Subgroups — C₅×#79594 #14435571

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5545	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5156	C₂	1	1	yes	maximal, characteristic
5	C₅×#5153	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5018	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4890	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4779	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4761	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4690	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3118	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₅×#938	C₂²	1	1	yes	characteristic
22	C₅×#936	C₂²	1	1	yes	characteristic, complemented
23	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×#214	C₂²	1	1	yes	characteristic
25	C₂×C₅×#213	C₂²	1	1	yes	characteristic
26	C₅×#929	—	2	1	no	—
27	C₄×C₅×#67	—	2	1	no	—
28	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
29	C₅×#924	—	2	1	no	—
30	C₂×C₅×#204	C₂²	1	1	yes	characteristic
31	C₅×#897	C₂²	1	1	yes	characteristic
32	C₅×#893	C₂²	1	1	yes	characteristic
33	C₅×#892	C₂²	1	1	yes	characteristic
34	C₅×#888	C₂²	1	1	yes	characteristic, complemented
35	C₅×#885	—	2	1	no	—
36	C₅×#67⋊C₄	—	2	1	no	—
37	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
38	C₅×#879	—	2	1	no	—
39	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
40	C₅×#872	C₂²	1	1	yes	characteristic
41	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#102	C₂²	1	1	yes	characteristic
44	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#832	C₂²	1	1	yes	characteristic
47	C₅×#832	C₂²	1	1	yes	characteristic, complemented
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×#817	C₂²	1	1	yes	characteristic, complemented
52	C₅×#816	C₂²	1	1	yes	characteristic, complemented
53	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×#810	C₂²	1	1	yes	characteristic, complemented
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#808	C₂²	1	1	yes	characteristic, complemented
58	C₅×#807	C₂²	1	1	yes	characteristic, complemented
59	C₅×#803	C₂²	1	1	yes	characteristic, complemented
60	#79594	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	—	3	1	no	—
62	C₅×#518	—	3	1	no	—
63	C₅×#485	—	3	1	no	—
64	C₅×#482	—	3	1	no	—
65	C₅×#476	—	3	1	no	—
66	C₅×#474	—	3	1	no	—
67	C₅×#463	—	3	1	no	—
68	C₅×#463	—	3	1	no	—
69	C₅×#450	—	3	1	no	—
70	C₅×#447	—	3	1	no	—
71	C₅×#442	—	3	1	no	—
72	C₅×#440	—	3	1	no	—
73	C₄×C₅×SD₁₆	—	3	1	no	—
74	C₄×C₅×D₈	D₃	1	1	yes	characteristic, complemented
75	C₅×#433	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₅×#67	—	2	1	no	—
82	C₂×C₅×#67	—	2	1	no	—
83	C₂²×C₅×Dic₃	—	2	1	no	—
84	C₅×D₃×D₄	—	2	2	no	—
85	C₅×D₃×D₄	—	2	2	no	—
86	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
87	C₂×C₄×C₅×D₃	—	2	1	no	—
88	C₂×C₄×C₅×D₃	—	2	1	no	—
89	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂×C₅×Dic₆	—	2	1	no	—
91	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
92	C₃×C₅×D₈	—	2	2	no	—
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#217	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	—	2	1	no	—
104	C₅×#214	—	2	2	no	—
105	C₅×#213	—	2	2	no	—
106	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
107	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
111	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
112	C₅×C₄⋊Dic₃	—	2	1	no	—
113	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
118	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₅×#204	—	2	2	no	—
125	#5561	C₂×C₅	1	1	yes	characteristic, complemented
126	#5545	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
128	#5156	C₂×C₅	1	1	yes	characteristic
129	#5153	C₂×C₅	1	1	yes	characteristic, complemented
130	#5018	C₂×C₅	1	1	yes	characteristic, complemented
131	#5014	C₂×C₅	1	1	yes	characteristic, complemented
132	#4890	C₂×C₅	1	1	yes	characteristic, complemented
133	#4888	C₂×C₅	1	1	yes	characteristic, complemented
134	#4787	C₂×C₅	1	1	yes	characteristic, complemented
135	#4779	C₂×C₅	1	1	yes	characteristic, complemented
136	#4776	C₂×C₅	1	1	yes	characteristic, complemented
137	#4761	C₂×C₅	1	1	yes	characteristic, complemented
138	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
139	#4690	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	—	3	1	no	—
141	C₂×C₅×SD₁₆	—	3	1	no	—
142	C₂×C₅×SD₁₆	—	3	1	no	—
143	C₂×C₅×D₈	—	3	1	no	—
144	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
145	C₅×C₄⋊Q₈	—	3	1	no	—
146	C₅×#126	—	6	1	no	—
147	C₅×#124	—	3	1	no	—
148	C₅×#124	—	6	1	no	—
149	C₅×#123	—	6	1	no	—
150	C₅×C₂²⋊Q₈	—	3	1	no	—
151	C₅×C₂²⋊Q₈	—	6	1	no	—
152	C₅×#121	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×D₄	—	3	1	no	—
155	C₄×C₅×D₄	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	6	1	no	—
158	C₄×C₅×D₄	—	6	1	no	—
159	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
160	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
161	C₅×#117	—	3	1	no	—
162	C₅×#117	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
167	C₅×#106	—	3	1	no	—
168	C₅×#106	—	3	1	no	—
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×#103	—	3	1	no	—
172	C₅×#103	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
178	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
179	C₅×C₂²⋊C₈	—	3	1	no	—
180	C₅×C₂²⋊C₈	—	3	1	no	—
181	C₅×#97	—	3	1	no	—
182	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
183	#3118	—	3	1	no	Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂²×C₅×D₃	—	2	1	no	—
187	C₂²×C₅×D₃	—	2	4	no	—
188	C₂²×C₅×D₃	—	8	1	no	—
189	C₂²×C₅×D₃	—	8	1	no	—
190	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
191	C₃×C₅×D₄	—	2	1	no	—
192	C₃×C₅×D₄	—	2	1	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	#41	1	2	yes	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	8	1	no	—
198	C₂×C₃×C₄×C₅	—	8	1	no	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₅×#67	—	2	4	no	—
203	C₅×#67	—	8	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	8	1	no	—
208	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
211	C₅×D₁₂	—	2	1	no	—
212	C₅×D₁₂	#41	1	2	yes	—
213	C₄×C₅×D₃	—	2	1	no	—
214	C₄×C₅×D₃	—	2	1	no	—
215	C₄×C₅×D₃	—	8	1	no	—
216	C₄×C₅×D₃	—	8	1	no	—
217	C₅×Dic₆	—	2	1	no	—
218	C₅×Dic₆	—	2	1	no	—
219	C₅×Dic₆	—	8	1	no	—
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
226	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
227	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
228	#938	C₂²×C₅	1	1	yes	characteristic
229	#936	C₂²×C₅	1	1	yes	characteristic, complemented
230	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
231	C₂×#214	C₂²×C₅	1	1	yes	characteristic
232	C₂×#213	C₂²×C₅	1	1	yes	characteristic
233	#929	—	2	1	no	—
234	C₄×#67	—	2	1	no	—
235	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
236	#924	—	2	1	no	—
237	C₂×#204	C₂²×C₅	1	1	yes	characteristic
238	#897	C₂²×C₅	1	1	yes	characteristic
239	#893	C₂²×C₅	1	1	yes	characteristic
240	#892	C₂²×C₅	1	1	yes	characteristic
241	#888	C₂²×C₅	1	1	yes	characteristic, complemented
242	#885	—	2	1	no	—
243	#67⋊C₄	—	2	1	no	—
244	D₃×C₂²⋊C₄	—	2	1	no	—
245	#879	—	2	1	no	—
246	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
247	#872	C₂²×C₅	1	1	yes	characteristic
248	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×#102	C₂²×C₅	1	1	yes	characteristic
251	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
253	#832	C₂²×C₅	1	1	yes	characteristic
254	#832	C₂²×C₅	1	1	yes	characteristic, complemented
255	#821	C₂²×C₅	1	1	yes	characteristic
256	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
258	#817	C₂²×C₅	1	1	yes	characteristic, complemented
259	#816	C₂²×C₅	1	1	yes	characteristic, complemented
260	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
261	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
262	#810	C₂²×C₅	1	1	yes	characteristic, complemented
263	#809	C₂²×C₅	1	1	yes	characteristic
264	#808	C₂²×C₅	1	1	yes	characteristic, complemented
265	#807	C₂²×C₅	1	1	yes	characteristic, complemented
266	#803	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	—	6	1	no	—
268	C₂×C₅×Q₈	—	3	1	no	—
269	C₂×C₅×Q₈	—	6	1	no	—
270	C₂×C₅×D₄	—	3	1	no	—
271	C₂×C₅×D₄	—	6	1	no	—
272	C₂×C₅×D₄	—	6	2	no	—
273	C₂×C₅×D₄	—	6	2	no	—
274	C₂×C₅×D₄	—	6	1	no	—
275	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	—	2	1	no	—
279	C₂²×C₄×C₅	—	3	1	no	—
280	C₂²×C₄×C₅	—	6	1	no	—
281	C₂²×C₄×C₅	—	6	1	no	—
282	C₂²×C₄×C₅	—	6	1	no	—
283	C₅×SD₁₆	—	6	2	no	—
284	C₅×SD₁₆	—	6	2	no	—
285	C₅×D₈	—	2	2	no	—
286	C₅×D₈	—	6	2	no	—
287	C₂×C₅×C₈	—	3	1	no	—
288	C₂×C₅×C₈	—	3	1	no	—
289	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	3	1	no	—
292	C₅×C₄⋊C₄	—	3	1	no	—
293	C₅×C₄⋊C₄	—	3	1	no	—
294	C₅×C₄⋊C₄	—	3	1	no	—
295	C₅×C₄⋊C₄	—	6	1	no	—
296	C₅×C₄⋊C₄	—	6	1	no	—
297	C₅×C₄⋊C₄	—	6	1	no	—
298	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₅×C₂²⋊C₄	—	3	1	no	—
304	C₅×C₂²⋊C₄	—	6	1	no	—
305	C₅×C₂²⋊C₄	—	6	1	no	—
306	C₅×C₂²⋊C₄	—	6	1	no	—
307	C₅×C₂²⋊C₄	—	6	1	no	—
308	C₅×C₂²⋊C₄	—	6	1	no	—
309	C₅×C₂²⋊C₄	—	6	1	no	—
310	C₅×C₂²⋊C₄	—	6	1	no	—
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₄²×C₅	—	3	1	no	—
313	C₄²×C₅	—	6	1	no	—
314	C₄²×C₅	—	6	1	no	—
315	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
316	#542	—	3	1	no	—
317	#518	—	3	1	no	—
318	#485	—	3	1	no	—
319	#482	—	3	1	no	—
320	#476	—	3	1	no	—
321	#474	—	3	1	no	—
322	#463	—	3	1	no	—
323	#463	—	3	1	no	—
324	#450	—	3	1	no	—
325	#447	—	3	1	no	—
326	#442	—	3	1	no	—
327	#440	—	3	1	no	—
328	C₄×SD₁₆	—	3	1	no	—
329	C₄×D₈	C₅×D₃	1	1	yes	characteristic, complemented
330	#433	—	3	1	no	—
331	C₂²×C₃×C₅	—	2	2	no	—
332	C₂²×C₃×C₅	—	4	1	no	—
333	C₂²×C₃×C₅	—	4	1	no	—
334	C₂²×C₃×C₅	—	4	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₅×D₃	—	2	1	no	—
339	C₂×C₅×D₃	—	2	2	no	—
340	C₂×C₅×D₃	—	2	1	no	—
341	C₂×C₅×D₃	—	2	1	no	—
342	C₂×C₅×D₃	—	4	1	no	—
343	C₂×C₅×D₃	—	4	1	no	—
344	C₂×C₅×D₃	—	8	4	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	2	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	2	1	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₂³×D₃	—	2	1	no	—
358	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	—	2	1	no	—
362	C₂×#67	—	2	1	no	—
363	C₂×#67	—	2	1	no	—
364	C₂²×Dic₃	—	2	1	no	—
365	D₃×D₄	—	2	2	no	—
366	D₃×D₄	—	2	2	no	—
367	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₄×D₃	—	2	1	no	—
369	C₂×C₄×D₃	—	2	1	no	—
370	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
371	C₂×Dic₆	—	2	1	no	—
372	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
373	C₃×D₈	—	2	2	no	—
374	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
376	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₂²⋊C₄	—	2	1	no	—
379	C₃×C₂²⋊C₄	—	2	1	no	—
380	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
381	#217	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	—	2	1	no	—
384	#217	—	2	1	no	—
385	#214	—	2	2	no	—
386	#213	—	2	2	no	—
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	(C₂×D₃)⋊C₄	—	2	1	no	—
389	(C₂×D₃)⋊C₄	—	2	1	no	—
390	(C₂×D₃)⋊C₄	—	2	1	no	—
391	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
392	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
393	C₄⋊Dic₃	—	2	1	no	—
394	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
395	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
399	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
400	C₄×Dic₃	—	2	1	no	—
401	C₄×Dic₃	—	2	1	no	—
402	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
405	#204	—	2	2	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	3	1	no	—
409	C₂³×C₅	—	6	4	no	—
410	C₂³×C₅	—	6	1	no	—
411	C₂³×C₅	—	24	1	no	—
412	C₂³×C₅	—	24	1	no	—
413	C₅×Q₈	—	6	1	no	—
414	C₅×Q₈	—	6	1	no	—
415	C₅×Q₈	—	24	1	no	—
416	C₅×D₄	—	2	1	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	2	1	no	—
419	C₅×D₄	—	3	2	no	—
420	C₅×D₄	—	6	4	no	—
421	C₅×D₄	—	6	1	no	—
422	C₅×D₄	—	24	1	no	—
423	C₅×D₄	#235	1	2	yes	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	3	1	no	—
427	C₂×C₄×C₅	—	3	1	no	—
428	C₂×C₄×C₅	—	3	1	no	—
429	C₂×C₄×C₅	—	6	1	no	—
430	C₂×C₄×C₅	—	6	1	no	—
431	C₂×C₄×C₅	—	6	1	no	—
432	C₂×C₄×C₅	—	6	1	no	—
433	C₂×C₄×C₅	—	6	1	no	—
434	C₂×C₄×C₅	—	8	1	no	—
435	C₂×C₄×C₅	—	8	1	no	—
436	C₂×C₄×C₅	—	24	1	no	—
437	C₂×C₄×C₅	—	24	1	no	—
438	C₂×C₄×C₅	—	24	1	no	—
439	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₅×C₈	—	6	1	no	—
445	C₅×C₈	—	6	1	no	—
446	C₂²×D₄	—	3	1	no	—
447	C₂×SD₁₆	—	3	1	no	—
448	C₂×SD₁₆	—	3	1	no	—
449	C₂×D₈	—	3	1	no	—
450	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
451	C₄⋊Q₈	—	3	1	no	—
452	#126	—	6	1	no	—
453	#124	—	3	1	no	—
454	#124	—	6	1	no	—
455	#123	—	6	1	no	—
456	C₂²⋊Q₈	—	3	1	no	—
457	C₂²⋊Q₈	—	6	1	no	—
458	#121	—	3	1	no	—
459	C₄×Q₈	—	3	1	no	—
460	C₄×D₄	—	3	1	no	—
461	C₄×D₄	—	3	1	no	—
462	C₄×D₄	—	3	1	no	—
463	C₄×D₄	—	6	1	no	—
464	C₄×D₄	—	6	1	no	—
465	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
466	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
467	#117	—	3	1	no	—
468	#117	—	3	1	no	—
469	C₂×C₂²⋊C₄	—	6	1	no	—
470	C₂×C₂²⋊C₄	—	6	1	no	—
471	#107	—	3	1	no	—
472	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
473	#106	—	3	1	no	—
474	#106	—	3	1	no	—
475	C₄⋊C₈	—	3	1	no	—
476	C₄⋊C₈	—	3	1	no	—
477	#103	—	3	1	no	—
478	#103	—	3	1	no	—
479	#102	—	3	1	no	—
480	#102	—	3	1	no	—
481	#102	—	3	1	no	—
482	#102	—	3	1	no	—
483	#102	C₂×C₅×D₃	1	1	yes	characteristic
484	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
485	C₂²⋊C₈	—	3	1	no	—
486	C₂²⋊C₈	—	3	1	no	—
487	#97	—	3	1	no	—
488	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
489	C₂×C₃×C₅	—	4	2	no	—
490	C₂×C₃×C₅	—	8	1	no	—
491	C₂×C₃×C₅	#525	1	1	yes	characteristic
492	C₂×C₃×C₅	#576	1	1	yes	characteristic
493	C₂×C₃×C₅	#577	1	1	yes	characteristic
494	C₅×D₃	—	4	1	no	—
495	C₅×D₃	—	4	2	no	—
496	C₂³×C₃	—	2	1	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂²×D₃	—	2	1	no	—
499	C₂²×D₃	—	2	4	no	—
500	C₂²×D₃	—	8	1	no	—
501	C₂²×D₃	—	8	1	no	—
502	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
503	C₃×D₄	—	2	1	no	—
504	C₃×D₄	—	2	1	no	—
505	C₃×D₄	—	2	1	no	—
506	C₃×D₄	C₅×#41	1	2	yes	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	8	1	no	—
510	C₂×C₃×C₄	—	8	1	no	—
511	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
514	#67	—	2	4	no	—
515	#67	—	8	1	no	—
516	C₂×Dic₃	—	2	1	no	—
517	C₂×Dic₃	—	2	1	no	—
518	C₂×Dic₃	—	2	1	no	—
519	C₂×Dic₃	—	8	1	no	—
520	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
522	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
523	D₁₂	—	2	1	no	—
524	D₁₂	C₅×#41	1	2	yes	—
525	C₄×D₃	—	2	1	no	—
526	C₄×D₃	—	2	1	no	—
527	C₄×D₃	—	8	1	no	—
528	C₄×D₃	—	8	1	no	—
529	Dic₆	—	2	1	no	—
530	Dic₆	—	2	1	no	—
531	Dic₆	—	8	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃⋊C₈	—	2	1	no	—
535	C₃⋊C₈	—	2	1	no	—
536	C₂²×C₅	—	2	2	no	—
537	C₂²×C₅	—	4	1	no	—
538	C₂²×C₅	—	4	1	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	6	1	no	—
543	C₂²×C₅	—	6	1	no	—
544	C₂²×C₅	—	6	1	no	—
545	C₂²×C₅	—	6	2	no	—
546	C₂²×C₅	—	12	1	no	—
547	C₂²×C₅	—	12	1	no	—
548	C₂²×C₅	—	24	4	no	—
549	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	2	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	—	6	1	no	—
555	C₄×C₅	—	6	1	no	—
556	C₄×C₅	—	6	1	no	—
557	C₄×C₅	—	12	1	no	—
558	C₄×C₅	—	12	1	no	—
559	C₄×C₅	—	12	1	no	—
560	C₄×C₅	C₂×#235	1	1	yes	characteristic
561	C₄×C₅	D₃×#41	1	1	yes	characteristic
562	C₂⁴	—	6	1	no	—
563	C₂×Q₈	—	3	1	no	—
564	C₂×Q₈	—	6	1	no	—
565	C₂×D₄	—	3	1	no	—
566	C₂×D₄	—	6	1	no	—
567	C₂×D₄	—	6	2	no	—
568	C₂×D₄	—	6	2	no	—
569	C₂×D₄	—	6	1	no	—
570	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
571	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	3	1	no	—
575	C₂²×C₄	—	6	1	no	—
576	C₂²×C₄	—	6	1	no	—
577	C₂²×C₄	—	6	1	no	—
578	SD₁₆	—	6	2	no	—
579	SD₁₆	—	6	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	6	2	no	—
582	C₂×C₈	—	3	1	no	—
583	C₂×C₈	—	3	1	no	—
584	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	3	1	no	—
588	C₄⋊C₄	—	3	1	no	—
589	C₄⋊C₄	—	3	1	no	—
590	C₄⋊C₄	—	6	1	no	—
591	C₄⋊C₄	—	6	1	no	—
592	C₄⋊C₄	—	6	1	no	—
593	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
594	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	3	1	no	—
598	C₂²⋊C₄	—	3	1	no	—
599	C₂²⋊C₄	—	6	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₂²⋊C₄	—	6	1	no	—
602	C₂²⋊C₄	—	6	1	no	—
603	C₂²⋊C₄	—	6	1	no	—
604	C₂²⋊C₄	—	6	1	no	—
605	C₂²⋊C₄	—	6	1	no	—
606	C₂²⋊C₄	—	6	1	no	—
607	C₄²	—	3	1	no	—
608	C₄²	—	6	1	no	—
609	C₄²	—	6	1	no	—
610	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
611	C₃×C₅	#3118	1	1	yes	characteristic, complemented, Hall
612	C₂²×C₃	—	2	2	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
619	C₂×D₃	—	2	1	no	—
620	C₂×D₃	—	2	2	no	—
621	C₂×D₃	—	2	1	no	—
622	C₂×D₃	—	2	1	no	—
623	C₂×D₃	—	4	1	no	—
624	C₂×D₃	—	4	1	no	—
625	C₂×D₃	—	8	4	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
631	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
632	Dic₃	—	2	1	no	—
633	Dic₃	—	2	1	no	—
634	Dic₃	—	2	1	no	—
635	Dic₃	—	4	1	no	—
636	Dic₃	—	4	1	no	—
637	Dic₃	—	4	1	no	—
638	C₂×C₅	—	4	2	no	—
639	C₂×C₅	—	8	1	no	—
640	C₂×C₅	—	12	1	no	—
641	C₂×C₅	—	12	2	no	—
642	C₂×C₅	#5547	1	1	yes	characteristic
643	C₂×C₅	#5757	1	1	yes	characteristic
644	C₂×C₅	#5770	1	1	yes	characteristic
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	3	1	no	—
648	C₂³	—	6	4	no	—
649	C₂³	—	6	1	no	—
650	C₂³	—	24	1	no	—
651	C₂³	—	24	1	no	—
652	Q₈	—	6	1	no	—
653	Q₈	—	6	1	no	—
654	Q₈	—	24	1	no	—
655	D₄	—	2	1	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	3	2	no	—
659	D₄	—	6	4	no	—
660	D₄	—	6	1	no	—
661	D₄	—	24	1	no	—
662	D₄	C₅×#235	1	2	yes	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	3	1	no	—
666	C₂×C₄	—	3	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	—	6	1	no	—
670	C₂×C₄	—	6	1	no	—
671	C₂×C₄	—	6	1	no	—
672	C₂×C₄	—	6	1	no	—
673	C₂×C₄	—	8	1	no	—
674	C₂×C₄	—	8	1	no	—
675	C₂×C₄	—	24	1	no	—
676	C₂×C₄	—	24	1	no	—
677	C₂×C₄	—	24	1	no	—
678	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
679	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	6	1	no	—
684	C₈	—	6	1	no	—
685	C₂×C₃	—	4	2	no	—
686	C₂×C₃	—	8	1	no	—
687	C₂×C₃	C₅×#525	1	1	yes	characteristic
688	C₂×C₃	C₅×#576	1	1	yes	characteristic
689	C₂×C₃	C₅×#577	1	1	yes	characteristic
690	D₃	—	4	1	no	—
691	D₃	—	4	2	no	—
692	C₅	#79594	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	6	1	no	—
700	C₂²	—	6	1	no	—
701	C₂²	—	6	1	no	—
702	C₂²	—	6	2	no	—
703	C₂²	—	12	1	no	—
704	C₂²	—	12	1	no	—
705	C₂²	—	24	4	no	—
706	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	6	1	no	—
712	C₄	—	6	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	12	1	no	—
715	C₄	—	12	1	no	—
716	C₄	—	12	1	no	—
717	C₄	C₂×C₅×#235	1	1	yes	characteristic
718	C₄	C₅×D₃×#41	1	1	yes	characteristic
719	C₃	C₅×#3118	1	1	yes	characteristic, complemented, Sylow
720	C₂	—	4	2	no	—
721	C₂	—	8	1	no	—
722	C₂	—	12	1	no	—
723	C₂	—	12	2	no	—
724	C₂	C₅×#5547	1	1	yes	characteristic
725	C₂	C₅×#5757	1	1	yes	characteristic
726	C₂	C₅×#5770	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×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5156	C₂
hypercenter	C₄×C₅×D₈	D₃
hypocenter	C₃	C₅×#3118
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₅×#5561	C₂	semidirect
2. C₅×#5545	C₂	semidirect
3. C₃×C₄×C₅×D₈	C₂	semidirect
5. C₅×#5153	C₂	semidirect
6. C₅×#5018	C₂	semidirect
7. C₅×#5014	C₂	semidirect
8. C₅×#4890	C₂	semidirect
9. C₅×#4888	C₂	semidirect
10. C₅×#4787	C₂	semidirect
11. C₅×#4779	C₂	semidirect
12. C₅×#4776	C₂	semidirect
13. C₅×#4761	C₂	semidirect
14. C₄×C₅×#204	C₂	semidirect
15. C₅×#4690	C₂	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₅×#936	C₂²	semidirect
34. C₅×#888	C₂²	semidirect
41. C₄×C₅×Dic₆	C₂²	semidirect
42. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#102	C₂²	semidirect
45. C₃×C₄×C₅×C₈	C₂²	semidirect
47. C₅×#832	C₂²	semidirect
51. C₅×#817	C₂²	semidirect
52. C₅×#816	C₂²	semidirect
53. C₅×Dic₃⋊C₈	C₂²	semidirect
54. C₅×Dic₃⋊C₈	C₂²	semidirect
55. C₅×#810	C₂²	semidirect
57. C₅×#808	C₂²	semidirect
58. C₅×#807	C₂²	semidirect
59. C₅×#803	C₂²	semidirect
60. #79594	C₅	direct (N × H)
74. C₄×C₅×D₈	D₃	semidirect
125. #5561	C₂×C₅	semidirect
126. #5545	C₂×C₅	semidirect
127. C₃×C₄×D₈	C₂×C₅	semidirect
129. #5153	C₂×C₅	semidirect
130. #5018	C₂×C₅	semidirect
131. #5014	C₂×C₅	semidirect
132. #4890	C₂×C₅	semidirect
133. #4888	C₂×C₅	semidirect
134. #4787	C₂×C₅	semidirect
135. #4779	C₂×C₅	semidirect
136. #4776	C₂×C₅	semidirect
137. #4761	C₂×C₅	semidirect
138. C₄×#204	C₂×C₅	semidirect
139. #4690	C₂×C₅	semidirect
160. C₄×C₅×D₄	C₂×D₃	semidirect
166. C₅×#107	C₂×D₃	semidirect
178. C₅×#102	C₂×D₃	semidirect
182. C₄×C₅×C₈	C₂×D₃	semidirect
227. C₃×C₄×D₄	C₂²×C₅	semidirect
229. #936	C₂²×C₅	semidirect
241. #888	C₂²×C₅	semidirect
248. C₄×Dic₆	C₂²×C₅	semidirect
249. C₃×#107	C₂²×C₅	semidirect
251. C₃×#102	C₂²×C₅	semidirect
252. C₃×C₄×C₈	C₂²×C₅	semidirect
254. #832	C₂²×C₅	semidirect
258. #817	C₂²×C₅	semidirect
259. #816	C₂²×C₅	semidirect
260. Dic₃⋊C₈	C₂²×C₅	semidirect
261. Dic₃⋊C₈	C₂²×C₅	semidirect
262. #810	C₂²×C₅	semidirect
264. #808	C₂²×C₅	semidirect
265. #807	C₂²×C₅	semidirect
266. #803	C₂²×C₅	semidirect
329. C₄×D₈	C₅×D₃	semidirect
466. C₄×D₄	C₂×C₅×D₃	semidirect
472. #107	C₂×C₅×D₃	semidirect
484. #102	C₂×C₅×D₃	semidirect
488. C₄×C₈	C₂×C₅×D₃	semidirect
611. C₃×C₅	#3118	semidirect
692. C₅	#79594	direct (N × H)
719. C₃	C₅×#3118	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5561	2
C₅×#5545	2
C₃×C₄×C₅×D₈	2
C₅×#5156	2
C₅×#5153	2
C₅×#5018	2
C₅×#5014	2
C₅×#4890	2
C₅×#4888	2
C₅×#4787	2
C₅×#4779	2
C₅×#4776	2
C₅×#4761	2
C₄×C₅×#204	2
C₅×#4690	2
C₅×#3118	3
#79594	5

Subgroups — C5×#79594 #14435571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79594 #14435571