Subgroups — C₅×#22648 #11945368

Order 1280.

1116 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	2	yes	maximal
2	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#1940	C₂	1	2	yes	maximal, complemented
6	C₅×#1851	C₂	1	2	yes	maximal, complemented
7	C₅×#1850	C₂	1	2	yes	maximal, complemented
8	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#435	—	2	8	no	—
20	C₅×#423	—	2	4	no	—
21	C₂×C₅×C₄⋊C₈	—	2	4	no	—
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	2	yes	—
26	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₂×C₅×#97	C₂²	1	2	yes	—
33	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	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	C₄	1	1	yes	characteristic
40	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₄³×C₅	C₂²	1	1	yes	characteristic
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	C₅×#336	C₂²	1	2	yes	—
46	#22648	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₅×D₄	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	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×M₁₆	—	2	4	no	—
55	C₂×C₅×M₁₆	—	2	4	no	—
56	C₂×C₅×M₁₆	—	4	2	no	—
57	C₂²×C₅×C₈	—	2	4	no	—
58	C₂²×C₅×C₈	—	2	4	no	—
59	C₂²×C₅×C₈	—	4	2	no	—
60	C₂²×C₅×C₈	C₂³	1	2	yes	—
61	C₂²×C₅×C₈	C₂³	1	2	yes	—
62	C₂²×C₅×C₈	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	C₂³	1	2	yes	—
64	C₄×C₅×D₄	—	2	4	no	—
65	C₄×C₅×D₄	—	2	4	no	—
66	C₄×C₅×D₄	D₄	1	4	yes	—
67	C₄×C₅×D₄	Q₈	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	—	2	2	no	—
78	C₂×C₄²×C₅	—	2	2	no	—
79	C₂×C₄²×C₅	—	2	2	no	—
80	C₂×C₄²×C₅	—	2	2	no	—
81	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊C₈	—	2	4	no	—
95	C₅×C₄⋊C₈	—	2	4	no	—
96	C₅×C₄⋊C₈	—	2	2	no	—
97	C₅×C₄⋊C₈	—	2	2	no	—
98	C₅×C₄⋊C₈	—	2	4	no	—
99	C₅×C₄⋊C₈	—	2	2	no	—
100	C₅×C₄⋊C₈	—	4	2	no	—
101	C₅×C₄⋊C₈	D₄	1	4	yes	complemented
102	C₅×C₂²⋊C₈	—	2	4	no	—
103	C₅×C₂²⋊C₈	—	2	4	no	—
104	C₅×#97	—	2	4	no	—
105	C₅×#95	C₂×C₄	1	1	yes	characteristic
106	C₅×#95	C₂×C₄	1	1	yes	characteristic
107	C₅×#95	C₂×C₄	1	1	yes	characteristic
108	C₅×#95	C₂×C₄	1	1	yes	characteristic
109	C₅×#95	C₂×C₄	1	1	yes	characteristic
110	C₅×#95	C₂×C₄	1	1	yes	characteristic
111	C₂×#435	C₂×C₅	1	2	yes	—
112	C₂×#423	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
114	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
115	#1940	C₂×C₅	1	2	yes	complemented
116	#1851	C₂×C₅	1	2	yes	complemented
117	#1850	C₂×C₅	1	2	yes	complemented
118	#1842	C₂×C₅	1	1	yes	characteristic, complemented
119	#1797	C₂×C₅	1	1	yes	characteristic, complemented
120	#1797	C₂×C₅	1	1	yes	characteristic, complemented
121	#1767	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	2	no	—
126	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	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	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	4	1	no	—
145	C₂²×C₄×C₅	—	4	1	no	—
146	C₂²×C₄×C₅	M₁₆	1	4	yes	complemented
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	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×M₁₆	—	4	8	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	—	2	2	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	—	2	2	no	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	4	8	no	—
177	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
185	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
186	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
187	C₄²×C₅	—	2	2	no	—
188	C₄²×C₅	—	2	2	no	—
189	C₄²×C₅	—	2	2	no	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	—	2	2	no	—
192	C₄²×C₅	—	2	2	no	—
193	C₄²×C₅	—	2	2	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	—	4	1	no	—
201	C₄²×C₅	C₂×D₄	1	2	yes	—
202	C₄²×C₅	C₂×D₄	1	2	yes	—
203	C₄²×C₅	C₂×Q₈	1	2	yes	—
204	C₄²×C₅	#41	1	2	yes	—
205	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
206	C₂³×C₈	C₂²×C₅	1	2	yes	—
207	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
208	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
212	#435	—	2	8	no	—
213	#423	—	2	4	no	—
214	C₂×C₄⋊C₈	—	2	4	no	—
215	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
220	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
225	C₂×#97	C₂²×C₅	1	2	yes	—
226	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
230	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
231	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
232	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
233	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₄³	C₂²×C₅	1	1	yes	characteristic
236	#336	C₂²×C₅	1	2	yes	—
237	#336	C₂²×C₅	1	2	yes	—
238	#336	C₂²×C₅	1	2	yes	—
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	—	2	1	no	—
244	C₂³×C₅	—	2	1	no	—
245	C₂³×C₅	—	2	1	no	—
246	C₂³×C₅	—	2	1	no	—
247	C₂³×C₅	—	2	1	no	—
248	C₂³×C₅	—	2	1	no	—
249	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
250	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
251	C₂³×C₅	C₂×M₁₆	1	2	yes	—
252	C₂³×C₅	C₂×M₁₆	1	2	yes	—
253	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₅×D₄	—	2	8	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	1	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	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	8	no	—
280	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
290	C₂×C₄×C₅	—	4	4	no	—
291	C₂×C₄×C₅	—	4	4	no	—
292	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
293	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
296	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
297	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
299	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
300	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
301	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
302	C₂×C₄×C₅	#131	1	2	yes	—
303	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
309	C₅×C₈	—	2	4	no	—
310	C₅×C₈	—	4	2	no	—
311	C₅×C₈	—	4	2	no	—
312	C₅×C₈	—	4	2	no	—
313	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
315	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
316	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	—	2	4	no	—
322	C₂×M₁₆	—	4	2	no	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	—	4	2	no	—
326	C₂²×C₈	C₂³×C₅	1	2	yes	—
327	C₂²×C₈	C₂³×C₅	1	2	yes	—
328	C₂²×C₈	C₂³×C₅	1	2	yes	—
329	C₂²×C₈	C₂³×C₅	1	2	yes	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	C₅×D₄	1	4	yes	—
333	C₄×D₄	C₅×Q₈	1	4	yes	—
334	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
352	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
354	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
360	C₄⋊C₈	—	2	4	no	—
361	C₄⋊C₈	—	2	4	no	—
362	C₄⋊C₈	—	2	2	no	—
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	—	2	4	no	—
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	4	2	no	—
367	C₄⋊C₈	C₅×D₄	1	4	yes	complemented
368	C₂²⋊C₈	—	2	4	no	—
369	C₂²⋊C₈	—	2	4	no	—
370	#97	—	2	4	no	—
371	#95	C₂×C₄×C₅	1	1	yes	characteristic
372	#95	C₂×C₄×C₅	1	1	yes	characteristic
373	#95	C₂×C₄×C₅	1	1	yes	characteristic
374	#95	C₂×C₄×C₅	1	1	yes	characteristic
375	#95	C₂×C₄×C₅	1	1	yes	characteristic
376	#95	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	2	2	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	2	2	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	#423	1	4	yes	complemented
391	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
392	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
393	C₂²×C₅	#520	1	1	yes	characteristic
394	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
395	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
396	C₂²×C₅	C₂×#131	1	1	yes	characteristic
397	C₂²×C₅	#568	1	1	yes	characteristic
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	1	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	#435	1	4	yes	complemented
410	C₄×C₅	D₄²	1	1	yes	characteristic
411	C₄×C₅	#547	1	1	yes	characteristic
412	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
413	C₄×C₅	#554	1	1	yes	characteristic
414	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
415	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	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	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	C₅×M₁₆	1	4	yes	complemented
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	C₂²×C₄×C₅	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
452	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
453	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
454	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
456	M₁₆	—	4	8	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	4	8	no	—
469	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
477	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
478	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	C₂×C₅×D₄	1	2	yes	—
494	C₄²	C₂×C₅×D₄	1	2	yes	—
495	C₄²	C₂×C₅×Q₈	1	2	yes	—
496	C₄²	C₅×#41	1	2	yes	—
497	C₂×C₅	—	2	4	no	—
498	C₂×C₅	—	4	2	no	—
499	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
500	C₂×C₅	C₂×#423	1	1	yes	characteristic
501	C₂×C₅	#2906	1	1	yes	characteristic
502	C₂×C₅	C₂×#435	1	1	yes	characteristic
503	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
504	C₂×C₅	#2989	1	1	yes	characteristic
505	C₂×C₅	#2990	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
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	C₂×C₅×C₄⋊C₄	1	2	yes	—
517	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
518	C₂³	C₂×C₅×M₁₆	1	2	yes	—
519	C₂³	C₂×C₅×M₁₆	1	2	yes	—
520	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
521	D₄	—	2	8	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	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	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	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
560	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
561	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
562	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
563	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
564	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
565	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
566	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
567	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
568	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
569	C₂×C₄	C₅×#131	1	2	yes	—
570	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
573	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
574	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
576	C₈	—	2	4	no	—
577	C₈	—	4	2	no	—
578	C₈	—	4	2	no	—
579	C₈	—	4	2	no	—
580	C₅	#22648	1	1	yes	characteristic, direct product factor, Sylow
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	C₅×#423	1	4	yes	complemented
595	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
596	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
597	C₂²	C₅×#520	1	1	yes	characteristic
598	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
599	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
600	C₂²	C₂×C₅×#131	1	1	yes	characteristic
601	C₂²	C₅×#568	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	C₅×#435	1	4	yes	complemented
614	C₄	C₅×D₄²	1	1	yes	characteristic
615	C₄	C₅×#547	1	1	yes	characteristic
616	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
617	C₄	C₅×#554	1	1	yes	characteristic
618	C₂	—	2	4	no	—
619	C₂	—	4	2	no	—
620	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
621	C₂	C₂×C₅×#423	1	1	yes	characteristic
622	C₂	C₅×#2906	1	1	yes	characteristic
623	C₂	C₂×C₅×#435	1	1	yes	characteristic
624	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
625	C₂	C₅×#2989	1	1	yes	characteristic
626	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
2. C₂×C₅×#423	C₂	semidirect
3. C₂²×C₅×C₄⋊C₈	C₂	semidirect
5. C₅×#1940	C₂	semidirect
6. C₅×#1851	C₂	semidirect
7. C₅×#1850	C₂	semidirect
8. C₅×#1842	C₂	semidirect
9. C₅×#1797	C₂	semidirect
10. C₅×#1797	C₂	semidirect
11. C₅×#1767	C₂	semidirect
46. #22648	C₅	direct (N × H)
101. C₅×C₄⋊C₈	D₄	semidirect
112. C₂×#423	C₂×C₅	semidirect
113. C₂²×C₄⋊C₈	C₂×C₅	semidirect
115. #1940	C₂×C₅	semidirect
116. #1851	C₂×C₅	semidirect
117. #1850	C₂×C₅	semidirect
118. #1842	C₂×C₅	semidirect
119. #1797	C₂×C₅	semidirect
120. #1797	C₂×C₅	semidirect
121. #1767	C₂×C₅	semidirect
146. C₂²×C₄×C₅	M₁₆	semidirect
186. C₅×C₂²⋊C₄	M₁₆	semidirect
367. C₄⋊C₈	C₅×D₄	semidirect
390. C₂²×C₅	#423	semidirect
409. C₄×C₅	#435	semidirect
438. C₂²×C₄	C₅×M₁₆	semidirect
478. C₂²⋊C₄	C₅×M₁₆	semidirect
580. C₅	#22648	direct (N × H)
594. C₂²	C₅×#423	semidirect
613. C₄	C₅×#435	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#435	2
C₂×C₅×#423	2
C₂²×C₅×C₄⋊C₈	2
C₄²×C₅×D₄	2
C₅×#1940	2
C₅×#1851	2
C₅×#1850	2
C₅×#1842	2
C₅×#1797	2
C₅×#1767	2
#22648	5

Subgroups — C5×#22648 #11945368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22648 #11945368