Subgroups — C₅×#22336 #11945056

Order 1280.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2392	C₂	1	1	yes	maximal, characteristic
2	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1818	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×#97	C₂²	1	1	yes	characteristic
35	C₂×C₅×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₅×#398	C₄	1	1	yes	characteristic
39	C₅×#397	C₄	1	1	yes	characteristic
40	C₅×#396	C₄	1	1	yes	characteristic
41	C₅×#396	C₄	1	1	yes	characteristic
42	C₅×#394	C₄	1	1	yes	characteristic
43	C₅×#394	C₄	1	1	yes	characteristic
44	C₅×#394	C₄	1	1	yes	characteristic
45	C₅×#392	C₄	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₂²⋊C₄	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	#22336	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₅×M₁₆	—	2	2	no	—
67	C₂×C₅×M₁₆	—	4	1	no	—
68	C₂×C₅×M₁₆	—	4	1	no	—
69	C₂²×C₅×C₈	—	2	2	no	—
70	C₂²×C₅×C₈	—	4	1	no	—
71	C₂²×C₅×C₈	—	4	1	no	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₄×C₅×D₄	—	4	1	no	—
81	C₄×C₅×D₄	—	4	1	no	—
82	C₄×C₅×D₄	—	4	1	no	—
83	C₄×C₅×D₄	—	4	1	no	—
84	C₄×C₅×D₄	—	4	1	no	—
85	C₄×C₅×D₄	—	4	1	no	—
86	C₅×#117	—	4	1	no	—
87	C₅×#117	—	4	1	no	—
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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	—	4	1	no	—
112	C₅×C₄⋊C₈	—	4	1	no	—
113	C₅×C₂²⋊C₈	—	2	2	no	—
114	C₅×C₂²⋊C₈	—	2	2	no	—
115	C₅×C₂²⋊C₈	—	2	2	no	—
116	C₅×C₂²⋊C₈	—	2	2	no	—
117	C₅×C₂²⋊C₈	—	4	1	no	—
118	C₅×C₂²⋊C₈	—	4	1	no	—
119	C₅×C₂²⋊C₈	—	4	1	no	—
120	C₅×C₂²⋊C₈	—	4	1	no	—
121	C₅×C₂²⋊C₈	—	4	1	no	—
122	C₅×C₂²⋊C₈	—	4	1	no	—
123	C₅×#97	—	4	1	no	—
124	C₅×#97	—	4	1	no	—
125	C₄×C₅×C₈	—	4	1	no	—
126	C₄×C₅×C₈	—	4	1	no	—
127	C₅×#95	C₂×C₄	1	1	yes	characteristic
128	C₅×#95	C₂×C₄	1	1	yes	characteristic
129	C₅×#95	C₂×C₄	1	1	yes	characteristic
130	C₅×#95	C₂×C₄	1	1	yes	characteristic
131	C₅×#95	C₂×C₄	1	1	yes	characteristic
132	C₅×#95	C₂×C₄	1	1	yes	characteristic
133	#2392	C₂×C₅	1	1	yes	characteristic
134	#1955	C₂×C₅	1	1	yes	characteristic, complemented
135	#1954	C₂×C₅	1	1	yes	characteristic, complemented
136	#1923	C₂×C₅	1	1	yes	characteristic, complemented
137	#1923	C₂×C₅	1	1	yes	characteristic, complemented
138	#1917	C₂×C₅	1	1	yes	characteristic, complemented
139	#1916	C₂×C₅	1	1	yes	characteristic, complemented
140	#1870	C₂×C₅	1	1	yes	characteristic, complemented
141	#1870	C₂×C₅	1	1	yes	characteristic, complemented
142	#1869	C₂×C₅	1	1	yes	characteristic, complemented
143	#1869	C₂×C₅	1	1	yes	characteristic, complemented
144	#1818	C₂×C₅	1	1	yes	characteristic, complemented
145	#1753	C₂×C₅	1	1	yes	characteristic, complemented
146	#1752	C₂×C₅	1	1	yes	characteristic, complemented
147	#1750	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	4	1	no	—
155	C₂×C₅×D₄	—	4	1	no	—
156	C₂×C₅×D₄	—	4	1	no	—
157	C₂×C₅×D₄	—	4	1	no	—
158	C₂×C₅×D₄	—	4	1	no	—
159	C₂×C₅×D₄	—	4	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₅×M₁₆	—	4	4	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	4	4	no	—
214	C₂×C₅×C₈	#41	1	2	yes	—
215	C₂×C₅×C₈	#41	1	2	yes	—
216	C₅×C₄⋊C₄	—	2	2	no	—
217	C₅×C₄⋊C₄	—	4	1	no	—
218	C₅×C₄⋊C₄	—	4	1	no	—
219	C₅×C₄⋊C₄	—	4	1	no	—
220	C₅×C₄⋊C₄	—	4	1	no	—
221	C₅×C₄⋊C₄	—	4	1	no	—
222	C₅×C₄⋊C₄	—	4	1	no	—
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	—	4	1	no	—
226	C₅×C₂²⋊C₄	—	4	1	no	—
227	C₅×C₂²⋊C₄	—	4	1	no	—
228	C₅×C₂²⋊C₄	—	4	1	no	—
229	C₅×C₂²⋊C₄	—	4	1	no	—
230	C₅×C₂²⋊C₄	—	4	1	no	—
231	C₅×C₂²⋊C₄	—	4	1	no	—
232	C₅×C₂²⋊C₄	—	4	1	no	—
233	C₅×C₂²⋊C₄	—	4	1	no	—
234	C₅×C₂²⋊C₄	—	4	1	no	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	—	2	1	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×#117	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×#97	C₂²×C₅	1	1	yes	characteristic
262	C₂×#97	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
265	#398	C₄×C₅	1	1	yes	characteristic
266	#397	C₄×C₅	1	1	yes	characteristic
267	#396	C₄×C₅	1	1	yes	characteristic
268	#396	C₄×C₅	1	1	yes	characteristic
269	#394	C₄×C₅	1	1	yes	characteristic
270	#394	C₄×C₅	1	1	yes	characteristic
271	#394	C₄×C₅	1	1	yes	characteristic
272	#392	C₄×C₅	1	1	yes	characteristic
273	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	#336	C₂²×C₅	1	1	yes	characteristic
277	#336	C₂²×C₅	1	1	yes	characteristic
278	#336	C₂²×C₅	1	1	yes	characteristic
279	#336	C₂²×C₅	1	1	yes	characteristic
280	#336	C₂²×C₅	1	1	yes	characteristic
281	#336	C₂²×C₅	1	1	yes	characteristic
282	#336	C₂²×C₅	1	1	yes	characteristic
283	#336	C₂²×C₅	1	1	yes	characteristic
284	#336	C₂²×C₅	1	1	yes	characteristic
285	#336	C₂²×C₅	1	1	yes	characteristic
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	1	no	—
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	#131	1	2	yes	—
307	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
308	C₅×D₄	—	4	4	no	—
309	C₅×D₄	—	4	4	no	—
310	C₅×D₄	—	4	4	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	#131	1	2	yes	—
356	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
362	C₅×C₈	—	2	2	no	—
363	C₅×C₈	—	2	2	no	—
364	C₅×C₈	—	4	1	no	—
365	C₅×C₈	—	4	1	no	—
366	C₅×C₈	—	4	1	no	—
367	C₅×C₈	—	4	1	no	—
368	C₅×C₈	—	4	1	no	—
369	C₅×C₈	—	4	1	no	—
370	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	4	1	no	—
378	C₂×M₁₆	—	4	1	no	—
379	C₂²×C₈	—	2	2	no	—
380	C₂²×C₈	—	4	1	no	—
381	C₂²×C₈	—	4	1	no	—
382	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₄×D₄	—	4	1	no	—
391	C₄×D₄	—	4	1	no	—
392	C₄×D₄	—	4	1	no	—
393	C₄×D₄	—	4	1	no	—
394	C₄×D₄	—	4	1	no	—
395	C₄×D₄	—	4	1	no	—
396	#117	—	4	1	no	—
397	#117	—	4	1	no	—
398	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
421	C₄⋊C₈	—	4	1	no	—
422	C₄⋊C₈	—	4	1	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	2	no	—
426	C₂²⋊C₈	—	2	2	no	—
427	C₂²⋊C₈	—	4	1	no	—
428	C₂²⋊C₈	—	4	1	no	—
429	C₂²⋊C₈	—	4	1	no	—
430	C₂²⋊C₈	—	4	1	no	—
431	C₂²⋊C₈	—	4	1	no	—
432	C₂²⋊C₈	—	4	1	no	—
433	#97	—	4	1	no	—
434	#97	—	4	1	no	—
435	C₄×C₈	—	4	1	no	—
436	C₄×C₈	—	4	1	no	—
437	#95	C₂×C₄×C₅	1	1	yes	characteristic
438	#95	C₂×C₄×C₅	1	1	yes	characteristic
439	#95	C₂×C₄×C₅	1	1	yes	characteristic
440	#95	C₂×C₄×C₅	1	1	yes	characteristic
441	#95	C₂×C₄×C₅	1	1	yes	characteristic
442	#95	C₂×C₄×C₅	1	1	yes	characteristic
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	2	2	no	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	4	1	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	—	4	1	no	—
449	C₂²×C₅	—	4	1	no	—
450	C₂²×C₅	—	4	1	no	—
451	C₂²×C₅	—	4	1	no	—
452	C₂²×C₅	—	4	1	no	—
453	C₂²×C₅	—	4	1	no	—
454	C₂²×C₅	—	4	1	no	—
455	C₂²×C₅	—	4	1	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	4	1	no	—
460	C₂²×C₅	—	4	1	no	—
461	C₂²×C₅	—	4	1	no	—
462	C₂²×C₅	—	4	1	no	—
463	C₂²×C₅	—	4	1	no	—
464	C₂²×C₅	C₄×#41	1	1	yes	characteristic
465	C₂²×C₅	#518	1	1	yes	characteristic
466	C₂²×C₅	#518	1	1	yes	characteristic
467	C₂²×C₅	C₂×#131	1	1	yes	characteristic
468	C₂²×C₅	C₂×#131	1	1	yes	characteristic
469	C₂²×C₅	#568	1	1	yes	characteristic
470	C₂²×C₅	#568	1	1	yes	characteristic
471	C₄×C₅	—	2	2	no	—
472	C₄×C₅	—	4	1	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	—	4	1	no	—
475	C₄×C₅	—	4	1	no	—
476	C₄×C₅	—	4	1	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	1	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	#538	1	1	yes	characteristic
483	C₄×C₅	#538	1	1	yes	characteristic
484	C₄×C₅	#540	1	1	yes	characteristic
485	C₄×C₅	#540	1	1	yes	characteristic
486	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
487	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
488	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	4	1	no	—
493	C₂×D₄	—	4	1	no	—
494	C₂×D₄	—	4	1	no	—
495	C₂×D₄	—	4	1	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	4	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
524	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
528	M₁₆	—	4	4	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	4	4	no	—
552	C₂×C₈	C₅×#41	1	2	yes	—
553	C₂×C₈	C₅×#41	1	2	yes	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	4	1	no	—
556	C₄⋊C₄	—	4	1	no	—
557	C₄⋊C₄	—	4	1	no	—
558	C₄⋊C₄	—	4	1	no	—
559	C₄⋊C₄	—	4	1	no	—
560	C₄⋊C₄	—	4	1	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	4	1	no	—
564	C₂²⋊C₄	—	4	1	no	—
565	C₂²⋊C₄	—	4	1	no	—
566	C₂²⋊C₄	—	4	1	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₂×C₅	—	4	2	no	—
582	C₂×C₅	—	8	1	no	—
583	C₂×C₅	—	8	1	no	—
584	C₂×C₅	#2333	1	1	yes	characteristic
585	C₂×C₅	#2968	1	1	yes	characteristic
586	C₂×C₅	#2969	1	1	yes	characteristic
587	C₂×C₅	#2976	1	1	yes	characteristic
588	C₂×C₅	#2977	1	1	yes	characteristic
589	C₂×C₅	#2978	1	1	yes	characteristic
590	C₂×C₅	#2981	1	1	yes	characteristic
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	C₅×#131	1	2	yes	—
612	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
613	D₄	—	4	4	no	—
614	D₄	—	4	4	no	—
615	D₄	—	4	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	C₅×#131	1	2	yes	—
661	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
662	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
663	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₅	#22336	1	1	yes	characteristic, direct product factor, Sylow
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	C₄×C₅×#41	1	1	yes	characteristic
698	C₂²	C₅×#518	1	1	yes	characteristic
699	C₂²	C₅×#518	1	1	yes	characteristic
700	C₂²	C₂×C₅×#131	1	1	yes	characteristic
701	C₂²	C₂×C₅×#131	1	1	yes	characteristic
702	C₂²	C₅×#568	1	1	yes	characteristic
703	C₂²	C₅×#568	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	C₅×#538	1	1	yes	characteristic
716	C₄	C₅×#538	1	1	yes	characteristic
717	C₄	C₅×#540	1	1	yes	characteristic
718	C₄	C₅×#540	1	1	yes	characteristic
719	C₂	—	4	2	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	1	no	—
722	C₂	C₅×#2333	1	1	yes	characteristic
723	C₂	C₅×#2968	1	1	yes	characteristic
724	C₂	C₅×#2969	1	1	yes	characteristic
725	C₂	C₅×#2976	1	1	yes	characteristic
726	C₂	C₅×#2977	1	1	yes	characteristic
727	C₂	C₅×#2978	1	1	yes	characteristic
728	C₂	C₅×#2981	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	C₅×#392	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×#1955	C₂	semidirect
3. C₅×#1954	C₂	semidirect
4. C₅×#1923	C₂	semidirect
5. C₅×#1923	C₂	semidirect
6. C₅×#1917	C₂	semidirect
7. C₅×#1916	C₂	semidirect
8. C₅×#1870	C₂	semidirect
9. C₅×#1870	C₂	semidirect
10. C₅×#1869	C₂	semidirect
11. C₅×#1869	C₂	semidirect
12. C₅×#1818	C₂	semidirect
13. C₅×#1753	C₂	semidirect
14. C₅×#1752	C₂	semidirect
15. C₅×#1750	C₂	semidirect
59. #22336	C₅	direct (N × H)
134. #1955	C₂×C₅	semidirect
135. #1954	C₂×C₅	semidirect
136. #1923	C₂×C₅	semidirect
137. #1923	C₂×C₅	semidirect
138. #1917	C₂×C₅	semidirect
139. #1916	C₂×C₅	semidirect
140. #1870	C₂×C₅	semidirect
141. #1870	C₂×C₅	semidirect
142. #1869	C₂×C₅	semidirect
143. #1869	C₂×C₅	semidirect
144. #1818	C₂×C₅	semidirect
145. #1753	C₂×C₅	semidirect
146. #1752	C₂×C₅	semidirect
147. #1750	C₂×C₅	semidirect
675. C₅	#22336	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×#2392	2
C₅×#1955	2
C₅×#1954	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1870	2
C₅×#1869	2
C₅×#1818	2
C₅×#1753	2
C₅×#1752	2
C₅×#1750	2
#22336	5

Subgroups — C5×#22336 #11945056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22336 #11945056