
418	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
419	#121	C₂×C₄×C₅	1	16	yes	—
420	C₄×Q₈	—	4	4	no	—
421	C₄×Q₈	—	4	4	no	—
422	C₄×D₄	—	4	4	no	—
423	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
424	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
425	#117	—	4	4	no	—
426	#117	—	4	4	no	—
427	#117	—	4	4	no	—
428	C₂×C₄⋊C₄	—	4	4	no	—
429	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
430	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
437	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
463	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₅	1	2	yes	—
466	C₂×C₄²	C₂³×C₅	1	2	yes	—
467	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₅	1	4	yes	—
471	C₂×C₄²	C₂³×C₅	1	4	yes	—
472	C₂×C₄²	C₂³×C₅	1	4	yes	—
473	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
475	#95	C₂³×C₅	1	2	yes	—
476	#95	C₂³×C₅	1	2	yes	—
477	#95	C₂³×C₅	1	4	yes	—
478	#95	C₂³×C₅	1	2	yes	—
479	#95	C₂³×C₅	1	4	yes	—
480	#95	C₂³×C₅	1	2	yes	—
481	#95	C₂³×C₅	1	4	yes	—
482	#95	C₂³×C₅	1	4	yes	—
483	#95	C₂³×C₅	1	4	yes	—
484	#95	C₂³×C₅	1	4	yes	—
485	#95	C₂³×C₅	1	2	yes	—
486	#95	C₂³×C₅	1	2	yes	—
487	C₂²×C₅	—	2	4	no	—
488	C₂²×C₅	—	2	4	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	2	4	no	—
491	C₂²×C₅	—	2	4	no	—
492	C₂²×C₅	—	2	4	no	—
493	C₂²×C₅	—	4	2	no	—
494	C₂²×C₅	—	4	2	no	—
495	C₂²×C₅	—	4	2	no	—
496	C₂²×C₅	—	4	2	no	—
497	C₂²×C₅	—	4	2	no	—
498	C₂²×C₅	—	4	2	no	—
499	C₂²×C₅	—	4	2	no	—
500	C₂²×C₅	—	4	2	no	—
501	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
502	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
506	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
507	C₂²×C₅	#585	1	1	yes	characteristic
508	C₄×C₅	—	2	4	no	—
509	C₄×C₅	—	2	8	no	—
510	C₄×C₅	—	2	4	no	—
511	C₄×C₅	—	2	2	no	—
512	C₄×C₅	—	2	2	no	—
513	C₄×C₅	—	4	1	no	—
514	C₄×C₅	—	4	4	no	—
515	C₄×C₅	—	4	2	no	—
516	C₄×C₅	—	4	2	no	—
517	C₄×C₅	—	4	1	no	—
518	C₄×C₅	—	4	2	no	—
519	C₄×C₅	—	4	1	no	—
520	C₄×C₅	—	4	2	no	—
521	C₄×C₅	#518	1	4	yes	—
522	C₄×C₅	#520	1	4	yes	—
523	C₂⁴	C₂⁴×C₅	1	2	yes	—
524	C₂⁴	C₂⁴×C₅	1	2	yes	—
525	#41	—	4	32	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	4	4	no	—
534	C₂×D₄	—	4	4	no	—
535	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
536	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
537	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	4	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
548	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
549	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
550	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	2	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
581	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
582	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	2	4	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	4	4	no	—
606	C₄²	—	4	4	no	—
607	C₄²	—	4	4	no	—
608	C₄²	—	4	1	no	—
609	C₄²	C₂²×C₄×C₅	1	4	yes	—
610	C₂×C₅	—	4	4	no	—
611	C₂×C₅	—	4	4	no	—
612	C₂×C₅	C₂×#518	1	1	yes	characteristic
613	C₂×C₅	C₂×#520	1	1	yes	characteristic
614	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂×C₅	#3546	1	1	yes	characteristic
616	C₂×C₅	#3547	1	1	yes	characteristic
617	C₂×C₅	#3548	1	1	yes	characteristic
618	C₂×C₅	#3552	1	1	yes	characteristic
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	C₂³×C₄×C₅	1	4	yes	—
632	C₂³	C₂³×C₄×C₅	1	4	yes	—
633	C₂³	C₂⁵×C₅	1	1	yes	characteristic
634	Q₈	—	2	16	no	—
635	D₄	—	2	8	no	—
636	D₄	—	2	8	no	—
637	D₄	—	4	16	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	16	no	—
649	C₂×C₄	—	2	16	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	4	16	no	—
675	C₂×C₄	—	8	8	no	—
676	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
677	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
678	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
679	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
680	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
681	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
682	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
683	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
684	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
685	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
686	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
687	C₅	#34480	1	1	yes	characteristic, direct product factor, Sylow
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
703	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂²	C₅×#585	1	1	yes	characteristic
709	C₄	—	2	4	no	—
710	C₄	—	2	8	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	C₅×#518	1	4	yes	—
723	C₄	C₅×#520	1	4	yes	—
724	C₂	—	4	4	no	—
725	C₂	—	4	4	no	—
726	C₂	C₂×C₅×#518	1	1	yes	characteristic
727	C₂	C₂×C₅×#520	1	1	yes	characteristic
728	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
729	C₂	C₅×#3546	1	1	yes	characteristic
730	C₂	C₅×#3547	1	1	yes	characteristic
731	C₂	C₅×#3548	1	1	yes	characteristic
732	C₂	C₅×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2376	C₂	semidirect
3. C₅×#2365	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2360	C₂	semidirect
6. C₅×#2354	C₂	semidirect
7. C₅×D₄×C₄⋊C₄	C₂	semidirect
8. C₅×#2345	C₂	semidirect
9. C₅×#2341	C₂	semidirect
10. C₅×#2335	C₂	semidirect
11. C₅×#2324	C₂	semidirect
12. C₅×#2323	C₂	semidirect
13. C₅×#2316	C₂	semidirect
14. C₅×#2311	C₂	semidirect
15. C₄×C₅×C₄⋊Q₈	C₂	semidirect
16. C₅×#2293	C₂	semidirect
17. C₅×#2293	C₂	semidirect
19. C₅×#547	C₄	semidirect
84. #34480	C₅	direct (N × H)
87. C₂×C₅×#41	C₂×C₄	semidirect
96. C₅×C₄⋊Q₈	C₂×C₄	semidirect
97. C₅×#123	C₂×C₄	semidirect
98. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
104. C₄×C₅×D₄	C₂×C₄	semidirect
109. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
168. #2376	C₂×C₅	semidirect
169. #2365	C₂×C₅	semidirect
170. #2363	C₂×C₅	semidirect
171. #2360	C₂×C₅	semidirect
172. #2354	C₂×C₅	semidirect
173. D₄×C₄⋊C₄	C₂×C₅	semidirect
174. #2345	C₂×C₅	semidirect
175. #2341	C₂×C₅	semidirect
176. #2335	C₂×C₅	semidirect
177. #2324	C₂×C₅	semidirect
178. #2323	C₂×C₅	semidirect
179. #2316	C₂×C₅	semidirect
180. #2311	C₂×C₅	semidirect
181. C₄×C₄⋊Q₈	C₂×C₅	semidirect
182. #2293	C₂×C₅	semidirect
183. #2293	C₂×C₅	semidirect
272. #547	C₄×C₅	semidirect
407. C₂×#41	C₂×C₄×C₅	semidirect
416. C₄⋊Q₈	C₂×C₄×C₅	semidirect
417. #123	C₂×C₄×C₅	semidirect
418. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
424. C₄×D₄	C₂×C₄×C₅	semidirect
429. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
687. C₅	#34480	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×#547	2
C₅×#2376	2
C₅×#2365	2
C₅×#2363	2
C₅×#2360	2
C₅×#2354	2
C₅×D₄×C₄⋊C₄	2
C₅×#2345	2
C₅×#2341	2
C₅×#2335	2
C₅×#2324	2
C₅×#2323	2
C₅×#2316	2
C₅×#2311	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2293	2
#34480	5

Subgroups — C5×#34480 #11957200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34480 #11957200