Subgroups — C₅×#78869 #14417722

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5827	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic
3	C₅×#5504	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5133	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4789	C₂	1	2	yes	maximal, complemented
9	C₅×#4788	C₂	1	2	yes	maximal, complemented
10	C₅×#4785	C₂	1	2	yes	maximal, complemented
11	C₅×#4758	C₂	1	2	yes	maximal, complemented
12	C₅×#2952	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₅×#950	C₄	1	8	yes	complemented
18	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×#216	C₂²	1	1	yes	characteristic
20	C₂×C₅×#215	C₂²	1	1	yes	characteristic
21	C₅×D₄×Dic₃	—	2	2	no	—
22	C₅×D₄×Dic₃	C₂²	1	2	yes	—
23	C₂×C₅×#214	C₂²	1	1	yes	characteristic
24	C₂×C₅×#213	C₂²	1	1	yes	characteristic
25	C₄×C₅×#67	—	2	2	no	—
26	C₅×#926	—	2	1	no	—
27	C₅×#926	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#893	C₂²	1	2	yes	—
32	C₅×#892	—	2	1	no	—
33	C₅×D₃×C₄⋊C₄	—	2	1	no	—
34	C₅×#887	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₅×#821	C₂²	1	2	yes	—
38	C₅×#816	C₂²	1	2	yes	—
39	C₅×#815	C₂²	1	2	yes	—
40	C₅×C₈×Dic₃	C₂²	1	2	yes	—
41	C₅×#808	C₂²	1	2	yes	—
42	C₅×#808	C₂²	1	2	yes	—
43	#78869	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#135	—	3	1	no	—
45	C₅×#520	—	3	1	no	—
46	C₅×#520	—	3	1	no	—
47	C₅×#442	—	3	2	no	—
48	C₅×#441	—	3	2	no	—
49	C₄×C₅×SD₁₆	—	3	2	no	—
50	C₄×C₅×SD₁₆	—	3	2	no	—
51	C₂×C₅×#106	—	3	1	no	—
52	C₅×#417	—	3	1	no	—
53	C₅×#417	D₃	1	1	yes	characteristic, complemented
54	C₅×#405	—	3	1	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₅×#67	—	2	1	no	—
64	C₂²×C₅×Dic₃	—	2	1	no	—
65	C₂²×C₅×Dic₃	—	2	2	no	—
66	C₅×#235	—	2	2	no	—
67	C₅×#235	C₂×C₄	1	4	yes	complemented
68	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
69	C₂×C₄×C₅×D₃	—	2	1	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
72	C₃×C₅×M₁₆	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₅×#217	—	2	2	no	—
77	C₅×#217	D₄	1	2	yes	—
78	C₅×#216	C₂×C₄	1	4	yes	complemented
79	C₅×#215	C₂×C₄	1	4	yes	complemented
80	C₅×#214	C₂×C₄	1	4	yes	complemented
81	C₅×#213	C₂×C₄	1	4	yes	complemented
82	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₅×C₄⋊Dic₃	—	2	1	no	—
84	C₅×C₄⋊Dic₃	—	2	2	no	—
85	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
86	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
87	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
88	C₅×Dic₃⋊C₄	—	2	2	no	—
89	C₄×C₅×Dic₃	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	2	no	—
91	C₄×C₅×Dic₃	C₂³	1	2	yes	—
92	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
93	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	#5827	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#950	C₂×C₅	1	1	yes	characteristic
97	#5504	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
99	#5133	C₂×C₅	1	1	yes	characteristic, complemented
100	#5122	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
102	#4789	C₂×C₅	1	2	yes	complemented
103	#4788	C₂×C₅	1	2	yes	complemented
104	#4785	C₂×C₅	1	2	yes	complemented
105	#4758	C₂×C₅	1	2	yes	complemented
106	C₂×C₅×#41	—	3	1	no	—
107	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
108	C₅×#135	—	3	8	no	—
109	C₂×C₅×Q₁₆	—	3	1	no	—
110	C₂×C₅×SD₁₆	—	3	1	no	—
111	C₂×C₅×SD₁₆	—	3	1	no	—
112	C₂×C₅×D₈	—	3	1	no	—
113	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	—	3	1	no	—
115	C₄×C₅×Q₈	—	3	2	no	—
116	C₄×C₅×Q₈	—	3	2	no	—
117	C₄×C₅×D₄	—	3	2	no	—
118	C₄×C₅×D₄	—	3	2	no	—
119	C₄×C₅×D₄	—	6	2	no	—
120	C₄×C₅×D₄	—	6	2	no	—
121	C₅×#117	—	3	1	no	—
122	C₅×#117	—	6	1	no	—
123	C₅×#117	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	—	3	1	no	—
125	C₂×C₅×C₄⋊C₄	—	6	1	no	—
126	C₂×C₅×C₄⋊C₄	—	6	1	no	—
127	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₅×#106	—	3	2	no	—
129	C₅×#106	—	3	2	no	—
130	C₅×#103	—	3	2	no	—
131	C₅×#103	C₂×D₃	1	2	yes	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	C₂×D₃	1	2	yes	—
134	C₅×#97	—	3	2	no	—
135	C₄×C₅×C₈	—	3	2	no	—
136	#2952	—	3	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₅×D₃	—	2	1	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	8	1	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₅×#67	—	2	4	no	—
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	8	2	no	—
157	C₂×C₅×Dic₃	—	8	1	no	—
158	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
159	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
160	C₅×D₁₂	—	2	1	no	—
161	C₅×D₁₂	C₂²×C₄	1	2	yes	—
162	C₄×C₅×D₃	—	2	4	no	—
163	C₄×C₅×D₃	—	8	2	no	—
164	C₅×Dic₆	—	2	1	no	—
165	C₅×Dic₆	C₂²×C₄	1	2	yes	—
166	C₃×C₅×C₈	—	2	2	no	—
167	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
168	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
170	C₂×#235	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	#950	C₄×C₅	1	8	yes	complemented
174	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
175	C₂×#216	C₂²×C₅	1	1	yes	characteristic
176	C₂×#215	C₂²×C₅	1	1	yes	characteristic
177	D₄×Dic₃	—	2	2	no	—
178	D₄×Dic₃	C₂²×C₅	1	2	yes	—
179	C₂×#214	C₂²×C₅	1	1	yes	characteristic
180	C₂×#213	C₂²×C₅	1	1	yes	characteristic
181	C₄×#67	—	2	2	no	—
182	#926	—	2	1	no	—
183	#926	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄⋊Dic₃	—	2	1	no	—
185	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
187	#893	C₂²×C₅	1	2	yes	—
188	#892	—	2	1	no	—
189	D₃×C₄⋊C₄	—	2	1	no	—
190	#887	C₂²×C₅	1	2	yes	—
191	C₃×#103	C₂²×C₅	1	2	yes	—
192	C₃×#102	C₂²×C₅	1	2	yes	—
193	#821	C₂²×C₅	1	2	yes	—
194	#816	C₂²×C₅	1	2	yes	—
195	#815	C₂²×C₅	1	2	yes	—
196	C₈×Dic₃	C₂²×C₅	1	2	yes	—
197	#808	C₂²×C₅	1	2	yes	—
198	#808	C₂²×C₅	1	2	yes	—
199	C₅×#41	—	2	2	no	—
200	C₅×#41	—	3	4	no	—
201	C₅×#41	—	6	2	no	—
202	C₅×#41	C₄×D₃	1	4	yes	complemented
203	C₂×C₅×Q₈	—	3	1	no	—
204	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	3	1	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	—	6	2	no	—
213	C₂²×C₄×C₅	—	6	1	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₅×Q₁₆	—	3	4	no	—
217	C₅×SD₁₆	—	3	4	no	—
218	C₅×SD₁₆	—	3	4	no	—
219	C₅×D₈	—	3	4	no	—
220	C₅×M₁₆	—	2	2	no	—
221	C₂×C₅×C₈	—	3	4	no	—
222	C₂×C₅×C₈	—	3	1	no	—
223	C₂×C₅×C₈	—	3	1	no	—
224	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	3	1	no	—
227	C₅×C₄⋊C₄	—	3	1	no	—
228	C₅×C₄⋊C₄	—	3	2	no	—
229	C₅×C₄⋊C₄	—	6	2	no	—
230	C₅×C₄⋊C₄	—	6	2	no	—
231	C₅×C₄⋊C₄	—	6	1	no	—
232	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
233	C₅×C₂²⋊C₄	—	3	2	no	—
234	C₅×C₂²⋊C₄	—	6	2	no	—
235	C₅×C₂²⋊C₄	—	6	2	no	—
236	C₄²×C₅	—	3	2	no	—
237	C₄²×C₅	—	6	2	no	—
238	C₄²×C₅	—	6	2	no	—
239	C₂×#135	—	3	1	no	—
240	#520	—	3	1	no	—
241	#520	—	3	1	no	—
242	#442	—	3	2	no	—
243	#441	—	3	2	no	—
244	C₄×SD₁₆	—	3	2	no	—
245	C₄×SD₁₆	—	3	2	no	—
246	C₂×#106	—	3	1	no	—
247	#417	—	3	1	no	—
248	#417	C₅×D₃	1	1	yes	characteristic, complemented
249	#405	—	3	1	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	—	4	1	no	—
255	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₅×D₃	—	2	2	no	—
258	C₂×C₅×D₃	—	4	1	no	—
259	C₂×C₅×D₃	—	4	1	no	—
260	C₃×C₄×C₅	—	2	2	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
263	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₅×Dic₃	—	2	2	no	—
266	C₅×Dic₃	—	2	2	no	—
267	C₅×Dic₃	—	2	2	no	—
268	C₅×Dic₃	—	4	2	no	—
269	C₃×#41	—	2	2	no	—
270	C₃×#41	C₂×C₄×C₅	1	4	yes	complemented
271	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃×D₄	—	2	1	no	—
273	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
274	C₂²×C₃×C₄	—	2	1	no	—
275	C₂²×C₃×C₄	—	2	1	no	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×#67	—	2	1	no	—
278	C₂²×Dic₃	—	2	1	no	—
279	C₂²×Dic₃	—	2	2	no	—
280	#235	—	2	2	no	—
281	#235	C₂×C₄×C₅	1	4	yes	complemented
282	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₄×D₃	—	2	1	no	—
284	C₂×C₄×D₃	—	2	2	no	—
285	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
286	C₃×M₁₆	—	2	2	no	—
287	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	#217	—	2	2	no	—
291	#217	C₅×D₄	1	2	yes	—
292	#216	C₂×C₄×C₅	1	4	yes	complemented
293	#215	C₂×C₄×C₅	1	4	yes	complemented
294	#214	C₂×C₄×C₅	1	4	yes	complemented
295	#213	C₂×C₄×C₅	1	4	yes	complemented
296	(C₂×D₃)⋊C₄	—	2	2	no	—
297	C₄⋊Dic₃	—	2	1	no	—
298	C₄⋊Dic₃	—	2	2	no	—
299	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
300	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
301	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
302	Dic₃⋊C₄	—	2	2	no	—
303	C₄×Dic₃	—	2	2	no	—
304	C₄×Dic₃	—	2	2	no	—
305	C₄×Dic₃	C₂³×C₅	1	2	yes	—
306	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
307	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	6	1	no	—
311	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
312	C₅×Q₈	—	2	1	no	—
313	C₅×Q₈	—	3	2	no	—
314	C₅×Q₈	—	6	1	no	—
315	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
316	C₅×D₄	—	2	4	no	—
317	C₅×D₄	—	2	1	no	—
318	C₅×D₄	—	3	2	no	—
319	C₅×D₄	—	6	4	no	—
320	C₅×D₄	—	6	1	no	—
321	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	4	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	3	2	no	—
326	C₂×C₄×C₅	—	3	2	no	—
327	C₂×C₄×C₅	—	6	1	no	—
328	C₂×C₄×C₅	—	6	4	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	8	1	no	—
331	C₂×C₄×C₅	—	24	2	no	—
332	C₂×C₄×C₅	—	24	2	no	—
333	C₂×C₄×C₅	—	24	1	no	—
334	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
335	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	#237	1	2	yes	—
337	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
338	C₅×C₈	—	2	2	no	—
339	C₅×C₈	—	3	2	no	—
340	C₅×C₈	—	3	2	no	—
341	C₂×#41	—	3	1	no	—
342	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
343	#135	—	3	8	no	—
344	C₂×Q₁₆	—	3	1	no	—
345	C₂×SD₁₆	—	3	1	no	—
346	C₂×SD₁₆	—	3	1	no	—
347	C₂×D₈	—	3	1	no	—
348	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
349	C₂²×C₈	—	3	1	no	—
350	C₄×Q₈	—	3	2	no	—
351	C₄×Q₈	—	3	2	no	—
352	C₄×D₄	—	3	2	no	—
353	C₄×D₄	—	3	2	no	—
354	C₄×D₄	—	6	2	no	—
355	C₄×D₄	—	6	2	no	—
356	#117	—	3	1	no	—
357	#117	—	6	1	no	—
358	#117	—	6	1	no	—
359	C₂×C₄⋊C₄	—	3	1	no	—
360	C₂×C₄⋊C₄	—	6	1	no	—
361	C₂×C₄⋊C₄	—	6	1	no	—
362	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
363	#106	—	3	2	no	—
364	#106	—	3	2	no	—
365	#103	—	3	2	no	—
366	#103	C₂×C₅×D₃	1	2	yes	—
367	#102	—	3	2	no	—
368	#102	C₂×C₅×D₃	1	2	yes	—
369	#97	—	3	2	no	—
370	C₄×C₈	—	3	2	no	—
371	C₂×C₃×C₅	—	2	2	no	—
372	C₂×C₃×C₅	—	4	2	no	—
373	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×C₃×C₅	#577	1	1	yes	characteristic
375	C₂×C₃×C₅	#577	1	1	yes	characteristic
376	C₅×D₃	—	4	2	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂²×D₃	—	2	1	no	—
380	C₃×Q₈	—	2	1	no	—
381	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
382	C₃×D₄	—	2	4	no	—
383	C₃×D₄	—	2	1	no	—
384	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	4	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	8	1	no	—
389	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
390	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃×C₄	C₅×#41	1	2	yes	—
392	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
393	#67	—	2	4	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	—	2	2	no	—
396	C₂×Dic₃	—	8	2	no	—
397	C₂×Dic₃	—	8	1	no	—
398	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
399	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
400	D₁₂	—	2	1	no	—
401	D₁₂	C₂²×C₄×C₅	1	2	yes	—
402	C₄×D₃	—	2	4	no	—
403	C₄×D₃	—	8	2	no	—
404	Dic₆	—	2	1	no	—
405	Dic₆	C₂²×C₄×C₅	1	2	yes	—
406	C₃×C₈	—	2	2	no	—
407	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
408	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
409	C₂²×C₅	—	2	1	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	—	6	2	no	—
415	C₂²×C₅	—	12	1	no	—
416	C₂²×C₅	—	12	1	no	—
417	C₂²×C₅	#67⋊C₄	1	2	yes	—
418	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	—	6	2	no	—
422	C₄×C₅	—	6	2	no	—
423	C₄×C₅	—	6	2	no	—
424	C₄×C₅	—	12	2	no	—
425	C₄×C₅	#67⋊C₄	1	2	yes	—
426	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
427	C₄×C₅	C₂×#237	1	1	yes	characteristic
428	#41	—	2	2	no	—
429	#41	—	3	4	no	—
430	#41	—	6	2	no	—
431	#41	C₄×C₅×D₃	1	4	yes	complemented
432	C₂×Q₈	—	3	1	no	—
433	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	6	1	no	—
437	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	6	2	no	—
441	C₂²×C₄	—	6	2	no	—
442	C₂²×C₄	—	6	1	no	—
443	C₂²×C₄	—	6	1	no	—
444	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
445	Q₁₆	—	3	4	no	—
446	SD₁₆	—	3	4	no	—
447	SD₁₆	—	3	4	no	—
448	D₈	—	3	4	no	—
449	M₁₆	—	2	2	no	—
450	C₂×C₈	—	3	4	no	—
451	C₂×C₈	—	3	1	no	—
452	C₂×C₈	—	3	1	no	—
453	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	3	1	no	—
456	C₄⋊C₄	—	3	1	no	—
457	C₄⋊C₄	—	3	2	no	—
458	C₄⋊C₄	—	6	2	no	—
459	C₄⋊C₄	—	6	2	no	—
460	C₄⋊C₄	—	6	1	no	—
461	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	—	6	2	no	—
464	C₂²⋊C₄	—	6	2	no	—
465	C₄²	—	3	2	no	—
466	C₄²	—	6	2	no	—
467	C₄²	—	6	2	no	—
468	C₃×C₅	#2952	1	1	yes	characteristic, complemented, Hall
469	C₂²×C₃	—	2	1	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
475	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
476	C₂×D₃	—	2	2	no	—
477	C₂×D₃	—	4	1	no	—
478	C₂×D₃	—	4	1	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	4	2	no	—
481	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
482	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
483	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
484	Dic₃	—	2	2	no	—
485	Dic₃	—	2	2	no	—
486	Dic₃	—	2	2	no	—
487	Dic₃	—	4	2	no	—
488	C₂×C₅	—	2	2	no	—
489	C₂×C₅	—	4	2	no	—
490	C₂×C₅	—	12	2	no	—
491	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
492	C₂×C₅	#5775	1	1	yes	characteristic
493	C₂×C₅	#5778	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	6	1	no	—
496	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	3	2	no	—
499	Q₈	—	6	1	no	—
500	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
501	D₄	—	2	4	no	—
502	D₄	—	2	1	no	—
503	D₄	—	3	2	no	—
504	D₄	—	6	4	no	—
505	D₄	—	6	1	no	—
506	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	3	2	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	6	1	no	—
513	C₂×C₄	—	6	4	no	—
514	C₂×C₄	—	6	2	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	—	24	2	no	—
517	C₂×C₄	—	24	2	no	—
518	C₂×C₄	—	24	1	no	—
519	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
520	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
521	C₂×C₄	C₅×#237	1	2	yes	—
522	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
523	C₈	—	2	2	no	—
524	C₈	—	3	2	no	—
525	C₈	—	3	2	no	—
526	C₂×C₃	—	2	2	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
529	C₂×C₃	C₅×#577	1	1	yes	characteristic
530	C₂×C₃	C₅×#577	1	1	yes	characteristic
531	D₃	—	4	2	no	—
532	C₅	#78869	1	1	yes	characteristic, direct product factor, Sylow
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	6	2	no	—
539	C₂²	—	12	1	no	—
540	C₂²	—	12	1	no	—
541	C₂²	C₅×#67⋊C₄	1	2	yes	—
542	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	6	2	no	—
546	C₄	—	6	2	no	—
547	C₄	—	6	2	no	—
548	C₄	—	12	2	no	—
549	C₄	C₅×#67⋊C₄	1	2	yes	—
550	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
551	C₄	C₂×C₅×#237	1	1	yes	characteristic
552	C₃	C₅×#2952	1	1	yes	characteristic, complemented, Sylow
553	C₂	—	2	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	12	2	no	—
556	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
557	C₂	C₅×#5775	1	1	yes	characteristic
558	C₂	C₅×#5778	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#417	D₃
hypocenter	C₃	C₅×#2952
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#417

Complements

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

N	H ≅ G/N	type
1. C₅×#5827	C₂	semidirect
3. C₅×#5504	C₂	semidirect
4. C₃×C₅×#417	C₂	semidirect
5. C₅×#5133	C₂	semidirect
6. C₅×#5122	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₅×#4789	C₂	semidirect
9. C₅×#4788	C₂	semidirect
10. C₅×#4785	C₂	semidirect
11. C₅×#4758	C₂	semidirect
17. C₅×#950	C₄	semidirect
43. #78869	C₅	direct (N × H)
53. C₅×#417	D₃	semidirect
56. C₃×C₅×#41	C₂×C₄	semidirect
67. C₅×#235	C₂×C₄	semidirect
78. C₅×#216	C₂×C₄	semidirect
79. C₅×#215	C₂×C₄	semidirect
80. C₅×#214	C₂×C₄	semidirect
81. C₅×#213	C₂×C₄	semidirect
92. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
95. #5827	C₂×C₅	semidirect
97. #5504	C₂×C₅	semidirect
98. C₃×#417	C₂×C₅	semidirect
99. #5133	C₂×C₅	semidirect
100. #5122	C₂×C₅	semidirect
101. C₂×#808	C₂×C₅	semidirect
102. #4789	C₂×C₅	semidirect
103. #4788	C₂×C₅	semidirect
104. #4785	C₂×C₅	semidirect
105. #4758	C₂×C₅	semidirect
173. #950	C₄×C₅	semidirect
202. C₅×#41	C₄×D₃	semidirect
248. #417	C₅×D₃	semidirect
270. C₃×#41	C₂×C₄×C₅	semidirect
281. #235	C₂×C₄×C₅	semidirect
292. #216	C₂×C₄×C₅	semidirect
293. #215	C₂×C₄×C₅	semidirect
294. #214	C₂×C₄×C₅	semidirect
295. #213	C₂×C₄×C₅	semidirect
306. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
431. #41	C₄×C₅×D₃	semidirect
468. C₃×C₅	#2952	semidirect
532. C₅	#78869	direct (N × H)
552. C₃	C₅×#2952	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5827	2
C₂×C₅×#950	2
C₅×#5504	2
C₃×C₅×#417	2
C₅×#5133	2
C₅×#5122	2
C₂×C₅×#808	2
C₅×#4789	2
C₅×#4788	2
C₅×#4785	2
C₅×#4758	2
C₅×#2952	3
#78869	5

Subgroups — C5×#78869 #14417722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78869 #14417722