Subgroups — C₅×#81062 #14430765

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5729	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5545	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5009	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4871	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4870	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4861	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4860	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4770	C₂	1	1	yes	maximal, characteristic
13	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic
14	C₅×#4763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3081	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₅×#946	—	2	1	no	—
21	C₅×#944	—	2	1	no	—
22	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
23	C₄×C₅×#67	—	2	1	no	—
24	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
25	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
27	C₅×#896	—	2	1	no	—
28	C₅×#893	C₂²	1	1	yes	characteristic
29	C₅×#892	C₂²	1	1	yes	characteristic
30	C₅×#892	C₂²	1	1	yes	characteristic
31	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×#890	C₂²	1	1	yes	characteristic, complemented
33	C₅×#889	—	2	1	no	—
34	C₅×#888	C₂²	1	1	yes	characteristic, complemented
35	C₅×#67⋊C₄	—	2	1	no	—
36	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
37	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
38	C₅×#872	C₂²	1	1	yes	characteristic
39	C₅×#870	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic
45	C₅×#832	C₂²	1	1	yes	characteristic
46	C₅×#832	C₂²	1	1	yes	characteristic
47	C₅×#821	C₂²	1	1	yes	characteristic
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×#818	C₂²	1	1	yes	characteristic, complemented
50	C₅×#817	C₂²	1	1	yes	characteristic, complemented
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×#809	C₂²	1	1	yes	characteristic
54	C₅×#809	C₂²	1	1	yes	characteristic
55	C₅×#808	C₂²	1	1	yes	characteristic, complemented
56	C₅×#807	C₂²	1	1	yes	characteristic, complemented
57	C₅×#807	C₂²	1	1	yes	characteristic, complemented
58	C₅×#807	C₂²	1	1	yes	characteristic, complemented
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	#81062	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#544	—	3	1	no	—
62	C₅×#518	—	3	1	no	—
63	C₅×#478	—	3	1	no	—
64	C₅×#478	—	3	1	no	—
65	C₅×#478	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#476	—	3	1	no	—
68	C₅×#476	D₃	1	1	yes	characteristic, complemented
69	C₅×#474	—	3	1	no	—
70	C₅×#474	—	3	1	no	—
71	C₅×#428	—	3	1	no	—
72	C₅×#427	—	3	1	no	—
73	C₅×#424	—	3	1	no	—
74	C₅×#418	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	—	2	1	no	—
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₅×#67	—	2	1	no	—
81	C₂²×C₅×Dic₃	—	2	1	no	—
82	C₅×D₃×D₄	—	2	2	no	—
83	C₅×D₃×D₄	Q₈	1	4	yes	complemented
84	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	—	2	1	no	—
86	C₂×C₄×C₅×D₃	—	2	1	no	—
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×Dic₆	—	2	1	no	—
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×#217	—	2	1	no	—
99	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
100	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
101	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
102	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
103	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
104	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
105	C₅×C₄⋊Dic₃	—	2	1	no	—
106	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₅×Dic₃⋊C₄	—	2	1	no	—
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
115	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
116	C₄×C₅×Dic₃	—	2	1	no	—
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
122	C₅×D₃×C₈	—	2	2	no	—
123	#5729	C₂×C₅	1	1	yes	characteristic, complemented
124	#5545	C₂×C₅	1	1	yes	characteristic
125	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
126	#5087	C₂×C₅	1	1	yes	characteristic, complemented
127	#5009	C₂×C₅	1	1	yes	characteristic, complemented
128	#4871	C₂×C₅	1	1	yes	characteristic, complemented
129	#4870	C₂×C₅	1	1	yes	characteristic, complemented
130	#4861	C₂×C₅	1	1	yes	characteristic, complemented
131	#4860	C₂×C₅	1	1	yes	characteristic, complemented
132	#4847	C₂×C₅	1	1	yes	characteristic, complemented
133	#4839	C₂×C₅	1	1	yes	characteristic, complemented
134	#4770	C₂×C₅	1	1	yes	characteristic
135	D₃×#102	C₂×C₅	1	1	yes	characteristic
136	#4763	C₂×C₅	1	1	yes	characteristic, complemented
137	#4759	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₅×D₄	—	3	1	no	—
139	C₂×C₅×M₁₆	—	3	1	no	—
140	C₂²×C₅×C₈	—	3	1	no	—
141	C₅×C₄⋊Q₈	—	3	1	no	—
142	C₅×C₄⋊Q₈	—	6	1	no	—
143	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
144	C₅×#125	—	3	1	no	—
145	C₅×#125	—	3	1	no	—
146	C₅×#125	—	6	1	no	—
147	C₅×C₂²⋊Q₈	—	6	1	no	—
148	C₅×C₂²⋊Q₈	—	6	1	no	—
149	C₄×C₅×D₄	—	3	1	no	—
150	C₄×C₅×D₄	—	3	1	no	—
151	C₄×C₅×D₄	—	3	1	no	—
152	C₄×C₅×D₄	—	6	1	no	—
153	C₄×C₅×D₄	—	6	1	no	—
154	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
155	C₅×#117	—	3	1	no	—
156	C₅×#117	—	3	1	no	—
157	C₅×#117	—	3	1	no	—
158	C₂×C₅×C₄⋊C₄	—	3	1	no	—
159	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
161	C₅×#107	—	3	1	no	—
162	C₅×#107	—	3	1	no	—
163	C₅×#107	—	3	1	no	—
164	C₅×#107	—	3	1	no	—
165	C₅×#106	—	3	1	no	—
166	C₅×#106	—	3	1	no	—
167	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
168	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×C₄⋊C₈	—	3	1	no	—
172	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
173	C₅×#102	—	3	1	no	—
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×#102	C₂×D₃	1	1	yes	characteristic
180	C₅×#102	C₂×D₃	1	1	yes	characteristic
181	#3081	—	3	1	no	Sylow
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂²×C₅×D₃	—	2	1	no	—
184	C₂²×C₅×D₃	—	2	4	no	—
185	C₂²×C₅×D₃	—	8	1	no	—
186	C₂²×C₅×D₃	—	8	1	no	—
187	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
188	C₃×C₅×Q₈	—	8	1	no	—
189	C₃×C₅×D₄	—	2	1	no	—
190	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	8	1	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₅×#67	—	2	4	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	8	1	no	—
203	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
206	C₅×D₁₂	—	2	1	no	—
207	C₅×D₁₂	C₂×Q₈	1	2	yes	—
208	C₄×C₅×D₃	—	8	1	no	—
209	C₄×C₅×D₃	—	8	1	no	—
210	C₄×C₅×D₃	—	8	1	no	—
211	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
212	C₄×C₅×D₃	#41	1	2	yes	—
213	C₅×Dic₆	—	8	1	no	—
214	C₃×C₅×C₈	—	2	1	no	—
215	C₃×C₅×C₈	—	2	1	no	—
216	C₅×C₃⋊C₈	—	2	1	no	—
217	C₅×C₃⋊C₈	—	2	1	no	—
218	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
219	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
220	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
221	#946	—	2	1	no	—
222	#944	—	2	1	no	—
223	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
224	C₄×#67	—	2	1	no	—
225	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
226	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
227	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
228	#896	—	2	1	no	—
229	#893	C₂²×C₅	1	1	yes	characteristic
230	#892	C₂²×C₅	1	1	yes	characteristic
231	#892	C₂²×C₅	1	1	yes	characteristic
232	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	#890	C₂²×C₅	1	1	yes	characteristic, complemented
234	#889	—	2	1	no	—
235	#888	C₂²×C₅	1	1	yes	characteristic, complemented
236	#67⋊C₄	—	2	1	no	—
237	D₃×C₂²⋊C₄	—	2	1	no	—
238	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
239	#872	C₂²×C₅	1	1	yes	characteristic
240	#870	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
244	C₃×#102	C₂²×C₅	1	1	yes	characteristic
245	C₃×#102	C₂²×C₅	1	1	yes	characteristic
246	#832	C₂²×C₅	1	1	yes	characteristic
247	#832	C₂²×C₅	1	1	yes	characteristic
248	#821	C₂²×C₅	1	1	yes	characteristic
249	#821	C₂²×C₅	1	1	yes	characteristic
250	#818	C₂²×C₅	1	1	yes	characteristic, complemented
251	#817	C₂²×C₅	1	1	yes	characteristic, complemented
252	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
253	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
254	#809	C₂²×C₅	1	1	yes	characteristic
255	#809	C₂²×C₅	1	1	yes	characteristic
256	#808	C₂²×C₅	1	1	yes	characteristic, complemented
257	#807	C₂²×C₅	1	1	yes	characteristic, complemented
258	#807	C₂²×C₅	1	1	yes	characteristic, complemented
259	#807	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂⁴×C₅	—	6	1	no	—
262	C₂×C₅×Q₈	—	2	1	no	—
263	C₂×C₅×Q₈	—	6	1	no	—
264	C₂×C₅×D₄	—	3	4	no	—
265	C₂×C₅×D₄	—	3	1	no	—
266	C₂×C₅×D₄	—	6	2	no	—
267	C₂×C₅×D₄	—	6	1	no	—
268	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	—	2	1	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₂²×C₄×C₅	—	6	1	no	—
272	C₂²×C₄×C₅	—	6	1	no	—
273	C₂²×C₄×C₅	—	6	1	no	—
274	C₂²×C₄×C₅	—	6	1	no	—
275	C₅×M₁₆	—	6	2	no	—
276	C₂×C₅×C₈	—	3	1	no	—
277	C₂×C₅×C₈	—	3	1	no	—
278	C₂×C₅×C₈	—	6	2	no	—
279	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	3	1	no	—
283	C₅×C₄⋊C₄	—	3	1	no	—
284	C₅×C₄⋊C₄	—	3	1	no	—
285	C₅×C₄⋊C₄	—	3	1	no	—
286	C₅×C₄⋊C₄	—	3	1	no	—
287	C₅×C₄⋊C₄	—	6	1	no	—
288	C₅×C₄⋊C₄	—	6	1	no	—
289	C₅×C₄⋊C₄	—	6	1	no	—
290	C₅×C₄⋊C₄	—	6	1	no	—
291	C₅×C₄⋊C₄	—	6	1	no	—
292	C₅×C₄⋊C₄	—	6	1	no	—
293	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
296	C₅×C₂²⋊C₄	—	2	1	no	—
297	C₅×C₂²⋊C₄	—	3	1	no	—
298	C₅×C₂²⋊C₄	—	3	1	no	—
299	C₅×C₂²⋊C₄	—	6	1	no	—
300	C₅×C₂²⋊C₄	—	6	1	no	—
301	C₅×C₂²⋊C₄	—	6	1	no	—
302	C₅×C₂²⋊C₄	—	6	1	no	—
303	C₅×C₂²⋊C₄	—	6	1	no	—
304	C₄²×C₅	—	3	1	no	—
305	C₄²×C₅	—	6	1	no	—
306	C₄²×C₅	—	6	1	no	—
307	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
308	#544	—	3	1	no	—
309	#518	—	3	1	no	—
310	#478	—	3	1	no	—
311	#478	—	3	1	no	—
312	#478	—	3	1	no	—
313	#478	—	3	1	no	—
314	#476	—	3	1	no	—
315	#476	C₅×D₃	1	1	yes	characteristic, complemented
316	#474	—	3	1	no	—
317	#474	—	3	1	no	—
318	#428	—	3	1	no	—
319	#427	—	3	1	no	—
320	#424	—	3	1	no	—
321	#418	—	3	1	no	—
322	C₂×#102	—	3	1	no	—
323	C₂²×C₃×C₅	—	2	2	no	—
324	C₂²×C₃×C₅	—	4	1	no	—
325	C₂²×C₃×C₅	—	4	1	no	—
326	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₅×D₃	—	2	1	no	—
328	C₂×C₅×D₃	—	2	1	no	—
329	C₂×C₅×D₃	—	2	2	no	—
330	C₂×C₅×D₃	—	4	1	no	—
331	C₂×C₅×D₃	—	4	1	no	—
332	C₂×C₅×D₃	—	8	4	no	—
333	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
334	C₃×C₄×C₅	—	2	1	no	—
335	C₃×C₄×C₅	—	2	1	no	—
336	C₃×C₄×C₅	—	4	1	no	—
337	C₃×C₄×C₅	—	4	1	no	—
338	C₃×C₄×C₅	—	4	1	no	—
339	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
340	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₅×Dic₃	—	2	1	no	—
342	C₅×Dic₃	—	2	1	no	—
343	C₅×Dic₃	—	4	1	no	—
344	C₅×Dic₃	—	4	1	no	—
345	C₅×Dic₃	—	4	1	no	—
346	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
347	C₂³×D₃	—	2	1	no	—
348	C₂×C₃×Q₈	—	2	1	no	—
349	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	—	2	1	no	—
351	C₂×#67	—	2	1	no	—
352	C₂²×Dic₃	—	2	1	no	—
353	D₃×D₄	—	2	2	no	—
354	D₃×D₄	C₅×Q₈	1	4	yes	complemented
355	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄×D₃	—	2	1	no	—
357	C₂×C₄×D₃	—	2	1	no	—
358	C₂×C₄×D₃	—	2	1	no	—
359	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
360	C₂×Dic₆	—	2	1	no	—
361	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₃×C₄⋊C₄	—	2	1	no	—
364	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
365	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
366	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
367	C₃×C₂²⋊C₄	—	2	1	no	—
368	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
369	#217	—	2	1	no	—
370	(C₂×D₃)⋊C₄	—	2	1	no	—
371	(C₂×D₃)⋊C₄	—	2	1	no	—
372	(C₂×D₃)⋊C₄	—	2	1	no	—
373	(C₂×D₃)⋊C₄	—	2	1	no	—
374	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
375	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
376	C₄⋊Dic₃	—	2	1	no	—
377	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
380	Dic₃⋊C₄	—	2	1	no	—
381	Dic₃⋊C₄	—	2	1	no	—
382	Dic₃⋊C₄	—	2	1	no	—
383	Dic₃⋊C₄	—	2	1	no	—
384	Dic₃⋊C₄	—	2	1	no	—
385	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
386	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
387	C₄×Dic₃	—	2	1	no	—
388	C₄×Dic₃	—	2	1	no	—
389	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
392	ΓL(1,𝔽₂₅)	—	2	2	no	—
393	D₃×C₈	—	2	2	no	—
394	C₂³×C₅	—	2	1	no	—
395	C₂³×C₅	—	3	1	no	—
396	C₂³×C₅	—	6	4	no	—
397	C₂³×C₅	—	6	1	no	—
398	C₂³×C₅	—	24	1	no	—
399	C₂³×C₅	—	24	1	no	—
400	C₅×Q₈	—	8	1	no	—
401	C₅×Q₈	—	24	1	no	—
402	C₅×D₄	—	2	1	no	—
403	C₅×D₄	—	3	2	no	—
404	C₅×D₄	—	6	4	no	—
405	C₅×D₄	—	6	1	no	—
406	C₅×D₄	D₃×Q₈	1	2	yes	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	3	1	no	—
411	C₂×C₄×C₅	—	3	2	no	—
412	C₂×C₄×C₅	—	3	2	no	—
413	C₂×C₄×C₅	—	3	1	no	—
414	C₂×C₄×C₅	—	3	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	—	8	1	no	—
419	C₂×C₄×C₅	—	24	1	no	—
420	C₂×C₄×C₅	—	24	1	no	—
421	C₂×C₄×C₅	—	24	1	no	—
422	C₂×C₄×C₅	—	24	1	no	—
423	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
425	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	—	2	1	no	—
428	C₅×C₈	—	6	1	no	—
429	C₅×C₈	—	6	1	no	—
430	C₂²×D₄	—	3	1	no	—
431	C₂×M₁₆	—	3	1	no	—
432	C₂²×C₈	—	3	1	no	—
433	C₄⋊Q₈	—	3	1	no	—
434	C₄⋊Q₈	—	6	1	no	—
435	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
436	#125	—	3	1	no	—
437	#125	—	3	1	no	—
438	#125	—	6	1	no	—
439	C₂²⋊Q₈	—	6	1	no	—
440	C₂²⋊Q₈	—	6	1	no	—
441	C₄×D₄	—	3	1	no	—
442	C₄×D₄	—	3	1	no	—
443	C₄×D₄	—	3	1	no	—
444	C₄×D₄	—	6	1	no	—
445	C₄×D₄	—	6	1	no	—
446	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
447	#117	—	3	1	no	—
448	#117	—	3	1	no	—
449	#117	—	3	1	no	—
450	C₂×C₄⋊C₄	—	3	1	no	—
451	C₂×C₂²⋊C₄	—	6	1	no	—
452	C₂×C₂²⋊C₄	—	6	1	no	—
453	#107	—	3	1	no	—
454	#107	—	3	1	no	—
455	#107	—	3	1	no	—
456	#107	—	3	1	no	—
457	#106	—	3	1	no	—
458	#106	—	3	1	no	—
459	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
460	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
461	C₄⋊C₈	—	3	1	no	—
462	C₄⋊C₈	—	3	1	no	—
463	C₄⋊C₈	—	3	1	no	—
464	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
465	#102	—	3	1	no	—
466	#102	—	3	1	no	—
467	#102	—	3	1	no	—
468	#102	—	3	1	no	—
469	#102	—	3	1	no	—
470	#102	—	3	1	no	—
471	#102	C₂×C₅×D₃	1	1	yes	characteristic
472	#102	C₂×C₅×D₃	1	1	yes	characteristic
473	C₂×C₃×C₅	—	4	2	no	—
474	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
475	C₂×C₃×C₅	#576	1	1	yes	characteristic
476	C₂×C₃×C₅	#577	1	1	yes	characteristic
477	C₅×D₃	—	2	2	no	—
478	C₅×D₃	—	4	2	no	—
479	C₂³×C₃	—	2	1	no	—
480	C₂²×D₃	—	2	1	no	—
481	C₂²×D₃	—	2	4	no	—
482	C₂²×D₃	—	8	1	no	—
483	C₂²×D₃	—	8	1	no	—
484	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
485	C₃×Q₈	—	8	1	no	—
486	C₃×D₄	—	2	1	no	—
487	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	8	1	no	—
492	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
495	#67	—	2	4	no	—
496	C₂×Dic₃	—	2	1	no	—
497	C₂×Dic₃	—	2	1	no	—
498	C₂×Dic₃	—	2	1	no	—
499	C₂×Dic₃	—	8	1	no	—
500	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
503	D₁₂	—	2	1	no	—
504	D₁₂	C₂×C₅×Q₈	1	2	yes	—
505	C₄×D₃	—	8	1	no	—
506	C₄×D₃	—	8	1	no	—
507	C₄×D₃	—	8	1	no	—
508	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
509	C₄×D₃	C₅×#41	1	2	yes	—
510	Dic₆	—	8	1	no	—
511	C₃×C₈	—	2	1	no	—
512	C₃×C₈	—	2	1	no	—
513	C₃⋊C₈	—	2	1	no	—
514	C₃⋊C₈	—	2	1	no	—
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	3	2	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	1	no	—
519	C₂²×C₅	—	6	1	no	—
520	C₂²×C₅	—	6	1	no	—
521	C₂²×C₅	—	6	2	no	—
522	C₂²×C₅	—	12	1	no	—
523	C₂²×C₅	—	12	1	no	—
524	C₂²×C₅	—	24	4	no	—
525	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
526	C₄×C₅	—	2	1	no	—
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	3	2	no	—
529	C₄×C₅	—	4	1	no	—
530	C₄×C₅	—	4	1	no	—
531	C₄×C₅	—	4	1	no	—
532	C₄×C₅	—	6	1	no	—
533	C₄×C₅	—	6	1	no	—
534	C₄×C₅	—	12	1	no	—
535	C₄×C₅	—	12	1	no	—
536	C₄×C₅	—	12	1	no	—
537	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
538	C₄×C₅	D₃×#41	1	1	yes	characteristic
539	C₂⁴	—	6	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	6	1	no	—
542	C₂×D₄	—	3	4	no	—
543	C₂×D₄	—	3	1	no	—
544	C₂×D₄	—	6	2	no	—
545	C₂×D₄	—	6	1	no	—
546	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	3	1	no	—
549	C₂²×C₄	—	6	1	no	—
550	C₂²×C₄	—	6	1	no	—
551	C₂²×C₄	—	6	1	no	—
552	C₂²×C₄	—	6	1	no	—
553	M₁₆	—	6	2	no	—
554	C₂×C₈	—	3	1	no	—
555	C₂×C₈	—	3	1	no	—
556	C₂×C₈	—	6	2	no	—
557	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
558	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	3	1	no	—
561	C₄⋊C₄	—	3	1	no	—
562	C₄⋊C₄	—	3	1	no	—
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	6	1	no	—
566	C₄⋊C₄	—	6	1	no	—
567	C₄⋊C₄	—	6	1	no	—
568	C₄⋊C₄	—	6	1	no	—
569	C₄⋊C₄	—	6	1	no	—
570	C₄⋊C₄	—	6	1	no	—
571	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
572	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
573	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	3	1	no	—
576	C₂²⋊C₄	—	3	1	no	—
577	C₂²⋊C₄	—	6	1	no	—
578	C₂²⋊C₄	—	6	1	no	—
579	C₂²⋊C₄	—	6	1	no	—
580	C₂²⋊C₄	—	6	1	no	—
581	C₂²⋊C₄	—	6	1	no	—
582	C₄²	—	3	1	no	—
583	C₄²	—	6	1	no	—
584	C₄²	—	6	1	no	—
585	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
587	C₂²×C₃	—	2	2	no	—
588	C₂²×C₃	—	4	1	no	—
589	C₂²×C₃	—	4	1	no	—
590	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
591	C₂×D₃	—	2	1	no	—
592	C₂×D₃	—	2	1	no	—
593	C₂×D₃	—	2	2	no	—
594	C₂×D₃	—	4	1	no	—
595	C₂×D₃	—	4	1	no	—
596	C₂×D₃	—	8	4	no	—
597	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	—	4	1	no	—
602	C₃×C₄	—	4	1	no	—
603	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
604	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
605	Dic₃	—	2	1	no	—
606	Dic₃	—	2	1	no	—
607	Dic₃	—	4	1	no	—
608	Dic₃	—	4	1	no	—
609	Dic₃	—	4	1	no	—
610	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
611	C₂×C₅	—	4	2	no	—
612	C₂×C₅	—	6	2	no	—
613	C₂×C₅	—	12	2	no	—
614	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
615	C₂×C₅	#5762	1	1	yes	characteristic
616	C₂×C₅	#5774	1	1	yes	characteristic
617	C₂³	—	2	1	no	—
618	C₂³	—	3	1	no	—
619	C₂³	—	6	4	no	—
620	C₂³	—	6	1	no	—
621	C₂³	—	24	1	no	—
622	C₂³	—	24	1	no	—
623	Q₈	—	8	1	no	—
624	Q₈	—	24	1	no	—
625	D₄	—	2	1	no	—
626	D₄	—	3	2	no	—
627	D₄	—	6	4	no	—
628	D₄	—	6	1	no	—
629	D₄	C₅×D₃×Q₈	1	2	yes	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	2	no	—
635	C₂×C₄	—	3	2	no	—
636	C₂×C₄	—	3	1	no	—
637	C₂×C₄	—	3	1	no	—
638	C₂×C₄	—	6	1	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	6	1	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	24	1	no	—
643	C₂×C₄	—	24	1	no	—
644	C₂×C₄	—	24	1	no	—
645	C₂×C₄	—	24	1	no	—
646	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
647	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
649	C₈	—	2	1	no	—
650	C₈	—	2	1	no	—
651	C₈	—	6	1	no	—
652	C₈	—	6	1	no	—
653	C₂×C₃	—	4	2	no	—
654	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
655	C₂×C₃	C₅×#576	1	1	yes	characteristic
656	C₂×C₃	C₅×#577	1	1	yes	characteristic
657	D₃	—	2	2	no	—
658	D₃	—	4	2	no	—
659	C₅	#81062	1	1	yes	characteristic, direct product factor, Sylow
660	C₂²	—	2	2	no	—
661	C₂²	—	3	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	6	1	no	—
665	C₂²	—	6	1	no	—
666	C₂²	—	6	2	no	—
667	C₂²	—	12	1	no	—
668	C₂²	—	12	1	no	—
669	C₂²	—	24	4	no	—
670	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	3	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	6	1	no	—
678	C₄	—	6	1	no	—
679	C₄	—	12	1	no	—
680	C₄	—	12	1	no	—
681	C₄	—	12	1	no	—
682	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
683	C₄	C₅×D₃×#41	1	1	yes	characteristic
684	C₃	C₅×#3081	1	1	yes	characteristic, complemented, Sylow
685	C₂	—	4	2	no	—
686	C₂	—	6	2	no	—
687	C₂	—	12	2	no	—
688	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
689	C₂	C₅×#5762	1	1	yes	characteristic
690	C₂	C₅×#5774	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#476	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#476	D₃
hypocenter	C₃	C₅×#3081
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#476

Complements

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

N	H ≅ G/N	type
1. C₅×#5729	C₂	semidirect
3. C₃×C₅×#476	C₂	semidirect
4. C₅×#5087	C₂	semidirect
5. C₅×#5009	C₂	semidirect
6. C₅×#4871	C₂	semidirect
7. C₅×#4870	C₂	semidirect
8. C₅×#4861	C₂	semidirect
9. C₅×#4860	C₂	semidirect
10. C₅×#4847	C₂	semidirect
11. C₅×#4839	C₂	semidirect
14. C₅×#4763	C₂	semidirect
15. C₅×#4759	C₂	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₅×#890	C₂²	semidirect
34. C₅×#888	C₂²	semidirect
39. C₅×#870	C₂²	semidirect
40. C₃×C₅×#106	C₂²	semidirect
41. C₃×C₅×#106	C₂²	semidirect
42. C₃×C₅×C₄⋊C₈	C₂²	semidirect
49. C₅×#818	C₂²	semidirect
50. C₅×#817	C₂²	semidirect
51. C₅×Dic₃⋊C₈	C₂²	semidirect
52. C₅×Dic₃⋊C₈	C₂²	semidirect
55. C₅×#808	C₂²	semidirect
56. C₅×#807	C₂²	semidirect
57. C₅×#807	C₂²	semidirect
58. C₅×#807	C₂²	semidirect
59. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
60. #81062	C₅	direct (N × H)
68. C₅×#476	D₃	semidirect
83. C₅×D₃×D₄	Q₈	semidirect
123. #5729	C₂×C₅	semidirect
125. C₃×#476	C₂×C₅	semidirect
126. #5087	C₂×C₅	semidirect
127. #5009	C₂×C₅	semidirect
128. #4871	C₂×C₅	semidirect
129. #4870	C₂×C₅	semidirect
130. #4861	C₂×C₅	semidirect
131. #4860	C₂×C₅	semidirect
132. #4847	C₂×C₅	semidirect
133. #4839	C₂×C₅	semidirect
136. #4763	C₂×C₅	semidirect
137. #4759	C₂×C₅	semidirect
143. C₅×C₄⋊Q₈	C₂×D₃	semidirect
167. C₅×#106	C₂×D₃	semidirect
168. C₅×#106	C₂×D₃	semidirect
172. C₅×C₄⋊C₈	C₂×D₃	semidirect
219. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
233. #890	C₂²×C₅	semidirect
235. #888	C₂²×C₅	semidirect
240. #870	C₂²×C₅	semidirect
241. C₃×#106	C₂²×C₅	semidirect
242. C₃×#106	C₂²×C₅	semidirect
243. C₃×C₄⋊C₈	C₂²×C₅	semidirect
250. #818	C₂²×C₅	semidirect
251. #817	C₂²×C₅	semidirect
252. Dic₃⋊C₈	C₂²×C₅	semidirect
253. Dic₃⋊C₈	C₂²×C₅	semidirect
256. #808	C₂²×C₅	semidirect
257. #807	C₂²×C₅	semidirect
258. #807	C₂²×C₅	semidirect
259. #807	C₂²×C₅	semidirect
260. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
315. #476	C₅×D₃	semidirect
354. D₃×D₄	C₅×Q₈	semidirect
435. C₄⋊Q₈	C₂×C₅×D₃	semidirect
459. #106	C₂×C₅×D₃	semidirect
460. #106	C₂×C₅×D₃	semidirect
464. C₄⋊C₈	C₂×C₅×D₃	semidirect
586. C₃×C₅	#3081	semidirect
659. C₅	#81062	direct (N × H)
684. C₃	C₅×#3081	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5729	2
C₅×#5545	2
C₃×C₅×#476	2
C₅×#5087	2
C₅×#5009	2
C₅×#4871	2
C₅×#4870	2
C₅×#4861	2
C₅×#4860	2
C₅×#4847	2
C₅×#4839	2
C₅×#4770	2
C₅×D₃×#102	2
C₅×#4763	2
C₅×#4759	2
C₅×#3081	3
#81062	5

Subgroups — C5×#81062 #14430765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81062 #14430765