Subgroups — C₅×#34334 #11957054

Order 1280.

2500 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#2369	C₂	1	2	yes	maximal, complemented
3	C₅×#2368	C₂	1	4	yes	maximal, complemented
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2360	C₂	1	2	yes	maximal, complemented
6	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2349	C₂	1	2	yes	maximal
8	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₅×Q₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#2331	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×#391	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	C₂³×C₅×Q₈	C₂²	1	2	yes	—
19	C₅×D₄×Q₈	C₄	1	16	yes	complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅	C₂²	1	2	yes	—
34	C₅×#391	C₂²	1	1	yes	characteristic
35	C₅×#391	C₂²	1	2	yes	—
36	C₅×#391	C₂²	1	4	yes	—
37	C₅×#391	C₂²	1	2	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	4	yes	—
40	C₅×#391	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	4	yes	—
42	C₅×#391	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	2	yes	—
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×#387	C₂²	1	2	yes	—
51	C₅×#387	C₂²	1	2	yes	—
52	C₅×#387	C₂²	1	4	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#385	C₂²	1	4	yes	—
57	C₅×#385	C₂²	1	4	yes	—
58	C₅×#385	C₂²	1	4	yes	—
59	C₅×#384	C₂²	1	1	yes	characteristic
60	C₅×#382	C₂²	1	2	yes	—
61	C₅×#380	C₂²	1	2	yes	—
62	C₅×#380	C₂²	1	4	yes	—
63	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
70	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₅×C₂²⋊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	4	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₅×#376	C₂²	1	2	yes	—
81	C₂×C₅×#95	C₂²	1	4	yes	—
82	C₂×C₅×#95	C₂²	1	4	yes	—
83	C₄³×C₅	C₂²	1	1	yes	characteristic
84	#34334	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂²×C₅×Q₈	—	4	4	no	—
86	C₂²×C₅×Q₈	—	4	4	no	—
87	C₂²×C₅×Q₈	C₂×C₄	1	16	yes	complemented
88	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Q₈	C₂³	1	2	yes	—
90	C₂²×C₅×Q₈	C₂³	1	4	yes	—
91	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₅	C₂³	1	2	yes	—
97	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₅×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
99	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
100	C₅×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
101	C₄×C₅×Q₈	—	4	4	no	—
102	C₄×C₅×Q₈	—	4	4	no	—
103	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
104	C₄×C₅×D₄	—	2	4	no	—
105	C₄×C₅×D₄	—	2	8	no	—
106	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
107	C₄×C₅×D₄	C₂×C₄	1	16	yes	—
108	C₄×C₅×D₄	Q₈	1	8	yes	complemented
109	C₂×C₅×C₄⋊C₄	—	4	4	no	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₄²×C₅	—	4	4	no	—
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
139	C₂×C₄²×C₅	C₂³	1	2	yes	—
140	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₅	C₂³	1	4	yes	—
142	C₂×C₄²×C₅	C₂³	1	4	yes	—
143	C₂×C₄²×C₅	C₂³	1	4	yes	—
144	C₂×C₄²×C₅	C₂³	1	2	yes	—
145	C₂×C₄²×C₅	C₂³	1	2	yes	—
146	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂³	1	2	yes	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₅×#95	C₂³	1	2	yes	—
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	4	yes	—
155	C₅×#95	C₂³	1	4	yes	—
156	C₅×#95	C₂³	1	4	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	2	yes	—
162	C₅×#95	C₂³	1	2	yes	—
163	C₅×#95	C₂³	1	2	yes	—
164	C₅×#95	C₂³	1	4	yes	—
165	C₅×#95	C₂³	1	4	yes	—
166	C₅×#95	C₂³	1	2	yes	—
167	C₂×D₄×Q₈	C₂×C₅	1	1	yes	characteristic
168	#2369	C₂×C₅	1	2	yes	complemented
169	#2368	C₂×C₅	1	4	yes	complemented
170	#2365	C₂×C₅	1	1	yes	characteristic, complemented
171	#2360	C₂×C₅	1	2	yes	complemented
172	#2355	C₂×C₅	1	1	yes	characteristic, complemented
173	#2349	C₂×C₅	1	2	yes	—
174	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
175	Q₈×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
176	#2331	C₂×C₅	1	2	yes	complemented
177	#2329	C₂×C₅	1	4	yes	complemented
178	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
179	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
180	#2295	C₂×C₅	1	1	yes	characteristic, complemented
181	C₂×#391	C₂×C₅	1	2	yes	complemented
182	#2275	C₂×C₅	1	2	yes	—
183	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
184	C₂⁴×C₅	C₂⁴	1	2	yes	—
185	C₂×C₅×Q₈	—	2	4	no	—
186	C₂×C₅×Q₈	—	2	4	no	—
187	C₂×C₅×Q₈	—	2	2	no	—
188	C₂×C₅×Q₈	—	2	2	no	—
189	C₂×C₅×Q₈	—	4	4	no	—
190	C₂×C₅×Q₈	—	4	4	no	—
191	C₂×C₅×Q₈	—	4	32	no	—
192	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
193	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
194	C₂×C₅×Q₈	C₂²×C₄	1	16	yes	—
195	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
196	C₂×C₅×D₄	C₂×Q₈	1	4	yes	—
197	C₂×C₅×D₄	#41	1	4	yes	—
198	C₂²×C₄×C₅	—	2	4	no	—
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	2	4	no	—
201	C₂²×C₄×C₅	—	2	8	no	—
202	C₂²×C₄×C₅	—	2	4	no	—
203	C₂²×C₄×C₅	—	4	2	no	—
204	C₂²×C₄×C₅	—	4	2	no	—
205	C₂²×C₄×C₅	—	4	2	no	—
206	C₂²×C₄×C₅	—	4	4	no	—
207	C₂²×C₄×C₅	—	4	4	no	—
208	C₂²×C₄×C₅	—	4	4	no	—
209	C₂²×C₄×C₅	—	4	4	no	—
210	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
211	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
212	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	complemented
213	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	2	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	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	2	yes	—
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	4	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	4	no	—
235	C₅×C₄⋊C₄	—	4	4	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	8	yes	—
243	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
244	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
245	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
246	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	8	no	—
249	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
250	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
251	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	complemented
252	C₄²×C₅	—	2	2	no	—
253	C₄²×C₅	—	2	4	no	—
254	C₄²×C₅	—	2	2	no	—
255	C₄²×C₅	—	2	4	no	—
256	C₄²×C₅	—	2	2	no	—
257	C₄²×C₅	—	2	2	no	—
258	C₄²×C₅	—	4	2	no	—
259	C₄²×C₅	—	4	2	no	—
260	C₄²×C₅	—	4	4	no	—
261	C₄²×C₅	—	4	1	no	—
262	C₄²×C₅	—	4	4	no	—
263	C₄²×C₅	—	4	4	no	—
264	C₄²×C₅	C₂²×C₄	1	8	yes	—
265	C₄²×C₅	C₂²×C₄	1	4	yes	—
266	C₄²×C₅	C₂×Q₈	1	4	yes	complemented
267	C₂³×Q₈	C₂²×C₅	1	2	yes	—
268	D₄×Q₈	C₄×C₅	1	16	yes	complemented
269	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
271	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
274	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
275	C₂×C₄×Q₈	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	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
282	C₂²×C₄²	C₂²×C₅	1	2	yes	—
283	#391	C₂²×C₅	1	2	yes	—
284	#391	C₂²×C₅	1	4	yes	—
285	#391	C₂²×C₅	1	4	yes	—
286	#391	C₂²×C₅	1	4	yes	—
287	#391	C₂²×C₅	1	1	yes	characteristic
288	#391	C₂²×C₅	1	2	yes	—
289	#391	C₂²×C₅	1	2	yes	—
290	#391	C₂²×C₅	1	4	yes	—
291	#391	C₂²×C₅	1	1	yes	characteristic
292	#389	C₂²×C₅	1	2	yes	—
293	#389	C₂²×C₅	1	2	yes	—
294	#389	C₂²×C₅	1	4	yes	—
295	#389	C₂²×C₅	1	2	yes	—
296	#389	C₂²×C₅	1	2	yes	—
297	#389	C₂²×C₅	1	1	yes	characteristic
298	#389	C₂²×C₅	1	1	yes	characteristic
299	#387	C₂²×C₅	1	2	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	4	yes	—
304	#387	C₂²×C₅	1	2	yes	—
305	#385	C₂²×C₅	1	4	yes	—
306	#385	C₂²×C₅	1	4	yes	—
307	#385	C₂²×C₅	1	4	yes	—
308	#384	C₂²×C₅	1	1	yes	characteristic
309	#382	C₂²×C₅	1	2	yes	—
310	#380	C₂²×C₅	1	4	yes	—
311	#380	C₂²×C₅	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
318	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
320	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
321	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
322	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
323	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
324	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
326	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
327	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
329	#376	C₂²×C₅	1	2	yes	—
330	C₂×#95	C₂²×C₅	1	4	yes	—
331	C₂×#95	C₂²×C₅	1	4	yes	—
332	C₄³	C₂²×C₅	1	1	yes	characteristic
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	2	2	no	—
337	C₂³×C₅	C₂³×C₄	1	4	yes	—
338	C₂³×C₅	C₂²×Q₈	1	4	yes	—
339	C₂³×C₅	C₂×#41	1	4	yes	—
340	C₂³×C₅	C₂⁵	1	1	yes	characteristic
341	C₅×Q₈	—	2	8	no	—
342	C₅×Q₈	—	2	16	no	—
343	C₅×Q₈	—	4	16	no	—
344	C₅×D₄	C₄×Q₈	1	16	yes	complemented
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	4	no	—
352	C₂×C₄×C₅	—	2	4	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	1	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	16	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	4	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	2	no	—
372	C₂×C₄×C₅	—	2	4	no	—
373	C₂×C₄×C₅	—	2	2	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	4	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	4	16	no	—
380	C₂×C₄×C₅	—	4	8	no	—
381	C₂×C₄×C₅	—	4	8	no	—
382	C₂×C₄×C₅	—	8	8	no	—
383	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
387	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
388	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
389	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
390	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
391	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
392	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
393	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
394	C₂×C₄×C₅	C₂×#41	1	2	yes	—
395	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
398	C₂²×Q₈	—	4	4	no	—
399	C₂²×Q₈	—	4	4	no	—
400	C₂²×Q₈	C₂×C₄×C₅	1	16	yes	complemented
401	C₂²×Q₈	C₂³×C₅	1	2	yes	—
402	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₅	1	4	yes	—
404	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₅	1	2	yes	—
406	C₂³×C₄	C₂³×C₅	1	2	yes	—
407	C₂³×C₄	C₂³×C₅	1	4	yes	—
408	C₂³×C₄	C₂³×C₅	1	4	yes	—
409	C₂³×C₄	C₂³×C₅	1	2	yes	—
410	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
411	C₄⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
412	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
413	C₂²⋊Q₈	C₂×C₄×C₅	1	32	yes	complemented
414	C₄×Q₈	—	4	4	no	—
415	C₄×Q₈	—	4	4	no	—
416	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
417	C₄×D₄	—	2	4	no	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
420	C₄×D₄	C₂×C₄×C₅	1	16	yes	—
421	C₄×D₄	C₅×Q₈	1	8	yes	complemented
422	C₂×C₄⋊C₄	—	4	4	no	—
423	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₅	1	2	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	1	yes	characteristic
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	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
446	C₂×C₄²	—	4	4	no	—
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	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	4	yes	—
454	C₂×C₄²	C₂³×C₅	1	4	yes	—
455	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅	1	4	yes	—
457	C₂×C₄²	C₂³×C₅	1	2	yes	—
458	C₂×C₄²	C₂³×C₅	1	2	yes	—
459	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₅	1	2	yes	—
461	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
462	#95	C₂³×C₅	1	2	yes	—
463	#95	C₂³×C₅	1	2	yes	—
464	#95	C₂³×C₅	1	4	yes	—
465	#95	C₂³×C₅	1	4	yes	—
466	#95	C₂³×C₅	1	4	yes	—
467	#95	C₂³×C₅	1	4	yes	—
468	#95	C₂³×C₅	1	4	yes	—
469	#95	C₂³×C₅	1	4	yes	—
470	#95	C₂³×C₅	1	2	yes	—
471	#95	C₂³×C₅	1	2	yes	—
472	#95	C₂³×C₅	1	2	yes	—
473	#95	C₂³×C₅	1	2	yes	—
474	#95	C₂³×C₅	1	2	yes	—
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	4	yes	—
479	#95	C₂³×C₅	1	2	yes	—
480	C₂²×C₅	—	2	4	no	—
481	C₂²×C₅	—	2	4	no	—
482	C₂²×C₅	—	2	4	no	—
483	C₂²×C₅	—	2	4	no	—
484	C₂²×C₅	—	2	4	no	—
485	C₂²×C₅	—	2	4	no	—
486	C₂²×C₅	C₂×C₄×Q₈	1	8	yes	—
487	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
488	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
489	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₅	#585	1	1	yes	characteristic
494	C₄×C₅	—	2	4	no	—
495	C₄×C₅	—	2	4	no	—
496	C₄×C₅	—	2	8	no	—
497	C₄×C₅	—	2	2	no	—
498	C₄×C₅	—	2	4	no	—
499	C₄×C₅	—	2	2	no	—
500	C₄×C₅	—	2	4	no	—
501	C₄×C₅	—	2	2	no	—
502	C₄×C₅	—	2	2	no	—
503	C₄×C₅	—	4	1	no	—
504	C₄×C₅	—	4	4	no	—
505	C₄×C₅	—	4	2	no	—
506	C₄×C₅	—	4	2	no	—
507	C₄×C₅	—	4	2	no	—
508	C₄×C₅	C₂×C₄×Q₈	1	4	yes	—
509	C₄×C₅	#518	1	4	yes	—
510	C₂⁴	C₂⁴×C₅	1	2	yes	—
511	C₂×Q₈	—	2	4	no	—
512	C₂×Q₈	—	2	4	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	4	4	no	—
516	C₂×Q₈	—	4	4	no	—
517	C₂×Q₈	—	4	32	no	—
518	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
519	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
520	C₂×Q₈	C₂²×C₄×C₅	1	16	yes	—
521	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
522	C₂×D₄	C₂×C₅×Q₈	1	4	yes	—
523	C₂×D₄	C₅×#41	1	4	yes	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
537	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
538	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	complemented
539	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	4	4	no	—
562	C₄⋊C₄	—	4	4	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
567	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
568	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
570	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
571	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
572	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	complemented
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	8	no	—
575	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
577	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	complemented
578	C₄²	—	2	2	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	2	4	no	—
582	C₄²	—	2	2	no	—
583	C₄²	—	2	2	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	4	4	no	—
587	C₄²	—	4	4	no	—
588	C₄²	—	4	4	no	—
589	C₄²	—	4	1	no	—
590	C₄²	C₂²×C₄×C₅	1	8	yes	—
591	C₄²	C₂²×C₄×C₅	1	4	yes	—
592	C₄²	C₂×C₅×Q₈	1	4	yes	complemented
593	C₂×C₅	—	2	8	no	—
594	C₂×C₅	C₂²×C₄×Q₈	1	1	yes	characteristic
595	C₂×C₅	C₂×#518	1	1	yes	characteristic
596	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
597	C₂×C₅	#3501	1	1	yes	characteristic
598	C₂×C₅	#3503	1	1	yes	characteristic
599	C₂×C₅	#3514	1	1	yes	characteristic
600	C₂×C₅	#3520	1	1	yes	characteristic
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	C₂³×C₄×C₅	1	4	yes	—
606	C₂³	C₂²×C₅×Q₈	1	4	yes	—
607	C₂³	C₂×C₅×#41	1	4	yes	—
608	C₂³	C₂⁵×C₅	1	1	yes	characteristic
609	Q₈	—	2	8	no	—
610	Q₈	—	2	16	no	—
611	Q₈	—	4	16	no	—
612	D₄	C₄×C₅×Q₈	1	16	yes	complemented
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	4	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	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	16	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	4	16	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	8	8	no	—
651	C₂×C₄	C₂³×C₄×C₅	1	2	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	4	yes	—
655	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
656	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
658	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
659	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
660	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
661	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
662	C₂×C₄	C₂×C₅×#41	1	2	yes	—
663	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
664	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
665	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
666	C₅	#34334	1	1	yes	characteristic, direct product factor, Sylow
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	C₂×C₄×C₅×Q₈	1	8	yes	—
674	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
675	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
676	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
677	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²	C₅×#585	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	8	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	C₂×C₄×C₅×Q₈	1	4	yes	—
696	C₄	C₅×#518	1	4	yes	—
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₄×C₅×Q₈	1	1	yes	characteristic
699	C₂	C₂×C₅×#518	1	1	yes	characteristic
700	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
701	C₂	C₅×#3501	1	1	yes	characteristic
702	C₂	C₅×#3503	1	1	yes	characteristic
703	C₂	C₅×#3514	1	1	yes	characteristic
704	C₂	C₅×#3520	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×#2369	C₂	semidirect
3. C₅×#2368	C₂	semidirect
4. C₅×#2365	C₂	semidirect
5. C₅×#2360	C₂	semidirect
6. C₅×#2355	C₂	semidirect
9. C₅×Q₈×C₂²⋊C₄	C₂	semidirect
10. C₅×#2331	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×#391	C₂	semidirect
19. C₅×D₄×Q₈	C₄	semidirect
84. #34334	C₅	direct (N × H)
87. C₂²×C₅×Q₈	C₂×C₄	semidirect
97. C₅×C₄⋊Q₈	C₂×C₄	semidirect
98. C₅×C₄⋊Q₈	C₂×C₄	semidirect
99. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
100. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
103. C₄×C₅×Q₈	C₂×C₄	semidirect
108. C₄×C₅×D₄	Q₈	semidirect
168. #2369	C₂×C₅	semidirect
169. #2368	C₂×C₅	semidirect
170. #2365	C₂×C₅	semidirect
171. #2360	C₂×C₅	semidirect
172. #2355	C₂×C₅	semidirect
175. Q₈×C₂²⋊C₄	C₂×C₅	semidirect
176. #2331	C₂×C₅	semidirect
177. #2329	C₂×C₅	semidirect
178. C₄×C₄⋊Q₈	C₂×C₅	semidirect
179. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
180. #2295	C₂×C₅	semidirect
181. C₂×#391	C₂×C₅	semidirect
212. C₂²×C₄×C₅	C₂×Q₈	semidirect
246. C₅×C₄⋊C₄	C₂×Q₈	semidirect
251. C₅×C₂²⋊C₄	C₂×Q₈	semidirect
266. C₄²×C₅	C₂×Q₈	semidirect
268. D₄×Q₈	C₄×C₅	semidirect
344. C₅×D₄	C₄×Q₈	semidirect
400. C₂²×Q₈	C₂×C₄×C₅	semidirect
410. C₄⋊Q₈	C₂×C₄×C₅	semidirect
411. C₄⋊Q₈	C₂×C₄×C₅	semidirect
412. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
413. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
416. C₄×Q₈	C₂×C₄×C₅	semidirect
421. C₄×D₄	C₅×Q₈	semidirect
538. C₂²×C₄	C₂×C₅×Q₈	semidirect
572. C₄⋊C₄	C₂×C₅×Q₈	semidirect
577. C₂²⋊C₄	C₂×C₅×Q₈	semidirect
592. C₄²	C₂×C₅×Q₈	semidirect
612. D₄	C₄×C₅×Q₈	semidirect
666. C₅	#34334	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×D₄×Q₈	2
C₅×#2369	2
C₅×#2368	2
C₅×#2365	2
C₅×#2360	2
C₅×#2355	2
C₅×#2349	2
C₅×D₄×C₄⋊C₄	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#2331	2
C₅×#2329	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₂×C₅×#391	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34334	5

Subgroups — C5×#34334 #11957054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34334 #11957054