Subgroups — C₅×#22797 #11945517

Order 1280.

960 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1955	C₂	1	2	yes	maximal
5	C₅×#1924	C₂	1	2	yes	maximal, complemented
6	C₅×#1923	C₂	1	2	yes	maximal, complemented
7	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1771	C₂	1	2	yes	maximal, complemented
11	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₅×#432	—	2	4	no	—
18	C₅×#431	—	2	4	no	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
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	2	yes	—
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₅×#97	C₂²	1	2	yes	—
30	C₂×C₅×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
36	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
37	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
38	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
39	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₄³×C₅	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#22797	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₄×C₅×D₄	—	2	4	no	—
58	C₄×C₅×D₄	—	2	4	no	—
59	C₄×C₅×D₄	—	2	2	no	—
60	C₄×C₅×D₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	4	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	4	2	no	—
92	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
93	C₅×C₂²⋊C₈	—	2	4	no	—
94	C₅×C₂²⋊C₈	—	2	4	no	—
95	C₅×C₂²⋊C₈	—	4	2	no	—
96	C₅×C₂²⋊C₈	—	4	2	no	—
97	C₅×#97	—	2	4	no	—
98	C₅×#97	—	2	4	no	—
99	C₄×C₅×C₈	—	2	4	no	—
100	C₅×#95	C₂×C₄	1	1	yes	characteristic
101	C₅×#95	C₂×C₄	1	1	yes	characteristic
102	C₅×#95	C₂×C₄	1	1	yes	characteristic
103	C₅×#95	C₂×C₄	1	1	yes	characteristic
104	C₅×#95	C₂×C₄	1	1	yes	characteristic
105	C₅×#95	C₂×C₄	1	1	yes	characteristic
106	C₂×#432	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
108	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
109	#1955	C₂×C₅	1	2	yes	—
110	#1924	C₂×C₅	1	2	yes	complemented
111	#1923	C₂×C₅	1	2	yes	complemented
112	#1842	C₂×C₅	1	1	yes	characteristic, complemented
113	#1797	C₂×C₅	1	1	yes	characteristic, complemented
114	#1797	C₂×C₅	1	1	yes	characteristic, complemented
115	#1771	C₂×C₅	1	2	yes	complemented
116	#1767	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	4	1	no	—
144	C₂²×C₄×C₅	—	4	1	no	—
145	C₂²×C₄×C₅	M₁₆	1	4	yes	—
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	2	2	no	—
168	C₂×C₅×C₈	—	2	2	no	—
169	C₂×C₅×C₈	—	2	2	no	—
170	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	2	2	no	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	M₁₆	1	4	yes	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	2	2	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	—	2	2	no	—
185	C₄²×C₅	—	2	2	no	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	—	2	1	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₄²×C₅	—	2	1	no	—
191	C₄²×C₅	—	2	1	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	4	1	no	—
194	C₄²×C₅	C₂×D₄	1	2	yes	—
195	C₄²×C₅	#41	1	2	yes	—
196	C₄²×C₅	#41	1	2	yes	—
197	C₄²×C₅	#41	1	2	yes	—
198	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
199	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
201	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
203	#432	—	2	4	no	—
204	#431	—	2	4	no	—
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
212	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
215	C₂×#97	C₂²×C₅	1	2	yes	—
216	C₂×#97	C₂²×C₅	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
218	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
220	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
222	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
223	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₄³	C₂²×C₅	1	1	yes	characteristic
228	#336	C₂²×C₅	1	2	yes	—
229	#336	C₂²×C₅	1	2	yes	—
230	#336	C₂²×C₅	1	2	yes	—
231	C₂³×C₅	—	2	1	no	—
232	C₂³×C₅	—	2	1	no	—
233	C₂³×C₅	—	2	1	no	—
234	C₂³×C₅	—	2	1	no	—
235	C₂³×C₅	—	2	1	no	—
236	C₂³×C₅	—	2	1	no	—
237	C₂³×C₅	—	2	1	no	—
238	C₂³×C₅	—	2	1	no	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	1	no	—
241	C₂³×C₅	—	2	1	no	—
242	C₂³×C₅	—	2	1	no	—
243	C₂³×C₅	C₂×M₁₆	1	2	yes	—
244	C₂³×C₅	C₂×M₁₆	1	2	yes	—
245	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₅×D₄	—	2	8	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	8	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
276	C₂×C₄×C₅	—	4	4	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	4	no	—
286	C₂×C₄×C₅	#117	1	2	yes	—
287	C₂×C₄×C₅	#117	1	2	yes	—
288	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
289	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
290	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
291	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
292	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
293	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
294	C₂×C₄×C₅	#131	1	2	yes	—
295	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
301	C₅×C₈	—	2	4	no	—
302	C₅×C₈	—	4	2	no	—
303	C₅×C₈	—	4	2	no	—
304	C₅×C₈	—	4	2	no	—
305	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
306	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
307	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₅	1	2	yes	—
313	C₂²×C₈	C₂³×C₅	1	2	yes	—
314	C₂²×C₈	C₂³×C₅	1	2	yes	—
315	C₂²×C₈	C₂³×C₅	1	2	yes	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
335	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
346	C₄⋊C₈	—	2	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	4	no	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	4	2	no	—
351	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
352	C₂²⋊C₈	—	2	4	no	—
353	C₂²⋊C₈	—	2	4	no	—
354	C₂²⋊C₈	—	4	2	no	—
355	C₂²⋊C₈	—	4	2	no	—
356	#97	—	2	4	no	—
357	#97	—	2	4	no	—
358	C₄×C₈	—	2	4	no	—
359	#95	C₂×C₄×C₅	1	1	yes	characteristic
360	#95	C₂×C₄×C₅	1	1	yes	characteristic
361	#95	C₂×C₄×C₅	1	1	yes	characteristic
362	#95	C₂×C₄×C₅	1	1	yes	characteristic
363	#95	C₂×C₄×C₅	1	1	yes	characteristic
364	#95	C₂×C₄×C₅	1	1	yes	characteristic
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	4	1	no	—
372	C₂²×C₅	—	4	1	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	C₂×#117	1	1	yes	characteristic
380	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
381	C₂²×C₅	#520	1	1	yes	characteristic
382	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
383	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
384	C₂²×C₅	C₂×#131	1	1	yes	characteristic
385	C₂²×C₅	#568	1	1	yes	characteristic
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	2	2	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	2	2	no	—
392	C₄×C₅	—	4	1	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	#435	1	4	yes	—
398	C₄×C₅	#547	1	1	yes	characteristic
399	C₄×C₅	#550	1	1	yes	characteristic
400	C₄×C₅	#555	1	1	yes	characteristic
401	C₄×C₅	#556	1	1	yes	characteristic
402	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
403	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	C₅×M₁₆	1	4	yes	—
431	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	C₅×M₁₆	1	4	yes	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	1	no	—
479	C₄²	C₂×C₅×D₄	1	2	yes	—
480	C₄²	C₅×#41	1	2	yes	—
481	C₄²	C₅×#41	1	2	yes	—
482	C₄²	C₅×#41	1	2	yes	—
483	C₂×C₅	—	4	2	no	—
484	C₂×C₅	—	4	2	no	—
485	C₂×C₅	#2354	1	1	yes	characteristic
486	C₂×C₅	#2920	1	1	yes	characteristic
487	C₂×C₅	#2925	1	1	yes	characteristic
488	C₂×C₅	C₂×#435	1	1	yes	characteristic
489	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
490	C₂×C₅	#2989	1	1	yes	characteristic
491	C₂×C₅	#2990	1	1	yes	characteristic
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	C₂×C₅×M₁₆	1	2	yes	—
505	C₂³	C₂×C₅×M₁₆	1	2	yes	—
506	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
507	D₄	—	2	8	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	8	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	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	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	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	C₅×#117	1	2	yes	—
548	C₂×C₄	C₅×#117	1	2	yes	—
549	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
550	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
551	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
552	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
553	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
554	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
555	C₂×C₄	C₅×#131	1	2	yes	—
556	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
558	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
559	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
560	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
562	C₈	—	2	4	no	—
563	C₈	—	4	2	no	—
564	C₈	—	4	2	no	—
565	C₈	—	4	2	no	—
566	C₅	#22797	1	1	yes	characteristic, direct product factor, Sylow
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	C₂×C₅×#117	1	1	yes	characteristic
582	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
583	C₂²	C₅×#520	1	1	yes	characteristic
584	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
585	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
586	C₂²	C₂×C₅×#131	1	1	yes	characteristic
587	C₂²	C₅×#568	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	C₅×#435	1	4	yes	—
600	C₄	C₅×#547	1	1	yes	characteristic
601	C₄	C₅×#550	1	1	yes	characteristic
602	C₄	C₅×#555	1	1	yes	characteristic
603	C₄	C₅×#556	1	1	yes	characteristic
604	C₂	—	4	2	no	—
605	C₂	—	4	2	no	—
606	C₂	C₅×#2354	1	1	yes	characteristic
607	C₂	C₅×#2920	1	1	yes	characteristic
608	C₂	C₅×#2925	1	1	yes	characteristic
609	C₂	C₂×C₅×#435	1	1	yes	characteristic
610	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
611	C₂	C₅×#2989	1	1	yes	characteristic
612	C₂	C₅×#2990	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	C₂²×C₅×D₄	C₂×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
1. C₂×C₅×#432	C₂	semidirect
2. C₂×C₅×#431	C₂	semidirect
5. C₅×#1924	C₂	semidirect
6. C₅×#1923	C₂	semidirect
7. C₅×#1842	C₂	semidirect
8. C₅×#1797	C₂	semidirect
9. C₅×#1797	C₂	semidirect
10. C₅×#1771	C₂	semidirect
11. C₅×#1767	C₂	semidirect
45. #22797	C₅	direct (N × H)
92. C₅×C₄⋊C₈	D₄	semidirect
106. C₂×#432	C₂×C₅	semidirect
107. C₂×#431	C₂×C₅	semidirect
110. #1924	C₂×C₅	semidirect
111. #1923	C₂×C₅	semidirect
112. #1842	C₂×C₅	semidirect
113. #1797	C₂×C₅	semidirect
114. #1797	C₂×C₅	semidirect
115. #1771	C₂×C₅	semidirect
116. #1767	C₂×C₅	semidirect
351. C₄⋊C₈	C₅×D₄	semidirect
566. C₅	#22797	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×#432	2
C₂×C₅×#431	2
C₄²×C₅×D₄	2
C₅×#1955	2
C₅×#1924	2
C₅×#1923	2
C₅×#1842	2
C₅×#1797	2
C₅×#1771	2
C₅×#1767	2
#22797	5

Subgroups — C5×#22797 #11945517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22797 #11945517