Subgroups — C₅×#78849 #14459937

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5824	C₂	1	1	yes	maximal, characteristic
2	C₅×#5533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5239	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5116	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×C₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4996	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4814	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4813	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4795	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4792	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4759	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4758	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3302	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	1	yes	characteristic
21	C₅×#946	C₂²	1	1	yes	characteristic
22	C₅×#944	C₂²	1	1	yes	characteristic
23	C₂×C₅×#216	C₂²	1	1	yes	characteristic
24	C₅×#939	—	2	1	no	—
25	C₅×#935	—	2	1	no	—
26	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×#214	C₂²	1	1	yes	characteristic
28	C₅×#929	—	2	1	no	—
29	C₄×C₅×#67	C₂²	1	1	yes	characteristic
30	C₅×#924	C₂²	1	1	yes	characteristic
31	C₅×#924	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
33	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
34	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₅×#897	C₂²	1	1	yes	characteristic
36	C₅×#892	C₂²	1	1	yes	characteristic
37	C₅×#888	C₂²	1	1	yes	characteristic
38	C₅×#887	C₂²	1	1	yes	characteristic
39	C₅×#885	—	2	1	no	—
40	C₅×#879	—	2	1	no	—
41	C₅×#876	—	2	1	no	—
42	C₄×C₅×Dic₆	—	2	1	no	—
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic
44	C₃×C₅×#103	C₂²	1	1	yes	characteristic
45	C₃×C₅×#102	C₂²	1	1	yes	characteristic
46	C₃×C₅×#102	C₂²	1	1	yes	characteristic
47	C₅×#835	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×#830	C₂²	1	1	yes	characteristic
50	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×#818	C₂²	1	1	yes	characteristic
52	C₅×#816	C₂²	1	1	yes	characteristic
53	C₅×#816	C₂²	1	1	yes	characteristic
54	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₅×#810	C₂²	1	1	yes	characteristic
57	C₅×#810	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic
59	C₅×#807	C₂²	1	1	yes	characteristic
60	#78849	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#556	—	3	1	no	—
62	C₅×#547	—	3	1	no	—
63	C₅×#487	—	3	1	no	—
64	C₅×#485	—	3	1	no	—
65	C₅×#485	—	3	1	no	—
66	C₅×#474	—	3	1	no	—
67	C₅×#467	—	3	1	no	—
68	C₅×#467	—	3	1	no	—
69	C₅×#462	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#452	—	3	1	no	—
72	C₄×C₅×SD₁₆	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₅×#416	—	3	1	no	—
75	C₅×#416	D₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	—	2	1	no	—
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	—	2	1	no	—
84	C₂×C₅×#67	D₄	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	—	2	1	no	—
86	C₂²×C₅×Dic₃	—	2	1	no	—
87	C₅×#237	—	2	2	no	—
88	C₅×#237	—	4	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	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	—	4	1	no	—
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₃×C₄²×C₅	—	2	1	no	—
100	C₅×#217	—	2	1	no	—
101	C₅×#217	—	2	1	no	—
102	C₅×#217	—	2	1	no	—
103	C₅×#217	D₄	1	1	yes	characteristic
104	C₅×#216	—	4	1	no	—
105	C₅×#214	—	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	D₄	1	1	yes	characteristic
110	C₅×C₄⋊Dic₃	—	2	1	no	—
111	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₅×Dic₃⋊C₄	—	2	1	no	—
120	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₅×Dic₁₂	—	4	1	no	—
127	C₅×D₃×C₈	—	4	1	no	—
128	#5824	C₂×C₅	1	1	yes	characteristic
129	#5533	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
131	#5239	C₂×C₅	1	1	yes	characteristic, complemented
132	#5116	C₂×C₅	1	1	yes	characteristic, complemented
133	C₈×#67	C₂×C₅	1	1	yes	characteristic, complemented
134	#4996	C₂×C₅	1	1	yes	characteristic, complemented
135	#4814	C₂×C₅	1	1	yes	characteristic, complemented
136	#4813	C₂×C₅	1	1	yes	characteristic, complemented
137	#4795	C₂×C₅	1	1	yes	characteristic, complemented
138	#4792	C₂×C₅	1	1	yes	characteristic, complemented
139	#4783	C₂×C₅	1	1	yes	characteristic, complemented
140	#4772	C₂×C₅	1	1	yes	characteristic, complemented
141	#4759	C₂×C₅	1	1	yes	characteristic, complemented
142	#4758	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	—	3	1	no	—
144	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	—	3	1	no	—
146	C₂×C₅×Q₁₆	—	3	1	no	—
147	C₂×C₅×SD₁₆	—	3	1	no	—
148	C₂²×C₅×C₈	—	3	1	no	—
149	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
150	C₅×C₄⋊Q₈	—	3	1	no	—
151	C₅×C₄⋊Q₈	—	3	1	no	—
152	C₅×#126	—	6	1	no	—
153	C₅×#126	—	6	1	no	—
154	C₅×#124	—	6	1	no	—
155	C₅×#123	—	6	1	no	—
156	C₅×#123	—	6	1	no	—
157	C₅×C₂²⋊Q₈	—	3	1	no	—
158	C₅×C₂²⋊Q₈	—	3	1	no	—
159	C₅×C₂²⋊Q₈	—	3	1	no	—
160	C₅×C₂²⋊Q₈	—	3	1	no	—
161	C₅×#121	—	6	1	no	—
162	C₄×C₅×Q₈	—	3	1	no	—
163	C₄×C₅×Q₈	—	6	1	no	—
164	C₄×C₅×D₄	—	3	1	no	—
165	C₄×C₅×D₄	—	3	1	no	—
166	C₅×#117	—	3	1	no	—
167	C₅×#117	C₂×D₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	—	6	1	no	—
169	C₅×#107	—	3	1	no	—
170	C₅×#107	—	3	1	no	—
171	C₅×#106	—	3	1	no	—
172	C₅×C₄⋊C₈	—	3	1	no	—
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	—	3	1	no	—
176	C₅×#103	—	3	1	no	—
177	C₅×#103	—	3	1	no	—
178	C₅×#103	C₂×D₃	1	1	yes	characteristic
179	C₅×#103	C₂×D₃	1	1	yes	characteristic
180	C₅×#102	—	3	1	no	—
181	C₅×#102	C₂×D₃	1	1	yes	characteristic
182	C₅×#102	C₂×D₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₄×C₅×C₈	—	3	1	no	—
186	#3302	—	3	1	no	Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×D₄	—	2	1	no	—
193	C₃×C₅×D₄	—	4	2	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	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	4	2	no	—
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₅×#67	—	2	2	no	—
204	C₅×#67	—	4	2	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	2	1	no	—
209	C₂×C₅×Dic₃	—	4	2	no	—
210	C₂×C₅×Dic₃	—	4	2	no	—
211	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
213	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
214	C₄×C₅×D₃	—	2	1	no	—
215	C₄×C₅×D₃	—	2	1	no	—
216	C₅×Dic₆	—	2	1	no	—
217	C₅×Dic₆	—	2	1	no	—
218	C₅×Dic₆	—	2	1	no	—
219	C₅×Dic₆	—	2	1	no	—
220	C₅×Dic₆	—	4	2	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₃×C₅×C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	—	2	1	no	—
224	C₅×C₃⋊C₈	—	2	1	no	—
225	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
226	C₂×#237	C₂²×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
228	C₃×#117	C₂²×C₅	1	1	yes	characteristic
229	#946	C₂²×C₅	1	1	yes	characteristic
230	#944	C₂²×C₅	1	1	yes	characteristic
231	C₂×#216	C₂²×C₅	1	1	yes	characteristic
232	#939	—	2	1	no	—
233	#935	—	2	1	no	—
234	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	C₂×#214	C₂²×C₅	1	1	yes	characteristic
236	#929	—	2	1	no	—
237	C₄×#67	C₂²×C₅	1	1	yes	characteristic
238	#924	C₂²×C₅	1	1	yes	characteristic
239	#924	C₂²×C₅	1	1	yes	characteristic
240	C₂×Dic₃⋊C₄	—	2	1	no	—
241	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
242	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
243	#897	C₂²×C₅	1	1	yes	characteristic
244	#892	C₂²×C₅	1	1	yes	characteristic
245	#888	C₂²×C₅	1	1	yes	characteristic
246	#887	C₂²×C₅	1	1	yes	characteristic
247	#885	—	2	1	no	—
248	#879	—	2	1	no	—
249	#876	—	2	1	no	—
250	C₄×Dic₆	—	2	1	no	—
251	C₃×#103	C₂²×C₅	1	1	yes	characteristic
252	C₃×#103	C₂²×C₅	1	1	yes	characteristic
253	C₃×#102	C₂²×C₅	1	1	yes	characteristic
254	C₃×#102	C₂²×C₅	1	1	yes	characteristic
255	#835	C₂²×C₅	1	1	yes	characteristic
256	#832	C₂²×C₅	1	1	yes	characteristic
257	#830	C₂²×C₅	1	1	yes	characteristic
258	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	#818	C₂²×C₅	1	1	yes	characteristic
260	#816	C₂²×C₅	1	1	yes	characteristic
261	#816	C₂²×C₅	1	1	yes	characteristic
262	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
264	#810	C₂²×C₅	1	1	yes	characteristic
265	#810	C₂²×C₅	1	1	yes	characteristic
266	#808	C₂²×C₅	1	1	yes	characteristic
267	#807	C₂²×C₅	1	1	yes	characteristic
268	C₅×#41	—	2	2	no	—
269	C₅×#41	—	4	1	no	—
270	C₅×#41	—	6	2	no	—
271	C₅×#41	—	12	1	no	—
272	C₂×C₅×Q₈	—	3	1	no	—
273	C₂×C₅×Q₈	—	3	1	no	—
274	C₂×C₅×Q₈	—	6	1	no	—
275	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	—	2	1	no	—
277	C₂×C₅×D₄	—	3	1	no	—
278	C₂×C₅×D₄	—	6	1	no	—
279	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	3	1	no	—
282	C₂²×C₄×C₅	—	6	1	no	—
283	C₂²×C₄×C₅	—	6	1	no	—
284	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
285	C₅×Q₁₆	—	12	1	no	—
286	C₅×Q₁₆	—	12	1	no	—
287	C₅×SD₁₆	—	6	2	no	—
288	C₂×C₅×C₈	—	3	1	no	—
289	C₂×C₅×C₈	—	3	1	no	—
290	C₂×C₅×C₈	—	4	1	no	—
291	C₂×C₅×C₈	—	12	1	no	—
292	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	—	3	1	no	—
295	C₅×C₄⋊C₄	—	3	1	no	—
296	C₅×C₄⋊C₄	—	3	1	no	—
297	C₅×C₄⋊C₄	—	6	1	no	—
298	C₅×C₄⋊C₄	—	6	1	no	—
299	C₅×C₄⋊C₄	—	6	1	no	—
300	C₅×C₄⋊C₄	—	6	1	no	—
301	C₅×C₄⋊C₄	—	6	1	no	—
302	C₅×C₄⋊C₄	—	6	1	no	—
303	C₅×C₄⋊C₄	—	6	1	no	—
304	C₅×C₄⋊C₄	—	6	1	no	—
305	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	3	1	no	—
309	C₅×C₂²⋊C₄	—	3	1	no	—
310	C₅×C₂²⋊C₄	—	6	1	no	—
311	C₅×C₂²⋊C₄	—	6	1	no	—
312	C₅×C₂²⋊C₄	—	6	1	no	—
313	C₅×C₂²⋊C₄	—	6	1	no	—
314	C₅×C₂²⋊C₄	—	6	1	no	—
315	C₅×C₂²⋊C₄	—	6	1	no	—
316	C₄²×C₅	—	2	1	no	—
317	C₄²×C₅	—	3	1	no	—
318	C₄²×C₅	—	6	1	no	—
319	C₄²×C₅	—	6	1	no	—
320	#556	—	3	1	no	—
321	#547	—	3	1	no	—
322	#487	—	3	1	no	—
323	#485	—	3	1	no	—
324	#485	—	3	1	no	—
325	#474	—	3	1	no	—
326	#467	—	3	1	no	—
327	#467	—	3	1	no	—
328	#462	—	3	1	no	—
329	#452	—	3	1	no	—
330	#452	—	3	1	no	—
331	C₄×SD₁₆	—	3	1	no	—
332	C₈×D₄	—	3	1	no	—
333	#416	—	3	1	no	—
334	#416	C₅×D₃	1	1	yes	characteristic, complemented
335	C₂²×C₃×C₅	—	2	2	no	—
336	C₂²×C₃×C₅	—	2	1	no	—
337	C₂²×C₃×C₅	—	2	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₅×D₃	—	2	1	no	—
343	C₂×C₅×D₃	—	2	1	no	—
344	C₂×C₅×D₃	—	2	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	4	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	H(5,𝔽₂)	1	1	yes	characteristic
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	—	2	1	no	—
353	C₅×Dic₃	—	4	1	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₅×Dic₃	#135	1	2	yes	—
358	C₃×#41	—	2	2	no	—
359	C₃×#41	—	4	1	no	—
360	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₃×D₄	—	2	1	no	—
362	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×#67	—	2	1	no	—
366	C₂×#67	C₅×D₄	1	1	yes	characteristic
367	C₂²×Dic₃	—	2	1	no	—
368	C₂²×Dic₃	—	2	1	no	—
369	#237	—	2	2	no	—
370	#237	—	4	1	no	—
371	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
372	C₂×Dic₆	—	2	1	no	—
373	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
374	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×C₈	—	4	1	no	—
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₃×C₂²⋊C₄	—	2	1	no	—
381	C₃×C₄²	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	—	2	1	no	—
384	#217	—	2	1	no	—
385	#217	C₅×D₄	1	1	yes	characteristic
386	#216	—	4	1	no	—
387	#214	—	2	2	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	C₄⋊Dic₃	—	2	1	no	—
393	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
395	Dic₃⋊C₄	—	2	1	no	—
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	—	2	1	no	—
399	Dic₃⋊C₄	—	2	1	no	—
400	Dic₃⋊C₄	—	2	1	no	—
401	Dic₃⋊C₄	—	2	1	no	—
402	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
403	C₄×Dic₃	—	2	1	no	—
404	C₄×Dic₃	—	2	1	no	—
405	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
408	Dic₁₂	—	4	1	no	—
409	D₃×C₈	—	4	1	no	—
410	C₂³×C₅	—	2	1	no	—
411	C₂³×C₅	—	3	1	no	—
412	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
413	C₅×Q₈	—	2	1	no	—
414	C₅×Q₈	—	2	1	no	—
415	C₅×Q₈	—	6	1	no	—
416	C₅×Q₈	—	6	1	no	—
417	C₅×Q₈	—	6	1	no	—
418	C₅×Q₈	—	6	1	no	—
419	C₅×Q₈	—	12	2	no	—
420	C₅×D₄	—	2	1	no	—
421	C₅×D₄	—	4	2	no	—
422	C₅×D₄	—	6	2	no	—
423	C₅×D₄	—	12	2	no	—
424	C₅×D₄	#235	1	2	yes	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	3	1	no	—
431	C₂×C₄×C₅	—	3	1	no	—
432	C₂×C₄×C₅	—	3	1	no	—
433	C₂×C₄×C₅	—	4	2	no	—
434	C₂×C₄×C₅	—	6	1	no	—
435	C₂×C₄×C₅	—	6	1	no	—
436	C₂×C₄×C₅	—	6	1	no	—
437	C₂×C₄×C₅	—	6	1	no	—
438	C₂×C₄×C₅	—	6	1	no	—
439	C₂×C₄×C₅	—	6	1	no	—
440	C₂×C₄×C₅	—	12	2	no	—
441	C₂×C₄×C₅	—	12	2	no	—
442	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
444	C₅×C₈	—	2	1	no	—
445	C₅×C₈	—	2	1	no	—
446	C₅×C₈	—	6	1	no	—
447	C₅×C₈	—	6	1	no	—
448	C₂×#41	—	3	1	no	—
449	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
450	C₂×Q₁₆	—	3	1	no	—
451	C₂×Q₁₆	—	3	1	no	—
452	C₂×SD₁₆	—	3	1	no	—
453	C₂²×C₈	—	3	1	no	—
454	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
455	C₄⋊Q₈	—	3	1	no	—
456	C₄⋊Q₈	—	3	1	no	—
457	#126	—	6	1	no	—
458	#126	—	6	1	no	—
459	#124	—	6	1	no	—
460	#123	—	6	1	no	—
461	#123	—	6	1	no	—
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	C₂²⋊Q₈	—	3	1	no	—
465	C₂²⋊Q₈	—	3	1	no	—
466	#121	—	6	1	no	—
467	C₄×Q₈	—	3	1	no	—
468	C₄×Q₈	—	6	1	no	—
469	C₄×D₄	—	3	1	no	—
470	C₄×D₄	—	3	1	no	—
471	#117	—	3	1	no	—
472	#117	C₂×C₅×D₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	6	1	no	—
474	#107	—	3	1	no	—
475	#107	—	3	1	no	—
476	#106	—	3	1	no	—
477	C₄⋊C₈	—	3	1	no	—
478	#103	—	3	1	no	—
479	#103	—	3	1	no	—
480	#103	—	3	1	no	—
481	#103	—	3	1	no	—
482	#103	—	3	1	no	—
483	#103	C₂×C₅×D₃	1	1	yes	characteristic
484	#103	C₂×C₅×D₃	1	1	yes	characteristic
485	#102	—	3	1	no	—
486	#102	C₂×C₅×D₃	1	1	yes	characteristic
487	#102	C₂×C₅×D₃	1	1	yes	characteristic
488	C₂²⋊C₈	—	3	1	no	—
489	C₂²⋊C₈	—	3	1	no	—
490	C₄×C₈	—	3	1	no	—
491	C₂×C₃×C₅	—	4	1	no	—
492	C₂×C₃×C₅	—	4	2	no	—
493	C₂×C₃×C₅	#546	1	1	yes	characteristic
494	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
495	C₂×C₃×C₅	#578	1	1	yes	characteristic
496	C₅×D₃	—	4	1	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
500	C₃×Q₈	—	2	1	no	—
501	C₃×Q₈	—	2	1	no	—
502	C₃×D₄	—	2	1	no	—
503	C₃×D₄	—	4	2	no	—
504	C₃×D₄	C₅×#41	1	2	yes	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	4	2	no	—
511	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	#67	—	2	2	no	—
514	#67	—	4	2	no	—
515	C₂×Dic₃	—	2	1	no	—
516	C₂×Dic₃	—	2	1	no	—
517	C₂×Dic₃	—	2	1	no	—
518	C₂×Dic₃	—	2	1	no	—
519	C₂×Dic₃	—	4	2	no	—
520	C₂×Dic₃	—	4	2	no	—
521	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
522	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
524	C₄×D₃	—	2	1	no	—
525	C₄×D₃	—	2	1	no	—
526	Dic₆	—	2	1	no	—
527	Dic₆	—	2	1	no	—
528	Dic₆	—	2	1	no	—
529	Dic₆	—	2	1	no	—
530	Dic₆	—	4	2	no	—
531	C₃×C₈	—	2	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃⋊C₈	—	2	1	no	—
534	C₃⋊C₈	—	2	1	no	—
535	C₂²×C₅	—	2	1	no	—
536	C₂²×C₅	—	2	2	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	1	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	6	1	no	—
542	C₂²×C₅	—	6	1	no	—
543	C₂²×C₅	—	6	1	no	—
544	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
545	C₄×C₅	—	2	1	no	—
546	C₄×C₅	—	3	2	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	—	4	1	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	6	1	no	—
551	C₄×C₅	—	6	1	no	—
552	C₄×C₅	—	12	1	no	—
553	C₄×C₅	—	12	1	no	—
554	C₄×C₅	—	12	1	no	—
555	C₄×C₅	—	12	1	no	—
556	C₄×C₅	C₂×#235	1	1	yes	characteristic
557	C₄×C₅	#1004	1	1	yes	characteristic
558	#41	—	2	2	no	—
559	#41	—	4	1	no	—
560	#41	—	6	2	no	—
561	#41	—	12	1	no	—
562	C₂×Q₈	—	3	1	no	—
563	C₂×Q₈	—	3	1	no	—
564	C₂×Q₈	—	6	1	no	—
565	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	3	1	no	—
568	C₂×D₄	—	6	1	no	—
569	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	3	1	no	—
572	C₂²×C₄	—	6	1	no	—
573	C₂²×C₄	—	6	1	no	—
574	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
575	Q₁₆	—	12	1	no	—
576	Q₁₆	—	12	1	no	—
577	SD₁₆	—	6	2	no	—
578	C₂×C₈	—	3	1	no	—
579	C₂×C₈	—	3	1	no	—
580	C₂×C₈	—	4	1	no	—
581	C₂×C₈	—	12	1	no	—
582	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
583	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
584	C₄⋊C₄	—	3	1	no	—
585	C₄⋊C₄	—	3	1	no	—
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	6	1	no	—
588	C₄⋊C₄	—	6	1	no	—
589	C₄⋊C₄	—	6	1	no	—
590	C₄⋊C₄	—	6	1	no	—
591	C₄⋊C₄	—	6	1	no	—
592	C₄⋊C₄	—	6	1	no	—
593	C₄⋊C₄	—	6	1	no	—
594	C₄⋊C₄	—	6	1	no	—
595	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
596	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	3	1	no	—
599	C₂²⋊C₄	—	3	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	C₄²	—	2	1	no	—
607	C₄²	—	3	1	no	—
608	C₄²	—	6	1	no	—
609	C₄²	—	6	1	no	—
610	C₃×C₅	#3302	1	1	yes	characteristic, complemented, Hall
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
618	C₂×D₃	—	2	1	no	—
619	C₂×D₃	—	2	1	no	—
620	C₂×D₃	—	2	1	no	—
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	4	1	no	—
623	C₃×C₄	—	4	1	no	—
624	C₃×C₄	—	4	1	no	—
625	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
626	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
627	Dic₃	—	2	1	no	—
628	Dic₃	—	2	1	no	—
629	Dic₃	—	4	1	no	—
630	Dic₃	—	4	1	no	—
631	Dic₃	—	4	1	no	—
632	Dic₃	—	4	1	no	—
633	Dic₃	C₅×#135	1	2	yes	—
634	C₂×C₅	—	4	1	no	—
635	C₂×C₅	—	4	2	no	—
636	C₂×C₅	—	12	1	no	—
637	C₂×C₅	#5490	1	1	yes	characteristic
638	C₂×C₅	D₃×#135	1	1	yes	characteristic
639	C₂×C₅	#5771	1	1	yes	characteristic
640	C₂³	—	2	1	no	—
641	C₂³	—	3	1	no	—
642	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
643	Q₈	—	2	1	no	—
644	Q₈	—	2	1	no	—
645	Q₈	—	6	1	no	—
646	Q₈	—	6	1	no	—
647	Q₈	—	6	1	no	—
648	Q₈	—	6	1	no	—
649	Q₈	—	12	2	no	—
650	D₄	—	2	1	no	—
651	D₄	—	4	2	no	—
652	D₄	—	6	2	no	—
653	D₄	—	12	2	no	—
654	D₄	C₅×#235	1	2	yes	—
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	—	2	1	no	—
660	C₂×C₄	—	3	1	no	—
661	C₂×C₄	—	3	1	no	—
662	C₂×C₄	—	3	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	6	1	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	6	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	—	6	1	no	—
670	C₂×C₄	—	12	2	no	—
671	C₂×C₄	—	12	2	no	—
672	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
674	C₈	—	2	1	no	—
675	C₈	—	2	1	no	—
676	C₈	—	6	1	no	—
677	C₈	—	6	1	no	—
678	C₂×C₃	—	4	1	no	—
679	C₂×C₃	—	4	2	no	—
680	C₂×C₃	C₅×#546	1	1	yes	characteristic
681	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
682	C₂×C₃	C₅×#578	1	1	yes	characteristic
683	D₃	—	4	1	no	—
684	C₅	#78849	1	1	yes	characteristic, direct product factor, Sylow
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	6	1	no	—
692	C₂²	—	6	1	no	—
693	C₂²	—	6	1	no	—
694	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	3	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	6	1	no	—
701	C₄	—	6	1	no	—
702	C₄	—	12	1	no	—
703	C₄	—	12	1	no	—
704	C₄	—	12	1	no	—
705	C₄	—	12	1	no	—
706	C₄	C₂×C₅×#235	1	1	yes	characteristic
707	C₄	C₅×#1004	1	1	yes	characteristic
708	C₃	C₅×#3302	1	1	yes	characteristic, complemented, Sylow
709	C₂	—	4	1	no	—
710	C₂	—	4	2	no	—
711	C₂	—	12	1	no	—
712	C₂	C₅×#5490	1	1	yes	characteristic
713	C₂	C₅×D₃×#135	1	1	yes	characteristic
714	C₂	C₅×#5771	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×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5824	C₂
hypercenter	C₅×#416	D₃
hypocenter	C₃	C₅×#3302
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#416

Complements

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

N	H ≅ G/N	type
2. C₅×#5533	C₂	semidirect
3. C₃×C₅×#416	C₂	semidirect
4. C₅×#5239	C₂	semidirect
5. C₅×#5116	C₂	semidirect
6. C₅×C₈×#67	C₂	semidirect
7. C₅×#4996	C₂	semidirect
8. C₅×#4814	C₂	semidirect
9. C₅×#4813	C₂	semidirect
10. C₅×#4795	C₂	semidirect
11. C₅×#4792	C₂	semidirect
12. C₅×#4783	C₂	semidirect
13. C₅×#4772	C₂	semidirect
14. C₅×#4759	C₂	semidirect
15. C₅×#4758	C₂	semidirect
60. #78849	C₅	direct (N × H)
75. C₅×#416	D₃	semidirect
129. #5533	C₂×C₅	semidirect
130. C₃×#416	C₂×C₅	semidirect
131. #5239	C₂×C₅	semidirect
132. #5116	C₂×C₅	semidirect
133. C₈×#67	C₂×C₅	semidirect
134. #4996	C₂×C₅	semidirect
135. #4814	C₂×C₅	semidirect
136. #4813	C₂×C₅	semidirect
137. #4795	C₂×C₅	semidirect
138. #4792	C₂×C₅	semidirect
139. #4783	C₂×C₅	semidirect
140. #4772	C₂×C₅	semidirect
141. #4759	C₂×C₅	semidirect
142. #4758	C₂×C₅	semidirect
334. #416	C₅×D₃	semidirect
610. C₃×C₅	#3302	semidirect
684. C₅	#78849	direct (N × H)
708. C₃	C₅×#3302	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5824	2
C₅×#5533	2
C₃×C₅×#416	2
C₅×#5239	2
C₅×#5116	2
C₅×C₈×#67	2
C₅×#4996	2
C₅×#4814	2
C₅×#4813	2
C₅×#4795	2
C₅×#4792	2
C₅×#4783	2
C₅×#4772	2
C₅×#4759	2
C₅×#4758	2
C₅×#3302	3
#78849	5

Subgroups — C5×#78849 #14459937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78849 #14459937