Subgroups — C₅×#22292 #11945012

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2396	C₂	1	1	yes	maximal, characteristic
2	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1851	C₂	1	1	yes	maximal, characteristic
11	C₅×#1851	C₂	1	1	yes	maximal, characteristic
12	C₅×#1798	C₂	1	1	yes	maximal, characteristic
13	C₅×#1752	C₂	1	1	yes	maximal, characteristic
14	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₅×#1729	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#400	C₄	1	1	yes	characteristic
33	C₅×#399	C₄	1	1	yes	characteristic
34	C₅×#398	C₄	1	1	yes	characteristic
35	C₅×#398	C₄	1	1	yes	characteristic
36	C₅×#396	C₄	1	1	yes	characteristic
37	C₅×#396	C₄	1	1	yes	characteristic
38	C₅×#395	C₄	1	1	yes	characteristic
39	C₅×#393	C₄	1	1	yes	characteristic
40	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×#336	C₂²	1	1	yes	characteristic
46	C₅×#336	C₂²	1	1	yes	characteristic
47	C₅×#336	C₂²	1	1	yes	characteristic
48	C₅×#336	C₂²	1	1	yes	characteristic
49	C₅×#336	C₂²	1	1	yes	characteristic
50	C₅×#336	C₂²	1	1	yes	characteristic
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	C₅×#336	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#22292	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₅×M₁₆	—	2	2	no	—
63	C₂×C₅×M₁₆	—	4	1	no	—
64	C₂×C₅×M₁₆	—	4	1	no	—
65	C₂²×C₅×C₈	—	4	1	no	—
66	C₂²×C₅×C₈	—	4	1	no	—
67	C₂²×C₅×C₈	Q₈	1	4	yes	complemented
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×Q₈	—	4	1	no	—
77	C₄×C₅×Q₈	—	4	1	no	—
78	C₅×#117	—	4	1	no	—
79	C₅×#117	—	4	1	no	—
80	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₈	—	4	1	no	—
104	C₅×C₄⋊C₈	—	4	1	no	—
105	C₅×C₄⋊C₈	—	4	1	no	—
106	C₅×C₄⋊C₈	—	4	1	no	—
107	C₅×C₄⋊C₈	—	4	1	no	—
108	C₅×C₄⋊C₈	—	4	1	no	—
109	C₅×C₂²⋊C₈	—	2	2	no	—
110	C₅×C₂²⋊C₈	—	2	2	no	—
111	C₅×#97	—	4	1	no	—
112	C₅×#97	—	4	1	no	—
113	C₄×C₅×C₈	—	4	1	no	—
114	C₄×C₅×C₈	—	4	1	no	—
115	C₅×#95	C₂×C₄	1	1	yes	characteristic
116	C₅×#95	C₂×C₄	1	1	yes	characteristic
117	C₅×#95	C₂×C₄	1	1	yes	characteristic
118	C₅×#95	C₂×C₄	1	1	yes	characteristic
119	C₅×#95	C₂×C₄	1	1	yes	characteristic
120	C₅×#95	C₂×C₄	1	1	yes	characteristic
121	C₅×#95	C₂×C₄	1	1	yes	characteristic
122	C₅×#95	C₂×C₄	1	1	yes	characteristic
123	C₅×#95	C₂×C₄	1	1	yes	characteristic
124	C₅×#95	C₂×C₄	1	1	yes	characteristic
125	#2396	C₂×C₅	1	1	yes	characteristic
126	#1985	C₂×C₅	1	1	yes	characteristic, complemented
127	#1984	C₂×C₅	1	1	yes	characteristic, complemented
128	#1940	C₂×C₅	1	1	yes	characteristic, complemented
129	#1939	C₂×C₅	1	1	yes	characteristic, complemented
130	#1917	C₂×C₅	1	1	yes	characteristic, complemented
131	#1917	C₂×C₅	1	1	yes	characteristic, complemented
132	#1916	C₂×C₅	1	1	yes	characteristic, complemented
133	#1916	C₂×C₅	1	1	yes	characteristic, complemented
134	#1851	C₂×C₅	1	1	yes	characteristic
135	#1851	C₂×C₅	1	1	yes	characteristic
136	#1798	C₂×C₅	1	1	yes	characteristic
137	#1752	C₂×C₅	1	1	yes	characteristic
138	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
139	#1729	C₂×C₅	1	1	yes	characteristic
140	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	4	1	no	—
143	C₂×C₅×Q₈	—	4	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₅	#41	1	2	yes	—
163	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×M₁₆	—	4	4	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	4	4	no	—
188	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
189	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	4	1	no	—
194	C₅×C₄⋊C₄	—	4	1	no	—
195	C₅×C₄⋊C₄	—	4	1	no	—
196	C₅×C₄⋊C₄	—	4	1	no	—
197	C₅×C₄⋊C₄	—	4	1	no	—
198	C₅×C₄⋊C₄	—	4	1	no	—
199	C₅×C₄⋊C₄	—	4	1	no	—
200	C₅×C₄⋊C₄	—	4	1	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	4	1	no	—
204	C₅×C₂²⋊C₄	—	4	1	no	—
205	C₅×C₂²⋊C₄	—	4	1	no	—
206	C₅×C₂²⋊C₄	—	4	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×#117	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×#97	C₂²×C₅	1	1	yes	characteristic
232	C₂×#97	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
235	#400	C₄×C₅	1	1	yes	characteristic
236	#399	C₄×C₅	1	1	yes	characteristic
237	#398	C₄×C₅	1	1	yes	characteristic
238	#398	C₄×C₅	1	1	yes	characteristic
239	#396	C₄×C₅	1	1	yes	characteristic
240	#396	C₄×C₅	1	1	yes	characteristic
241	#395	C₄×C₅	1	1	yes	characteristic
242	#393	C₄×C₅	1	1	yes	characteristic
243	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	#336	C₂²×C₅	1	1	yes	characteristic
249	#336	C₂²×C₅	1	1	yes	characteristic
250	#336	C₂²×C₅	1	1	yes	characteristic
251	#336	C₂²×C₅	1	1	yes	characteristic
252	#336	C₂²×C₅	1	1	yes	characteristic
253	#336	C₂²×C₅	1	1	yes	characteristic
254	#336	C₂²×C₅	1	1	yes	characteristic
255	#336	C₂²×C₅	1	1	yes	characteristic
256	#336	C₂²×C₅	1	1	yes	characteristic
257	#336	C₂²×C₅	1	1	yes	characteristic
258	#336	C₂²×C₅	1	1	yes	characteristic
259	#336	C₂²×C₅	1	1	yes	characteristic
260	#336	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	1	no	—
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	C₄×Q₈	1	2	yes	—
269	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₅×Q₈	—	4	4	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
312	C₂×C₄×C₅	#131	1	2	yes	—
313	C₂×C₄×C₅	#131	1	2	yes	—
314	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
320	C₅×C₈	—	2	2	no	—
321	C₅×C₈	—	2	2	no	—
322	C₅×C₈	—	4	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	—	4	1	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	1	no	—
328	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	4	1	no	—
332	C₂×M₁₆	—	4	1	no	—
333	C₂²×C₈	—	4	1	no	—
334	C₂²×C₈	—	4	1	no	—
335	C₂²×C₈	C₅×Q₈	1	4	yes	complemented
336	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₄×Q₈	—	4	1	no	—
345	C₄×Q₈	—	4	1	no	—
346	#117	—	4	1	no	—
347	#117	—	4	1	no	—
348	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
371	C₄⋊C₈	—	4	1	no	—
372	C₄⋊C₈	—	4	1	no	—
373	C₄⋊C₈	—	4	1	no	—
374	C₄⋊C₈	—	4	1	no	—
375	C₄⋊C₈	—	4	1	no	—
376	C₄⋊C₈	—	4	1	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	—	2	2	no	—
379	#97	—	4	1	no	—
380	#97	—	4	1	no	—
381	C₄×C₈	—	4	1	no	—
382	C₄×C₈	—	4	1	no	—
383	#95	C₂×C₄×C₅	1	1	yes	characteristic
384	#95	C₂×C₄×C₅	1	1	yes	characteristic
385	#95	C₂×C₄×C₅	1	1	yes	characteristic
386	#95	C₂×C₄×C₅	1	1	yes	characteristic
387	#95	C₂×C₄×C₅	1	1	yes	characteristic
388	#95	C₂×C₄×C₅	1	1	yes	characteristic
389	#95	C₂×C₄×C₅	1	1	yes	characteristic
390	#95	C₂×C₄×C₅	1	1	yes	characteristic
391	#95	C₂×C₄×C₅	1	1	yes	characteristic
392	#95	C₂×C₄×C₅	1	1	yes	characteristic
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
401	C₂²×C₅	#518	1	1	yes	characteristic
402	C₂²×C₅	#520	1	1	yes	characteristic
403	C₂²×C₅	C₂×#131	1	1	yes	characteristic
404	C₂²×C₅	C₂×#131	1	1	yes	characteristic
405	C₂²×C₅	#568	1	1	yes	characteristic
406	C₂²×C₅	#568	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	4	1	no	—
415	C₄×C₅	—	4	1	no	—
416	C₄×C₅	—	4	1	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	#538	1	1	yes	characteristic
421	C₄×C₅	#539	1	1	yes	characteristic
422	C₄×C₅	#543	1	1	yes	characteristic
423	C₄×C₅	#544	1	1	yes	characteristic
424	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	4	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
446	C₂²×C₄	C₅×#41	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
448	M₁₆	—	4	4	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	4	no	—
472	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
473	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₂×C₅	—	4	2	no	—
504	C₂×C₅	#2329	1	1	yes	characteristic
505	C₂×C₅	#2960	1	1	yes	characteristic
506	C₂×C₅	#2961	1	1	yes	characteristic
507	C₂×C₅	#2976	1	1	yes	characteristic
508	C₂×C₅	#2981	1	1	yes	characteristic
509	C₂×C₅	#2992	1	1	yes	characteristic
510	C₂×C₅	#2993	1	1	yes	characteristic
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	C₄×C₅×Q₈	1	2	yes	—
518	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
519	Q₈	—	4	4	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
561	C₂×C₄	C₅×#131	1	2	yes	—
562	C₂×C₄	C₅×#131	1	2	yes	—
563	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
564	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
565	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₅	#22292	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
586	C₂²	C₅×#518	1	1	yes	characteristic
587	C₂²	C₅×#520	1	1	yes	characteristic
588	C₂²	C₂×C₅×#131	1	1	yes	characteristic
589	C₂²	C₂×C₅×#131	1	1	yes	characteristic
590	C₂²	C₅×#568	1	1	yes	characteristic
591	C₂²	C₅×#568	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	C₅×#538	1	1	yes	characteristic
606	C₄	C₅×#539	1	1	yes	characteristic
607	C₄	C₅×#543	1	1	yes	characteristic
608	C₄	C₅×#544	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	C₅×#2329	1	1	yes	characteristic
611	C₂	C₅×#2960	1	1	yes	characteristic
612	C₂	C₅×#2961	1	1	yes	characteristic
613	C₂	C₅×#2976	1	1	yes	characteristic
614	C₂	C₅×#2981	1	1	yes	characteristic
615	C₂	C₅×#2992	1	1	yes	characteristic
616	C₂	C₅×#2993	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×#1985	C₂	semidirect
3. C₅×#1984	C₂	semidirect
4. C₅×#1940	C₂	semidirect
5. C₅×#1939	C₂	semidirect
6. C₅×#1917	C₂	semidirect
7. C₅×#1917	C₂	semidirect
8. C₅×#1916	C₂	semidirect
9. C₅×#1916	C₂	semidirect
59. #22292	C₅	direct (N × H)
67. C₂²×C₅×C₈	Q₈	semidirect
126. #1985	C₂×C₅	semidirect
127. #1984	C₂×C₅	semidirect
128. #1940	C₂×C₅	semidirect
129. #1939	C₂×C₅	semidirect
130. #1917	C₂×C₅	semidirect
131. #1917	C₂×C₅	semidirect
132. #1916	C₂×C₅	semidirect
133. #1916	C₂×C₅	semidirect
335. C₂²×C₈	C₅×Q₈	semidirect
577. C₅	#22292	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×#2396	2
C₅×#1985	2
C₅×#1984	2
C₅×#1940	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1851	2
C₅×#1798	2
C₅×#1752	2
C₅×C₈×C₂²⋊C₄	2
C₅×#1729	2
#22292	5

Subgroups — C5×#22292 #11945012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22292 #11945012