Subgroups — C₅×#34332 #11957052

Order 1280.

2388 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×#554	C₂	1	1	yes	maximal, characteristic
2	C₅×#2370	C₂	1	2	yes	maximal, complemented
3	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2360	C₂	1	2	yes	maximal, complemented
5	C₅×#2360	C₂	1	4	yes	maximal, complemented
6	C₅×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₅×D₄×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₅×#2345	C₂	1	2	yes	maximal, complemented
10	C₅×#2330	C₂	1	2	yes	maximal, complemented
11	C₅×#2329	C₂	1	4	yes	maximal, complemented
12	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#389	C₂	1	2	yes	maximal, complemented
16	C₅×#2275	C₂	1	2	yes	maximal
17	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
18	C₅×#554	C₄	1	16	yes	complemented
19	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#125	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	—
33	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₅	C₂²	1	2	yes	—
35	C₅×#391	C₂²	1	1	yes	characteristic
36	C₅×#391	C₂²	1	1	yes	characteristic
37	C₅×#391	C₂²	1	2	yes	—
38	C₅×#391	C₂²	1	4	yes	—
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	2	yes	—
41	C₅×#389	C₂²	1	4	yes	—
42	C₅×#389	C₂²	1	2	yes	—
43	C₅×#389	C₂²	1	2	yes	—
44	C₅×#389	C₂²	1	4	yes	—
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	2	yes	—
47	C₅×#389	C₂²	1	4	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#389	C₂²	1	4	yes	—
51	C₅×#387	C₂²	1	2	yes	—
52	C₅×#387	C₂²	1	2	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#387	C₂²	1	4	yes	—
57	C₅×#385	C₂²	1	4	yes	—
58	C₅×#385	C₂²	1	4	yes	—
59	C₅×#385	C₂²	1	4	yes	—
60	C₅×#384	C₂²	1	1	yes	characteristic
61	C₅×#384	C₂²	1	2	yes	—
62	C₅×#380	C₂²	1	2	yes	—
63	C₅×#380	C₂²	1	4	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
74	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
75	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₅×#376	C₂²	1	2	yes	—
82	C₂×C₅×#95	C₂²	1	4	yes	—
83	C₄³×C₅	C₂²	1	1	yes	characteristic
84	#34332	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Q₈	C₂³	1	2	yes	—
87	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	2	yes	—
89	C₂³×C₄×C₅	C₂³	1	2	yes	—
90	C₂³×C₄×C₅	C₂³	1	4	yes	—
91	C₂³×C₄×C₅	C₂³	1	4	yes	—
92	C₂³×C₄×C₅	C₂³	1	2	yes	—
93	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
94	C₅×#125	C₂×C₄	1	16	yes	complemented
95	C₅×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
96	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
97	C₄×C₅×Q₈	—	4	4	no	—
98	C₄×C₅×Q₈	—	4	4	no	—
99	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
100	C₄×C₅×D₄	—	2	4	no	—
101	C₄×C₅×D₄	—	2	8	no	—
102	C₄×C₅×D₄	C₂×C₄	1	16	yes	—
103	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
104	C₄×C₅×D₄	Q₈	1	8	yes	complemented
105	C₂×C₅×C₄⋊C₄	—	4	4	no	—
106	C₂×C₅×C₄⋊C₄	—	4	8	no	—
107	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
108	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	2	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	4	yes	—
120	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₄²×C₅	—	4	4	no	—
135	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂³	1	2	yes	—
140	C₂×C₄²×C₅	C₂³	1	2	yes	—
141	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₅	C₂³	1	4	yes	—
143	C₂×C₄²×C₅	C₂³	1	4	yes	—
144	C₂×C₄²×C₅	C₂³	1	4	yes	—
145	C₂×C₄²×C₅	C₂³	1	2	yes	—
146	C₂×C₄²×C₅	C₂³	1	2	yes	—
147	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₅	C₂³	1	2	yes	—
149	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₅×#95	C₂³	1	2	yes	—
151	C₅×#95	C₂³	1	4	yes	—
152	C₅×#95	C₂³	1	4	yes	—
153	C₅×#95	C₂³	1	4	yes	—
154	C₅×#95	C₂³	1	2	yes	—
155	C₅×#95	C₂³	1	2	yes	—
156	C₅×#95	C₂³	1	2	yes	—
157	C₅×#95	C₂³	1	2	yes	—
158	C₅×#95	C₂³	1	2	yes	—
159	C₅×#95	C₂³	1	2	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	2	yes	—
165	C₅×#95	C₂³	1	2	yes	—
166	C₂×#554	C₂×C₅	1	1	yes	characteristic
167	#2370	C₂×C₅	1	2	yes	complemented
168	#2369	C₂×C₅	1	1	yes	characteristic, complemented
169	#2360	C₂×C₅	1	4	yes	complemented
170	#2360	C₂×C₅	1	2	yes	complemented
171	Q₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
172	D₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
173	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
174	#2345	C₂×C₅	1	2	yes	complemented
175	#2330	C₂×C₅	1	2	yes	complemented
176	#2329	C₂×C₅	1	4	yes	complemented
177	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
178	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
179	#2295	C₂×C₅	1	1	yes	characteristic, complemented
180	C₂×#389	C₂×C₅	1	2	yes	complemented
181	#2275	C₂×C₅	1	2	yes	—
182	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
183	C₂⁴×C₅	C₂⁴	1	2	yes	—
184	C₂×C₅×Q₈	—	2	2	no	—
185	C₂×C₅×Q₈	—	2	2	no	—
186	C₂×C₅×Q₈	—	4	2	no	—
187	C₂×C₅×Q₈	—	4	2	no	—
188	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
189	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
190	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
191	C₂×C₅×D₄	C₂×Q₈	1	4	yes	—
192	C₂×C₅×D₄	#41	1	4	yes	—
193	C₂²×C₄×C₅	—	2	4	no	—
194	C₂²×C₄×C₅	—	2	4	no	—
195	C₂²×C₄×C₅	—	2	4	no	—
196	C₂²×C₄×C₅	—	2	8	no	—
197	C₂²×C₄×C₅	—	2	4	no	—
198	C₂²×C₄×C₅	—	4	2	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	—	4	4	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	4	4	no	—
203	C₂²×C₄×C₅	—	4	4	no	—
204	C₂²×C₄×C₅	—	4	4	no	—
205	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
206	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
207	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₅×C₄⋊C₄	—	2	2	no	—
225	C₅×C₄⋊C₄	—	2	4	no	—
226	C₅×C₄⋊C₄	—	2	4	no	—
227	C₅×C₄⋊C₄	—	2	2	no	—
228	C₅×C₄⋊C₄	—	2	8	no	—
229	C₅×C₄⋊C₄	—	2	4	no	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	4	4	no	—
232	C₅×C₄⋊C₄	—	4	4	no	—
233	C₅×C₄⋊C₄	—	4	4	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	4	4	no	—
237	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
238	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
239	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
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	8	yes	—
243	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
244	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	8	no	—
247	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
248	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
249	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
250	C₄²×C₅	—	2	2	no	—
251	C₄²×C₅	—	2	4	no	—
252	C₄²×C₅	—	2	2	no	—
253	C₄²×C₅	—	2	4	no	—
254	C₄²×C₅	—	2	2	no	—
255	C₄²×C₅	—	2	2	no	—
256	C₄²×C₅	—	4	2	no	—
257	C₄²×C₅	—	4	2	no	—
258	C₄²×C₅	—	4	4	no	—
259	C₄²×C₅	—	4	1	no	—
260	C₄²×C₅	—	4	4	no	—
261	C₄²×C₅	—	4	4	no	—
262	C₄²×C₅	C₂²×C₄	1	8	yes	—
263	C₄²×C₅	C₂²×C₄	1	4	yes	—
264	C₄²×C₅	C₂×Q₈	1	4	yes	—
265	#554	C₄×C₅	1	16	yes	complemented
266	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×#125	C₂²×C₅	1	2	yes	—
268	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
270	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
271	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
272	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
275	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
281	C₂²×C₄²	C₂²×C₅	1	2	yes	—
282	#391	C₂²×C₅	1	2	yes	—
283	#391	C₂²×C₅	1	4	yes	—
284	#391	C₂²×C₅	1	1	yes	characteristic
285	#391	C₂²×C₅	1	1	yes	characteristic
286	#389	C₂²×C₅	1	2	yes	—
287	#389	C₂²×C₅	1	2	yes	—
288	#389	C₂²×C₅	1	4	yes	—
289	#389	C₂²×C₅	1	4	yes	—
290	#389	C₂²×C₅	1	2	yes	—
291	#389	C₂²×C₅	1	2	yes	—
292	#389	C₂²×C₅	1	4	yes	—
293	#389	C₂²×C₅	1	1	yes	characteristic
294	#389	C₂²×C₅	1	2	yes	—
295	#389	C₂²×C₅	1	2	yes	—
296	#389	C₂²×C₅	1	4	yes	—
297	#389	C₂²×C₅	1	1	yes	characteristic
298	#387	C₂²×C₅	1	2	yes	—
299	#387	C₂²×C₅	1	4	yes	—
300	#387	C₂²×C₅	1	4	yes	—
301	#387	C₂²×C₅	1	4	yes	—
302	#387	C₂²×C₅	1	4	yes	—
303	#387	C₂²×C₅	1	2	yes	—
304	#385	C₂²×C₅	1	4	yes	—
305	#385	C₂²×C₅	1	4	yes	—
306	#385	C₂²×C₅	1	4	yes	—
307	#384	C₂²×C₅	1	1	yes	characteristic
308	#384	C₂²×C₅	1	2	yes	—
309	#380	C₂²×C₅	1	4	yes	—
310	#380	C₂²×C₅	1	2	yes	—
311	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
315	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
317	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
319	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
320	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
321	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
322	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
323	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
324	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
326	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
327	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
328	#376	C₂²×C₅	1	2	yes	—
329	C₂×#95	C₂²×C₅	1	4	yes	—
330	C₄³	C₂²×C₅	1	1	yes	characteristic
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	C₂³×C₄	1	4	yes	—
336	C₂³×C₅	C₂²×Q₈	1	4	yes	—
337	C₂³×C₅	C₂×#41	1	4	yes	—
338	C₂³×C₅	C₂⁵	1	1	yes	characteristic
339	C₅×Q₈	—	2	8	no	—
340	C₅×Q₈	—	4	8	no	—
341	C₅×D₄	C₄×Q₈	1	16	yes	complemented
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	4	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	1	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	16	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	2	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	4	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	4	no	—
368	C₂×C₄×C₅	—	2	4	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	4	16	no	—
377	C₂×C₄×C₅	—	4	8	no	—
378	C₂×C₄×C₅	—	4	8	no	—
379	C₂×C₄×C₅	—	8	8	no	—
380	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
382	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
383	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
385	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
386	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
387	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
388	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
389	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
390	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
391	C₂×C₄×C₅	C₂×#41	1	2	yes	—
392	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
393	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
395	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₅	1	2	yes	—
397	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₅	1	2	yes	—
399	C₂³×C₄	C₂³×C₅	1	2	yes	—
400	C₂³×C₄	C₂³×C₅	1	4	yes	—
401	C₂³×C₄	C₂³×C₅	1	4	yes	—
402	C₂³×C₄	C₂³×C₅	1	2	yes	—
403	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
404	#125	C₂×C₄×C₅	1	16	yes	complemented
405	C₂²⋊Q₈	C₂×C₄×C₅	1	32	yes	complemented
406	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
407	C₄×Q₈	—	4	4	no	—
408	C₄×Q₈	—	4	4	no	—
409	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
410	C₄×D₄	—	2	4	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	C₂×C₄×C₅	1	16	yes	—
413	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
414	C₄×D₄	C₅×Q₈	1	8	yes	complemented
415	C₂×C₄⋊C₄	—	4	4	no	—
416	C₂×C₄⋊C₄	—	4	8	no	—
417	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
418	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
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	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
438	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
444	C₂×C₄²	—	4	4	no	—
445	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₅	1	2	yes	—
447	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₅	1	2	yes	—
449	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₅	1	4	yes	—
452	C₂×C₄²	C₂³×C₅	1	4	yes	—
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₄²	C₂³×C₅	1	4	yes	—
455	C₂×C₄²	C₂³×C₅	1	2	yes	—
456	C₂×C₄²	C₂³×C₅	1	2	yes	—
457	C₂×C₄²	C₂³×C₅	1	2	yes	—
458	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
460	#95	C₂³×C₅	1	2	yes	—
461	#95	C₂³×C₅	1	4	yes	—
462	#95	C₂³×C₅	1	4	yes	—
463	#95	C₂³×C₅	1	4	yes	—
464	#95	C₂³×C₅	1	2	yes	—
465	#95	C₂³×C₅	1	2	yes	—
466	#95	C₂³×C₅	1	2	yes	—
467	#95	C₂³×C₅	1	2	yes	—
468	#95	C₂³×C₅	1	2	yes	—
469	#95	C₂³×C₅	1	2	yes	—
470	#95	C₂³×C₅	1	2	yes	—
471	#95	C₂³×C₅	1	4	yes	—
472	#95	C₂³×C₅	1	4	yes	—
473	#95	C₂³×C₅	1	4	yes	—
474	#95	C₂³×C₅	1	2	yes	—
475	#95	C₂³×C₅	1	2	yes	—
476	C₂²×C₅	—	2	4	no	—
477	C₂²×C₅	—	2	4	no	—
478	C₂²×C₅	—	2	4	no	—
479	C₂²×C₅	—	2	4	no	—
480	C₂²×C₅	—	2	4	no	—
481	C₂²×C₅	—	2	4	no	—
482	C₂²×C₅	C₂×C₄×Q₈	1	8	yes	—
483	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
484	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
485	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
486	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂²×C₅	#585	1	1	yes	characteristic
490	C₄×C₅	—	2	4	no	—
491	C₄×C₅	—	2	4	no	—
492	C₄×C₅	—	2	4	no	—
493	C₄×C₅	—	2	8	no	—
494	C₄×C₅	—	2	2	no	—
495	C₄×C₅	—	2	2	no	—
496	C₄×C₅	—	2	4	no	—
497	C₄×C₅	—	2	2	no	—
498	C₄×C₅	—	2	2	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	2	no	—
501	C₄×C₅	—	4	2	no	—
502	C₄×C₅	—	4	4	no	—
503	C₄×C₅	—	4	2	no	—
504	C₄×C₅	C₂×C₄×Q₈	1	4	yes	—
505	C₄×C₅	#520	1	4	yes	—
506	C₂⁴	C₂⁴×C₅	1	2	yes	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	4	2	no	—
510	C₂×Q₈	—	4	2	no	—
511	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
512	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
513	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
514	C₂×D₄	C₂×C₅×Q₈	1	4	yes	—
515	C₂×D₄	C₅×#41	1	4	yes	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
529	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
530	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	—
531	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
536	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
539	C₂²×C₄	C₂⁴×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	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
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	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	8	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₄⋊C₄	—	4	4	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
562	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
563	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
565	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
566	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
567	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
572	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	4	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	4	no	—
582	C₄²	—	4	4	no	—
583	C₄²	—	4	4	no	—
584	C₄²	—	4	1	no	—
585	C₄²	C₂²×C₄×C₅	1	8	yes	—
586	C₄²	C₂²×C₄×C₅	1	4	yes	—
587	C₄²	C₂×C₅×Q₈	1	4	yes	—
588	C₂×C₅	—	2	8	no	—
589	C₂×C₅	C₂²×C₄×Q₈	1	1	yes	characteristic
590	C₂×C₅	C₂×#520	1	1	yes	characteristic
591	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂×C₅	#3501	1	1	yes	characteristic
593	C₂×C₅	#3503	1	1	yes	characteristic
594	C₂×C₅	#3515	1	1	yes	characteristic
595	C₂×C₅	#3519	1	1	yes	characteristic
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	C₂³×C₄×C₅	1	4	yes	—
601	C₂³	C₂²×C₅×Q₈	1	4	yes	—
602	C₂³	C₂×C₅×#41	1	4	yes	—
603	C₂³	C₂⁵×C₅	1	1	yes	characteristic
604	Q₈	—	2	8	no	—
605	Q₈	—	4	8	no	—
606	D₄	C₄×C₅×Q₈	1	16	yes	complemented
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	16	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	4	16	no	—
642	C₂×C₄	—	4	8	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	8	8	no	—
645	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
647	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
649	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
650	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
652	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
653	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
654	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
655	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
656	C₂×C₄	C₂×C₅×#41	1	2	yes	—
657	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
658	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
659	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
660	C₅	#34332	1	1	yes	characteristic, direct product factor, Sylow
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	C₂×C₄×C₅×Q₈	1	8	yes	—
668	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
669	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
670	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
671	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂²	C₅×#585	1	1	yes	characteristic
675	C₄	—	2	4	no	—
676	C₄	—	2	4	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	8	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	4	no	—
689	C₄	C₂×C₄×C₅×Q₈	1	4	yes	—
690	C₄	C₅×#520	1	4	yes	—
691	C₂	—	2	8	no	—
692	C₂	C₂²×C₄×C₅×Q₈	1	1	yes	characteristic
693	C₂	C₂×C₅×#520	1	1	yes	characteristic
694	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂	C₅×#3501	1	1	yes	characteristic
696	C₂	C₅×#3503	1	1	yes	characteristic
697	C₂	C₅×#3515	1	1	yes	characteristic
698	C₂	C₅×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×D₄	C₂³
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×#2370	C₂	semidirect
3. C₅×#2369	C₂	semidirect
4. C₅×#2360	C₂	semidirect
5. C₅×#2360	C₂	semidirect
6. C₅×Q₈×C₄⋊C₄	C₂	semidirect
9. C₅×#2345	C₂	semidirect
10. C₅×#2330	C₂	semidirect
11. C₅×#2329	C₂	semidirect
12. C₄×C₅×C₄⋊Q₈	C₂	semidirect
13. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
14. C₅×#2295	C₂	semidirect
15. C₂×C₅×#389	C₂	semidirect
18. C₅×#554	C₄	semidirect
84. #34332	C₅	direct (N × H)
93. C₅×C₄⋊Q₈	C₂×C₄	semidirect
94. C₅×#125	C₂×C₄	semidirect
95. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
96. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₄×C₅×Q₈	C₂×C₄	semidirect
104. C₄×C₅×D₄	Q₈	semidirect
107. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
167. #2370	C₂×C₅	semidirect
168. #2369	C₂×C₅	semidirect
169. #2360	C₂×C₅	semidirect
170. #2360	C₂×C₅	semidirect
171. Q₈×C₄⋊C₄	C₂×C₅	semidirect
174. #2345	C₂×C₅	semidirect
175. #2330	C₂×C₅	semidirect
176. #2329	C₂×C₅	semidirect
177. C₄×C₄⋊Q₈	C₂×C₅	semidirect
178. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
179. #2295	C₂×C₅	semidirect
180. C₂×#389	C₂×C₅	semidirect
265. #554	C₄×C₅	semidirect
341. C₅×D₄	C₄×Q₈	semidirect
403. C₄⋊Q₈	C₂×C₄×C₅	semidirect
404. #125	C₂×C₄×C₅	semidirect
405. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
406. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
409. C₄×Q₈	C₂×C₄×C₅	semidirect
414. C₄×D₄	C₅×Q₈	semidirect
417. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
606. D₄	C₄×C₅×Q₈	semidirect
660. C₅	#34332	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×#554	2
C₅×#2370	2
C₅×#2369	2
C₅×#2360	2
C₅×Q₈×C₄⋊C₄	2
C₅×D₄×C₄⋊C₄	2
C₅×#2345	2
C₅×#2330	2
C₅×#2329	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₂×C₅×#389	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34332	5

Subgroups — C5×#34332 #11957052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34332 #11957052