Subgroups — C₅×#24163 #11946883

Order 1280.

1078 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2324	C₂	1	1	yes	maximal, characteristic
5	C₅×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2000	C₂	1	1	yes	maximal, characteristic
8	C₅×#2000	C₂	1	1	yes	maximal, characteristic
9	C₅×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1798	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₅×#541	—	2	4	no	—
19	C₅×#541	—	2	4	no	—
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#126	—	2	1	no	—
22	C₂×C₅×#126	—	2	1	no	—
23	C₂×C₅×#125	—	2	1	no	—
24	C₂×C₅×#125	—	2	1	no	—
25	C₂×C₅×#125	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#121	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₅×#478	—	2	4	no	—
34	C₅×#461	—	2	4	no	—
35	C₂×C₅×#107	C₂²	1	1	yes	characteristic
36	C₂×C₅×#106	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×#103	C₂²	1	1	yes	characteristic
40	C₂×C₅×#103	C₂²	1	1	yes	characteristic
41	C₂×C₅×#103	C₂²	1	1	yes	characteristic
42	C₂×C₅×#103	C₂²	1	1	yes	characteristic
43	C₂×C₅×#103	C₂²	1	1	yes	characteristic
44	C₂×C₅×#103	C₂²	1	1	yes	characteristic
45	C₂×C₅×#102	C₂²	1	1	yes	characteristic
46	C₂×C₅×#102	C₂²	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×#390	—	2	1	no	—
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#388	—	2	1	no	—
53	C₅×#386	—	2	1	no	—
54	C₅×#385	—	2	1	no	—
55	C₅×#380	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#340	C₂²	1	1	yes	characteristic
60	C₅×#340	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#24163	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	—	2	1	no	—
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	—	2	2	no	—
71	C₂×C₅×SD₁₆	—	2	2	no	—
72	C₂×C₅×SD₁₆	—	2	2	no	—
73	C₂×C₅×SD₁₆	—	2	2	no	—
74	C₂×C₅×SD₁₆	—	4	1	no	—
75	C₂×C₅×SD₁₆	—	4	1	no	—
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	C₅×C₄⋊Q₈	—	2	2	no	—
81	C₅×C₄⋊Q₈	D₄	1	4	yes	complemented
82	C₅×#126	—	2	8	no	—
83	C₅×#126	—	2	8	no	—
84	C₅×#125	—	2	8	no	—
85	C₅×#125	—	2	8	no	—
86	C₅×#125	—	2	2	no	—
87	C₅×#125	D₄	1	4	yes	complemented
88	C₅×C₂²⋊Q₈	—	2	2	no	—
89	C₅×C₂²⋊Q₈	—	2	2	no	—
90	C₅×C₂²⋊Q₈	—	2	2	no	—
91	C₅×C₂²⋊Q₈	—	2	2	no	—
92	C₅×#121	—	2	2	no	—
93	C₅×#121	—	2	2	no	—
94	C₄×C₅×Q₈	—	2	2	no	—
95	C₄×C₅×Q₈	—	2	2	no	—
96	C₄×C₅×Q₈	—	2	2	no	—
97	C₄×C₅×Q₈	—	2	2	no	—
98	C₄×C₅×D₄	—	2	2	no	—
99	C₄×C₅×D₄	—	2	2	no	—
100	C₅×#117	—	2	2	no	—
101	C₅×#117	—	2	2	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×C₅×C₄⋊C₄	—	2	1	no	—
109	C₂×C₅×C₄⋊C₄	—	2	1	no	—
110	C₂×C₅×C₄⋊C₄	—	2	1	no	—
111	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₅	—	2	1	no	—
128	C₂×C₄²×C₅	—	2	1	no	—
129	C₂×C₄²×C₅	—	2	1	no	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₅×#107	—	2	2	no	—
133	C₅×#106	—	2	2	no	—
134	C₅×C₄⋊C₈	—	2	2	no	—
135	C₅×C₄⋊C₈	—	2	2	no	—
136	C₅×#103	—	2	2	no	—
137	C₅×#103	—	2	2	no	—
138	C₅×#103	—	2	2	no	—
139	C₅×#103	—	2	2	no	—
140	C₅×#103	—	4	1	no	—
141	C₅×#103	—	4	1	no	—
142	C₅×#102	—	2	2	no	—
143	C₅×#102	—	2	2	no	—
144	C₅×C₂²⋊C₈	—	4	1	no	—
145	C₅×C₂²⋊C₈	—	4	1	no	—
146	C₅×#95	—	2	1	no	—
147	C₅×#95	—	2	1	no	—
148	C₅×#95	—	2	1	no	—
149	C₂×#541	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×#478	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
152	#2324	C₂×C₅	1	1	yes	characteristic
153	#2036	C₂×C₅	1	1	yes	characteristic, complemented
154	#2035	C₂×C₅	1	1	yes	characteristic, complemented
155	#2000	C₂×C₅	1	1	yes	characteristic
156	#2000	C₂×C₅	1	1	yes	characteristic
157	#1989	C₂×C₅	1	1	yes	characteristic, complemented
158	#1981	C₂×C₅	1	1	yes	characteristic, complemented
159	#1880	C₂×C₅	1	1	yes	characteristic, complemented
160	#1880	C₂×C₅	1	1	yes	characteristic, complemented
161	#1865	C₂×C₅	1	1	yes	characteristic, complemented
162	#1863	C₂×C₅	1	1	yes	characteristic, complemented
163	#1798	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂⁴×C₅	—	2	1	no	—
165	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	2	1	no	—
168	C₂×C₅×Q₈	—	2	1	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	1	no	—
171	C₂×C₅×Q₈	—	2	1	no	—
172	C₂×C₅×Q₈	—	2	1	no	—
173	C₂×C₅×Q₈	—	2	1	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	1	no	—
176	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
177	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
178	C₂×C₅×D₄	—	2	4	no	—
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	1	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	1	no	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	8	1	no	—
185	C₂×C₅×D₄	—	8	1	no	—
186	C₂×C₅×D₄	#41	1	2	yes	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	4	2	no	—
201	C₂²×C₄×C₅	—	8	1	no	—
202	C₂²×C₄×C₅	—	8	1	no	—
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₅×SD₁₆	—	4	4	no	—
210	C₅×SD₁₆	—	4	4	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	4	no	—
224	C₅×C₄⋊C₄	—	2	4	no	—
225	C₅×C₄⋊C₄	—	2	4	no	—
226	C₅×C₄⋊C₄	—	2	4	no	—
227	C₅×C₄⋊C₄	—	2	4	no	—
228	C₅×C₄⋊C₄	—	2	4	no	—
229	C₅×C₄⋊C₄	—	2	4	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	1	no	—
237	C₅×C₄⋊C₄	—	2	1	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	8	1	no	—
241	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
243	C₅×C₄⋊C₄	#41	1	2	yes	—
244	C₅×C₂²⋊C₄	—	2	4	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	4	2	no	—
250	C₅×C₂²⋊C₄	—	8	1	no	—
251	C₅×C₂²⋊C₄	—	8	1	no	—
252	C₅×C₂²⋊C₄	—	8	1	no	—
253	C₄²×C₅	—	2	4	no	—
254	C₄²×C₅	—	2	4	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	8	1	no	—
258	C₄²×C₅	C₂×D₄	1	2	yes	—
259	C₄²×C₅	C₂×D₄	1	2	yes	—
260	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
261	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
262	#541	—	2	4	no	—
263	#541	—	2	4	no	—
264	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×#126	—	2	1	no	—
266	C₂×#126	—	2	1	no	—
267	C₂×#125	—	2	1	no	—
268	C₂×#125	—	2	1	no	—
269	C₂×#125	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×#121	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×#117	C₂²×C₅	1	1	yes	characteristic
277	#478	—	2	4	no	—
278	#461	—	2	4	no	—
279	C₂×#107	C₂²×C₅	1	1	yes	characteristic
280	C₂×#106	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	C₂×#103	C₂²×C₅	1	1	yes	characteristic
284	C₂×#103	C₂²×C₅	1	1	yes	characteristic
285	C₂×#103	C₂²×C₅	1	1	yes	characteristic
286	C₂×#103	C₂²×C₅	1	1	yes	characteristic
287	C₂×#103	C₂²×C₅	1	1	yes	characteristic
288	C₂×#103	C₂²×C₅	1	1	yes	characteristic
289	C₂×#102	C₂²×C₅	1	1	yes	characteristic
290	C₂×#102	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
293	#390	—	2	1	no	—
294	#390	C₂²×C₅	1	1	yes	characteristic
295	#389	C₂²×C₅	1	1	yes	characteristic
296	#388	—	2	1	no	—
297	#386	—	2	1	no	—
298	#385	—	2	1	no	—
299	#380	C₂²×C₅	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	#340	C₂²×C₅	1	1	yes	characteristic
302	#340	C₂²×C₅	1	1	yes	characteristic
303	#340	C₂²×C₅	1	1	yes	characteristic
304	#340	C₂²×C₅	1	1	yes	characteristic
305	#336	C₂²×C₅	1	1	yes	characteristic
306	#336	C₂²×C₅	1	1	yes	characteristic
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	4	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
322	C₅×Q₈	—	2	2	no	—
323	C₅×Q₈	—	2	2	no	—
324	C₅×Q₈	—	2	2	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	4	1	no	—
327	C₅×Q₈	—	4	1	no	—
328	C₅×Q₈	—	4	1	no	—
329	C₅×Q₈	—	4	1	no	—
330	C₅×D₄	—	2	2	no	—
331	C₅×D₄	—	2	2	no	—
332	C₅×D₄	—	4	1	no	—
333	C₅×D₄	—	4	1	no	—
334	C₅×D₄	—	8	4	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	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	8	4	no	—
374	C₂×C₄×C₅	#120	1	2	yes	—
375	C₂×C₄×C₅	#120	1	2	yes	—
376	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
381	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
382	C₅×C₈	—	4	1	no	—
383	C₅×C₈	—	4	1	no	—
384	C₅×C₈	—	4	1	no	—
385	C₅×C₈	—	4	1	no	—
386	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
387	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂×SD₁₆	—	2	2	no	—
393	C₂×SD₁₆	—	2	2	no	—
394	C₂×SD₁₆	—	2	2	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×SD₁₆	—	4	1	no	—
397	C₂×SD₁₆	—	4	1	no	—
398	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
402	C₄⋊Q₈	—	2	2	no	—
403	C₄⋊Q₈	C₅×D₄	1	4	yes	complemented
404	#126	—	2	8	no	—
405	#126	—	2	8	no	—
406	#125	—	2	8	no	—
407	#125	—	2	8	no	—
408	#125	—	2	2	no	—
409	#125	C₅×D₄	1	4	yes	complemented
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	2	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	#121	—	2	2	no	—
415	#121	—	2	2	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
454	#107	—	2	2	no	—
455	#106	—	2	2	no	—
456	C₄⋊C₈	—	2	2	no	—
457	C₄⋊C₈	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	4	1	no	—
463	#103	—	4	1	no	—
464	#102	—	2	2	no	—
465	#102	—	2	2	no	—
466	C₂²⋊C₈	—	4	1	no	—
467	C₂²⋊C₈	—	4	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	C₂²×C₅	—	4	1	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	1	no	—
474	C₂²×C₅	—	4	2	no	—
475	C₂²×C₅	—	4	1	no	—
476	C₂²×C₅	—	4	2	no	—
477	C₂²×C₅	—	4	1	no	—
478	C₂²×C₅	—	4	1	no	—
479	C₂²×C₅	—	4	1	no	—
480	C₂²×C₅	—	4	1	no	—
481	C₂²×C₅	—	8	1	no	—
482	C₂²×C₅	—	8	1	no	—
483	C₂²×C₅	—	8	1	no	—
484	C₂²×C₅	—	8	1	no	—
485	C₂²×C₅	C₂×#120	1	1	yes	characteristic
486	C₂²×C₅	#525	1	1	yes	characteristic
487	C₂²×C₅	#537	1	1	yes	characteristic
488	C₂²×C₅	#577	1	1	yes	characteristic
489	C₂²×C₅	#577	1	1	yes	characteristic
490	C₂²×C₅	#577	1	1	yes	characteristic
491	C₂²×C₅	#578	1	1	yes	characteristic
492	C₄×C₅	—	2	2	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	4	2	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	2	no	—
497	C₄×C₅	—	4	2	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	2	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	4	2	no	—
502	C₄×C₅	—	8	1	no	—
503	C₄×C₅	—	8	1	no	—
504	C₄×C₅	#546	1	1	yes	characteristic
505	C₄×C₅	#547	1	1	yes	characteristic
506	C₄×C₅	#548	1	1	yes	characteristic
507	C₄×C₅	#550	1	1	yes	characteristic
508	C₂⁴	—	2	1	no	—
509	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
521	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	8	1	no	—
529	C₂×D₄	—	8	1	no	—
530	C₂×D₄	C₅×#41	1	2	yes	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
553	SD₁₆	—	4	4	no	—
554	SD₁₆	—	4	4	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	8	1	no	—
585	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
586	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
587	C₄⋊C₄	C₅×#41	1	2	yes	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	8	1	no	—
595	C₂²⋊C₄	—	8	1	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	8	1	no	—
602	C₄²	C₂×C₅×D₄	1	2	yes	—
603	C₄²	C₂×C₅×D₄	1	2	yes	—
604	C₂×C₅	—	8	1	no	—
605	C₂×C₅	—	8	2	no	—
606	C₂×C₅	#2407	1	1	yes	characteristic
607	C₂×C₅	#3010	1	1	yes	characteristic
608	C₂×C₅	#3013	1	1	yes	characteristic
609	C₂×C₅	#3120	1	1	yes	characteristic
610	C₂×C₅	#3123	1	1	yes	characteristic
611	C₂×C₅	#3258	1	1	yes	characteristic
612	C₂×C₅	#3260	1	1	yes	characteristic
613	C₂³	—	2	1	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	8	4	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	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₅×#120	1	2	yes	—
681	C₂×C₄	C₅×#120	1	2	yes	—
682	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
684	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
685	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
686	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₅	#24163	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	C₂×C₅×#120	1	1	yes	characteristic
708	C₂²	C₅×#525	1	1	yes	characteristic
709	C₂²	C₅×#537	1	1	yes	characteristic
710	C₂²	C₅×#577	1	1	yes	characteristic
711	C₂²	C₅×#577	1	1	yes	characteristic
712	C₂²	C₅×#577	1	1	yes	characteristic
713	C₂²	C₅×#578	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	C₅×#546	1	1	yes	characteristic
727	C₄	C₅×#547	1	1	yes	characteristic
728	C₄	C₅×#548	1	1	yes	characteristic
729	C₄	C₅×#550	1	1	yes	characteristic
730	C₂	—	8	1	no	—
731	C₂	—	8	2	no	—
732	C₂	C₅×#2407	1	1	yes	characteristic
733	C₂	C₅×#3010	1	1	yes	characteristic
734	C₂	C₅×#3013	1	1	yes	characteristic
735	C₂	C₅×#3120	1	1	yes	characteristic
736	C₂	C₅×#3123	1	1	yes	characteristic
737	C₂	C₅×#3258	1	1	yes	characteristic
738	C₂	C₅×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×#541	C₂	semidirect
2. C₂×C₅×#478	C₂	semidirect
3. C₂×C₅×#461	C₂	semidirect
5. C₅×#2036	C₂	semidirect
6. C₅×#2035	C₂	semidirect
9. C₅×#1989	C₂	semidirect
10. C₅×#1981	C₂	semidirect
11. C₅×#1880	C₂	semidirect
12. C₅×#1880	C₂	semidirect
13. C₅×#1865	C₂	semidirect
14. C₅×#1863	C₂	semidirect
15. C₅×#1798	C₂	semidirect
63. #24163	C₅	direct (N × H)
81. C₅×C₄⋊Q₈	D₄	semidirect
87. C₅×#125	D₄	semidirect
149. C₂×#541	C₂×C₅	semidirect
150. C₂×#478	C₂×C₅	semidirect
151. C₂×#461	C₂×C₅	semidirect
153. #2036	C₂×C₅	semidirect
154. #2035	C₂×C₅	semidirect
157. #1989	C₂×C₅	semidirect
158. #1981	C₂×C₅	semidirect
159. #1880	C₂×C₅	semidirect
160. #1880	C₂×C₅	semidirect
161. #1865	C₂×C₅	semidirect
162. #1863	C₂×C₅	semidirect
163. #1798	C₂×C₅	semidirect
403. C₄⋊Q₈	C₅×D₄	semidirect
409. #125	C₅×D₄	semidirect
692. C₅	#24163	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×#541	2
C₂×C₅×#478	2
C₂×C₅×#461	2
C₅×#2324	2
C₅×#2036	2
C₅×#2035	2
C₅×#2000	2
C₅×#1989	2
C₅×#1981	2
C₅×#1880	2
C₅×#1865	2
C₅×#1863	2
C₅×#1798	2
#24163	5

Subgroups — C5×#24163 #11946883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24163 #11946883