Subgroups — C₅×#22293 #11945013

Order 1280.

754 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₂²⋊Q₈	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×#1797	C₂	1	1	yes	maximal, characteristic
13	C₅×#1753	C₂	1	1	yes	maximal, characteristic
14	C₅×#1753	C₂	1	1	yes	maximal, characteristic
15	C₅×#1728	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₅	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×C₄⋊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×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#391	C₄	1	1	yes	characteristic
34	C₅×#389	C₄	1	1	yes	characteristic
35	C₅×#387	C₄	1	1	yes	characteristic
36	C₅×#387	C₄	1	1	yes	characteristic
37	C₅×#385	C₄	1	1	yes	characteristic
38	C₅×#385	C₄	1	1	yes	characteristic
39	C₅×#380	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	#22293	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	4	1	no	—
66	C₂×C₅×M₁₆	—	4	1	no	—
67	C₂×C₅×M₁₆	—	4	1	no	—
68	C₂×C₅×M₁₆	—	4	1	no	—
69	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₅×C₂²⋊Q₈	—	2	4	no	—
79	C₄×C₅×Q₈	—	4	1	no	—
80	C₄×C₅×Q₈	—	4	1	no	—
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×C₂²⋊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×C₄²×C₅	—	4	1	no	—
95	C₂×C₄²×C₅	—	4	1	no	—
96	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂×C₄	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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	—	4	1	no	—
110	C₅×C₂²⋊C₈	—	2	2	no	—
111	C₅×C₂²⋊C₈	—	2	2	no	—
112	C₅×#97	—	4	1	no	—
113	C₅×#97	—	4	1	no	—
114	C₄×C₅×C₈	—	4	1	no	—
115	C₄×C₅×C₈	—	4	1	no	—
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	C₅×#95	C₂×C₄	1	1	yes	characteristic
126	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
127	#1985	C₂×C₅	1	1	yes	characteristic, complemented
128	#1984	C₂×C₅	1	1	yes	characteristic, complemented
129	#1940	C₂×C₅	1	1	yes	characteristic, complemented
130	#1939	C₂×C₅	1	1	yes	characteristic, complemented
131	#1917	C₂×C₅	1	1	yes	characteristic, complemented
132	#1917	C₂×C₅	1	1	yes	characteristic, complemented
133	#1916	C₂×C₅	1	1	yes	characteristic, complemented
134	#1916	C₂×C₅	1	1	yes	characteristic, complemented
135	#1851	C₂×C₅	1	1	yes	characteristic
136	#1851	C₂×C₅	1	1	yes	characteristic
137	#1797	C₂×C₅	1	1	yes	characteristic
138	#1753	C₂×C₅	1	1	yes	characteristic
139	#1753	C₂×C₅	1	1	yes	characteristic
140	#1728	C₂×C₅	1	1	yes	characteristic
141	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	2	2	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	—	4	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	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
153	C₂²×C₄×C₅	—	4	1	no	—
154	C₂²×C₄×C₅	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₅	#41	1	2	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₅×M₁₆	—	4	4	no	—
172	C₅×M₁₆	—	4	4	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	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	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	C₂×Q₈	1	2	yes	—
196	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	4	1	no	—
201	C₅×C₄⋊C₄	—	4	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	M₁₆	1	4	yes	complemented
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	4	1	no	—
209	C₅×C₂²⋊C₄	—	4	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	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	4	1	no	—
223	C₄²×C₅	—	4	1	no	—
224	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄⋊C₈	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	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×#97	C₂²×C₅	1	1	yes	characteristic
238	C₂×#97	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
241	#391	C₄×C₅	1	1	yes	characteristic
242	#389	C₄×C₅	1	1	yes	characteristic
243	#387	C₄×C₅	1	1	yes	characteristic
244	#387	C₄×C₅	1	1	yes	characteristic
245	#385	C₄×C₅	1	1	yes	characteristic
246	#385	C₄×C₅	1	1	yes	characteristic
247	#380	C₄×C₅	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	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	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	—	2	1	no	—
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	C₄×Q₈	1	2	yes	—
274	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₅×Q₈	—	4	4	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	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	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	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	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	4	4	no	—
315	C₂×C₄×C₅	—	4	4	no	—
316	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
317	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
318	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
319	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
320	C₂×C₄×C₅	#131	1	2	yes	—
321	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
327	C₅×C₈	—	2	2	no	—
328	C₅×C₈	—	2	2	no	—
329	C₅×C₈	—	4	1	no	—
330	C₅×C₈	—	4	1	no	—
331	C₅×C₈	—	4	1	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
336	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	4	1	no	—
341	C₂×M₁₆	—	4	1	no	—
342	C₂×M₁₆	—	4	1	no	—
343	C₂×M₁₆	—	4	1	no	—
344	C₂×M₁₆	C₅×Q₈	1	4	yes	complemented
345	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
353	C₂²⋊Q₈	—	2	4	no	—
354	C₄×Q₈	—	4	1	no	—
355	C₄×Q₈	—	4	1	no	—
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×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	C₂×C₄²	—	4	1	no	—
370	C₂×C₄²	—	4	1	no	—
371	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
379	C₄⋊C₈	—	4	1	no	—
380	C₄⋊C₈	—	4	1	no	—
381	C₄⋊C₈	—	4	1	no	—
382	C₄⋊C₈	—	4	1	no	—
383	C₄⋊C₈	—	4	1	no	—
384	C₄⋊C₈	—	4	1	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	#97	—	4	1	no	—
388	#97	—	4	1	no	—
389	C₄×C₈	—	4	1	no	—
390	C₄×C₈	—	4	1	no	—
391	#95	C₂×C₄×C₅	1	1	yes	characteristic
392	#95	C₂×C₄×C₅	1	1	yes	characteristic
393	#95	C₂×C₄×C₅	1	1	yes	characteristic
394	#95	C₂×C₄×C₅	1	1	yes	characteristic
395	#95	C₂×C₄×C₅	1	1	yes	characteristic
396	#95	C₂×C₄×C₅	1	1	yes	characteristic
397	#95	C₂×C₄×C₅	1	1	yes	characteristic
398	#95	C₂×C₄×C₅	1	1	yes	characteristic
399	#95	C₂×C₄×C₅	1	1	yes	characteristic
400	#95	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
409	C₂²×C₅	#518	1	1	yes	characteristic
410	C₂²×C₅	#520	1	1	yes	characteristic
411	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
412	C₂²×C₅	C₂×#131	1	1	yes	characteristic
413	C₂²×C₅	#568	1	1	yes	characteristic
414	C₂²×C₅	#568	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	2	no	—
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	1	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	1	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	#538	1	1	yes	characteristic
429	C₄×C₅	#539	1	1	yes	characteristic
430	C₄×C₅	#543	1	1	yes	characteristic
431	C₄×C₅	#544	1	1	yes	characteristic
432	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
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	C₂²×C₄×C₅	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
460	C₂²×C₄	C₅×#41	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
462	M₁₆	—	4	4	no	—
463	M₁₆	—	4	4	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	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
487	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	C₅×M₁₆	1	4	yes	complemented
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	1	no	—
515	C₂×C₅	—	4	2	no	—
516	C₂×C₅	#2329	1	1	yes	characteristic
517	C₂×C₅	#2962	1	1	yes	characteristic
518	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
519	C₂×C₅	#2974	1	1	yes	characteristic
520	C₂×C₅	#2978	1	1	yes	characteristic
521	C₂×C₅	#2989	1	1	yes	characteristic
522	C₂×C₅	#2993	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	C₄×C₅×Q₈	1	2	yes	—
530	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
531	Q₈	—	4	4	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	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	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	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
573	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
574	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
575	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
576	C₂×C₄	C₅×#131	1	2	yes	—
577	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
578	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
579	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₅	#22293	1	1	yes	characteristic, direct product factor, Sylow
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
600	C₂²	C₅×#518	1	1	yes	characteristic
601	C₂²	C₅×#520	1	1	yes	characteristic
602	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
603	C₂²	C₂×C₅×#131	1	1	yes	characteristic
604	C₂²	C₅×#568	1	1	yes	characteristic
605	C₂²	C₅×#568	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	C₅×#538	1	1	yes	characteristic
620	C₄	C₅×#539	1	1	yes	characteristic
621	C₄	C₅×#543	1	1	yes	characteristic
622	C₄	C₅×#544	1	1	yes	characteristic
623	C₂	—	4	2	no	—
624	C₂	C₅×#2329	1	1	yes	characteristic
625	C₂	C₅×#2962	1	1	yes	characteristic
626	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic
627	C₂	C₅×#2974	1	1	yes	characteristic
628	C₂	C₅×#2978	1	1	yes	characteristic
629	C₂	C₅×#2989	1	1	yes	characteristic
630	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. #22293	C₅	direct (N × H)
69. C₂×C₅×M₁₆	Q₈	semidirect
127. #1985	C₂×C₅	semidirect
128. #1984	C₂×C₅	semidirect
129. #1940	C₂×C₅	semidirect
130. #1939	C₂×C₅	semidirect
131. #1917	C₂×C₅	semidirect
132. #1917	C₂×C₅	semidirect
133. #1916	C₂×C₅	semidirect
134. #1916	C₂×C₅	semidirect
205. C₅×C₄⋊C₄	M₁₆	semidirect
344. C₂×M₁₆	C₅×Q₈	semidirect
496. C₄⋊C₄	C₅×M₁₆	semidirect
591. C₅	#22293	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₂²⋊Q₈	2
C₅×#1985	2
C₅×#1984	2
C₅×#1940	2
C₅×#1939	2
C₅×#1917	2
C₅×#1916	2
C₅×#1851	2
C₅×#1797	2
C₅×#1753	2
C₅×#1728	2
#22293	5

Subgroups — C5×#22293 #11945013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22293 #11945013