Subgroups — C₅×#22321 #11945041

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#1924	C₂	1	1	yes	maximal, characteristic
5	C₅×#1924	C₂	1	1	yes	maximal, characteristic
6	C₅×#1923	C₂	1	1	yes	maximal, characteristic
7	C₅×#1923	C₂	1	1	yes	maximal, characteristic
8	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1817	C₂	1	1	yes	maximal, characteristic
13	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	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×C₂²⋊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×#97	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	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	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	#22321	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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₅×C₂²⋊Q₈	—	2	4	no	—
73	C₄×C₅×Q₈	—	4	1	no	—
74	C₄×C₅×Q₈	—	4	1	no	—
75	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	—	4	1	no	—
89	C₂×C₄²×C₅	—	4	1	no	—
90	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×C₄⋊C₈	—	2	2	no	—
99	C₅×C₄⋊C₈	—	2	2	no	—
100	C₅×C₄⋊C₈	—	4	1	no	—
101	C₅×C₄⋊C₈	—	4	1	no	—
102	C₅×C₂²⋊C₈	—	2	2	no	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×C₂²⋊C₈	—	4	1	no	—
105	C₅×C₂²⋊C₈	—	4	1	no	—
106	C₅×#97	—	2	2	no	—
107	C₅×#97	—	4	1	no	—
108	C₄×C₅×C₈	—	2	2	no	—
109	C₄×C₅×C₈	—	4	1	no	—
110	C₄×C₅×C₈	—	4	1	no	—
111	C₄×C₅×C₈	—	4	1	no	—
112	C₅×#95	C₂×C₄	1	1	yes	characteristic
113	C₅×#95	C₂×C₄	1	1	yes	characteristic
114	C₅×#95	C₂×C₄	1	1	yes	characteristic
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	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
123	#1985	C₂×C₅	1	1	yes	characteristic, complemented
124	#1984	C₂×C₅	1	1	yes	characteristic, complemented
125	#1924	C₂×C₅	1	1	yes	characteristic
126	#1924	C₂×C₅	1	1	yes	characteristic
127	#1923	C₂×C₅	1	1	yes	characteristic
128	#1923	C₂×C₅	1	1	yes	characteristic
129	#1917	C₂×C₅	1	1	yes	characteristic, complemented
130	#1916	C₂×C₅	1	1	yes	characteristic, complemented
131	#1916	C₂×C₅	1	1	yes	characteristic, complemented
132	#1916	C₂×C₅	1	1	yes	characteristic, complemented
133	#1817	C₂×C₅	1	1	yes	characteristic
134	#1771	C₂×C₅	1	1	yes	characteristic, complemented
135	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
137	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Q₈	—	2	2	no	—
139	C₂×C₅×Q₈	—	2	2	no	—
140	C₂×C₅×Q₈	—	4	1	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	—	2	2	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	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
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	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	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	#41	1	2	yes	—
190	C₂×C₅×C₈	#41	1	2	yes	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	2	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	M₁₆	1	4	yes	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	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	—	4	1	no	—
217	C₄²×C₅	—	4	1	no	—
218	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₄⋊C₈	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×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×#97	C₂²×C₅	1	1	yes	characteristic
230	C₂×#97	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	#391	C₄×C₅	1	1	yes	characteristic
236	#389	C₄×C₅	1	1	yes	characteristic
237	#387	C₄×C₅	1	1	yes	characteristic
238	#387	C₄×C₅	1	1	yes	characteristic
239	#385	C₄×C₅	1	1	yes	characteristic
240	#385	C₄×C₅	1	1	yes	characteristic
241	#380	C₄×C₅	1	1	yes	characteristic
242	C₄×C₄⋊C₄	C₂²×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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	#336	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	C₂³×C₅	—	2	1	no	—
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	#131	1	2	yes	—
268	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
269	C₅×Q₈	—	4	4	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	—	2	1	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	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	—	4	4	no	—
305	C₂×C₄×C₅	—	4	4	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
311	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
312	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
313	C₂×C₄×C₅	#131	1	2	yes	—
314	C₂×C₄×C₅	#131	1	2	yes	—
315	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×#41	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	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
321	C₅×C₈	—	2	2	no	—
322	C₅×C₈	—	2	2	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	C₅×C₈	—	4	1	no	—
329	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
330	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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⋊Q₈	—	2	4	no	—
342	C₄×Q₈	—	4	1	no	—
343	C₄×Q₈	—	4	1	no	—
344	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
357	C₂×C₄²	—	4	1	no	—
358	C₂×C₄²	—	4	1	no	—
359	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	4	1	no	—
370	C₄⋊C₈	—	4	1	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	4	1	no	—
374	C₂²⋊C₈	—	4	1	no	—
375	#97	—	2	2	no	—
376	#97	—	4	1	no	—
377	C₄×C₈	—	2	2	no	—
378	C₄×C₈	—	4	1	no	—
379	C₄×C₈	—	4	1	no	—
380	C₄×C₈	—	4	1	no	—
381	#95	C₂×C₄×C₅	1	1	yes	characteristic
382	#95	C₂×C₄×C₅	1	1	yes	characteristic
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	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	4	1	no	—
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	C₄×#41	1	1	yes	characteristic
399	C₂²×C₅	#518	1	1	yes	characteristic
400	C₂²×C₅	#519	1	1	yes	characteristic
401	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
402	C₂²×C₅	C₂×#131	1	1	yes	characteristic
403	C₂²×C₅	C₂×#131	1	1	yes	characteristic
404	C₂²×C₅	C₂×#131	1	1	yes	characteristic
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	2	2	no	—
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	#539	1	1	yes	characteristic
419	C₄×C₅	#539	1	1	yes	characteristic
420	C₄×C₅	#542	1	1	yes	characteristic
421	C₄×C₅	#542	1	1	yes	characteristic
422	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
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	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	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	C₅×#41	1	2	yes	—
475	C₂×C₈	C₅×#41	1	2	yes	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	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	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₂×C₅	—	4	2	no	—
504	C₂×C₅	#2332	1	1	yes	characteristic
505	C₂×C₅	#2965	1	1	yes	characteristic
506	C₂×C₅	#2966	1	1	yes	characteristic
507	C₂×C₅	#2974	1	1	yes	characteristic
508	C₂×C₅	#2977	1	1	yes	characteristic
509	C₂×C₅	#2984	1	1	yes	characteristic
510	C₂×C₅	#2986	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	C₅×#131	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	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	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	—	4	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
561	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
562	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
563	C₂×C₄	C₅×#131	1	2	yes	—
564	C₂×C₄	C₅×#131	1	2	yes	—
565	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
567	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
570	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₅	#22321	1	1	yes	characteristic, direct product factor, Sylow
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₄×C₅×#41	1	1	yes	characteristic
588	C₂²	C₅×#518	1	1	yes	characteristic
589	C₂²	C₅×#519	1	1	yes	characteristic
590	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
591	C₂²	C₂×C₅×#131	1	1	yes	characteristic
592	C₂²	C₂×C₅×#131	1	1	yes	characteristic
593	C₂²	C₂×C₅×#131	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	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	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	C₅×#539	1	1	yes	characteristic
608	C₄	C₅×#539	1	1	yes	characteristic
609	C₄	C₅×#542	1	1	yes	characteristic
610	C₄	C₅×#542	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	C₅×#2332	1	1	yes	characteristic
613	C₂	C₅×#2965	1	1	yes	characteristic
614	C₂	C₅×#2966	1	1	yes	characteristic
615	C₂	C₅×#2974	1	1	yes	characteristic
616	C₂	C₅×#2977	1	1	yes	characteristic
617	C₂	C₅×#2984	1	1	yes	characteristic
618	C₂	C₅×#2986	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
8. C₅×#1917	C₂	semidirect
9. C₅×#1916	C₂	semidirect
10. C₅×#1916	C₂	semidirect
11. C₅×#1916	C₂	semidirect
13. C₅×#1771	C₂	semidirect
14. C₅×C₈×C₄⋊C₄	C₂	semidirect
59. #22321	C₅	direct (N × H)
123. #1985	C₂×C₅	semidirect
124. #1984	C₂×C₅	semidirect
129. #1917	C₂×C₅	semidirect
130. #1916	C₂×C₅	semidirect
131. #1916	C₂×C₅	semidirect
132. #1916	C₂×C₅	semidirect
134. #1771	C₂×C₅	semidirect
135. C₈×C₄⋊C₄	C₂×C₅	semidirect
579. C₅	#22321	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×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1817	2
C₅×#1771	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×C₂²⋊C₈	2
#22321	5

Subgroups — C5×#22321 #11945041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22321 #11945041