Subgroups — C₅×#86766 #14483054

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5831	C₂	1	2	yes	maximal, complemented
4	C₅×#5717	C₂	1	3	yes	maximal, complemented
5	C₅×#5716	C₂	1	3	yes	maximal, complemented
6	C₅×#5612	C₂	1	6	yes	maximal, complemented
7	C₅×#5606	C₂	1	6	yes	maximal, complemented
8	C₅×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5551	C₂	1	3	yes	maximal, complemented
11	C₄×C₅×D₃×D₄	C₂	1	3	yes	maximal, complemented
12	C₅×D₄×#41	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
14	C₅×D₃×#41	—	2	16	no	—
15	C₂×C₅×#239	C₂²	1	1	yes	characteristic
16	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
17	C₂×C₅×#237	C₂²	1	6	yes	complemented
18	C₂×C₅×D₃×D₄	C₂²	1	3	yes	—
19	C₂×C₅×D₃×D₄	C₂²	1	6	yes	complemented
20	C₂×C₅×#235	C₂²	1	6	yes	complemented
21	C₂²×C₄×C₅×D₃	C₂²	1	6	yes	complemented
22	C₃×C₅×#127	C₂²	1	3	yes	complemented
23	C₃×C₅×#121	C₂²	1	6	yes	complemented
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	C₂²	1	3	yes	complemented
26	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₅×#938	C₂²	1	6	yes	complemented
28	C₅×#938	C₂²	1	6	yes	complemented
29	C₅×#938	C₂²	1	6	yes	complemented
30	C₅×#937	C₂²	1	12	yes	complemented
31	C₅×#936	C₂²	1	6	yes	complemented
32	C₅×D₄×Dic₃	C₂²	1	3	yes	complemented
33	C₅×D₄×Dic₃	C₂²	1	6	yes	complemented
34	C₄×C₅×#67	C₂²	1	6	yes	complemented
35	C₅×#924	C₂²	1	6	yes	complemented
36	C₅×#897	C₂²	1	6	yes	complemented
37	C₅×#893	C₂²	1	1	yes	characteristic
38	C₅×#893	C₂²	1	3	yes	complemented
39	C₅×#892	C₂²	1	3	yes	complemented
40	C₅×D₃×C₄⋊C₄	C₂²	1	3	yes	complemented
41	C₅×#883	C₂²	1	12	yes	complemented
42	C₅×#67⋊C₄	C₂²	1	6	yes	complemented
43	C₅×D₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
44	C₄×C₅×D₁₂	C₂²	1	3	yes	—
45	C₄×C₅×D₁₂	C₂²	1	3	yes	complemented
46	C₄²×C₅×D₃	C₂²	1	3	yes	complemented
47	C₅×#869	C₂²	1	3	yes	complemented
48	#86766	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₂²×C₅×#41	—	3	2	no	—
50	C₅×#550	D₃	1	1	yes	characteristic, complemented
51	C₅×D₄×Q₈	—	3	1	no	—
52	C₅×#548	—	3	2	no	—
53	C₅×#547	—	3	3	no	—
54	C₅×#546	—	3	6	no	—
55	C₅×D₄²	—	3	3	no	—
56	C₅×#532	—	3	3	no	—
57	C₅×#525	—	3	6	no	—
58	C₄×C₅×#41	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	3	no	—
60	C₂³×C₅×D₃	C₂³	1	6	yes	—
61	C₃×C₅×#41	—	2	8	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
67	C₂×C₅×#67	C₂³	1	6	yes	—
68	C₂×C₅×#67	C₂³	1	12	yes	—
69	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
70	C₅×#239	D₄	1	8	yes	complemented
71	C₅×D₃×Q₈	—	2	8	no	—
72	C₅×#237	—	2	24	no	—
73	C₅×D₃×D₄	—	2	24	no	—
74	C₅×D₃×D₄	—	2	12	no	—
75	C₅×#235	—	2	24	no	—
76	C₂×C₅×D₁₂	C₂³	1	3	yes	—
77	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	—	2	24	no	—
79	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
80	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
81	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
82	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
83	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
84	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
85	C₂×C₅×Dic₆	C₂³	1	6	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₃×C₄²×C₅	C₂³	1	3	yes	—
90	C₅×#217	C₂³	1	6	yes	—
91	C₅×#217	C₂³	1	12	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
95	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
96	C₅×C₄⋊Dic₃	C₂³	1	6	yes	—
97	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
98	C₅×Dic₃⋊C₄	C₂³	1	6	yes	—
99	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₄×C₅×Dic₃	C₂³	1	3	yes	—
101	C₄×C₅×Dic₃	C₂³	1	3	yes	—
102	C₂×D₃×#41	C₂×C₅	1	2	yes	complemented
103	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
104	#5831	C₂×C₅	1	2	yes	complemented
105	#5717	C₂×C₅	1	3	yes	complemented
106	#5716	C₂×C₅	1	3	yes	complemented
107	#5612	C₂×C₅	1	6	yes	complemented
108	#5606	C₂×C₅	1	6	yes	complemented
109	Q₈×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
110	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
111	#5551	C₂×C₅	1	3	yes	complemented
112	C₄×D₃×D₄	C₂×C₅	1	3	yes	complemented
113	C₂×C₅×#41	—	3	1	no	—
114	C₂×C₅×#41	—	3	6	no	—
115	C₂×C₅×#41	—	3	6	no	—
116	C₂×C₅×#41	—	6	16	no	—
117	C₂×C₅×#41	C₂×D₃	1	2	yes	complemented
118	C₂²×C₅×Q₈	—	3	2	no	—
119	C₂²×C₅×D₄	—	3	3	no	—
120	C₂²×C₅×D₄	—	3	6	no	—
121	C₂³×C₄×C₅	—	3	6	no	—
122	C₅×C₄⋊Q₈	—	3	3	no	—
123	C₅×#127	C₂×D₃	1	3	yes	complemented
124	C₅×#124	—	3	6	no	—
125	C₅×#123	—	3	12	no	—
126	C₅×C₂²⋊Q₈	—	3	6	no	—
127	C₅×C₂²⋊Q₈	—	3	6	no	—
128	C₅×#121	—	3	6	no	—
129	C₅×#121	—	3	6	no	—
130	C₅×#121	—	3	6	no	—
131	C₅×#121	C₂×D₃	1	6	yes	complemented
132	C₅×#120	—	3	12	no	—
133	C₄×C₅×Q₈	—	3	1	no	—
134	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
135	C₄×C₅×D₄	—	3	3	no	—
136	C₄×C₅×D₄	—	3	6	no	—
137	C₄×C₅×D₄	—	3	6	no	—
138	C₄×C₅×D₄	—	3	1	no	—
139	C₄×C₅×D₄	—	3	3	no	—
140	C₄×C₅×D₄	—	3	6	no	—
141	C₄×C₅×D₄	—	3	3	no	—
142	C₄×C₅×D₄	—	3	3	no	—
143	C₄×C₅×D₄	C₂×D₃	1	3	yes	complemented
144	C₅×#117	—	3	3	no	—
145	C₂×C₅×C₄⋊C₄	—	3	3	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
147	C₂×C₄²×C₅	—	3	3	no	—
148	D₄×#41	—	3	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
150	C₂²×C₅×D₃	—	2	12	no	—
151	C₂²×C₅×D₃	—	2	12	no	—
152	C₂²×C₅×D₃	—	4	6	no	—
153	C₂²×C₅×D₃	C₂⁴	1	3	yes	—
154	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
155	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
156	C₃×C₅×D₄	—	2	12	no	—
157	C₃×C₅×D₄	—	2	6	no	—
158	C₃×C₅×D₄	—	4	6	no	—
159	C₂×C₃×C₄×C₅	—	2	12	no	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×#67	—	2	24	no	—
165	C₅×#67	—	2	12	no	—
166	C₂×C₅×Dic₃	—	2	12	no	—
167	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
169	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
170	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
171	C₅×D₁₂	C₂×D₄	1	12	yes	complemented
172	C₅×D₁₂	#41	1	4	yes	complemented
173	C₄×C₅×D₃	—	2	12	no	—
174	C₄×C₅×D₃	—	2	12	no	—
175	C₄×C₅×D₃	—	2	6	no	—
176	C₄×C₅×D₃	—	2	4	no	—
177	C₄×C₅×D₃	—	4	3	no	—
178	C₄×C₅×D₃	C₂×D₄	1	12	yes	complemented
179	C₅×Dic₆	—	2	12	no	—
180	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
181	D₃×#41	—	2	16	no	—
182	C₂×#239	C₂²×C₅	1	1	yes	characteristic
183	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
184	C₂×#237	C₂²×C₅	1	6	yes	complemented
185	C₂×D₃×D₄	C₂²×C₅	1	3	yes	—
186	C₂×D₃×D₄	C₂²×C₅	1	6	yes	complemented
187	C₂×#235	C₂²×C₅	1	6	yes	complemented
188	C₂²×C₄×D₃	C₂²×C₅	1	6	yes	complemented
189	C₃×#127	C₂²×C₅	1	3	yes	complemented
190	C₃×#121	C₂²×C₅	1	6	yes	complemented
191	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₃×C₄×D₄	C₂²×C₅	1	3	yes	complemented
193	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
194	#938	C₂²×C₅	1	6	yes	complemented
195	#938	C₂²×C₅	1	6	yes	complemented
196	#938	C₂²×C₅	1	6	yes	complemented
197	#937	C₂²×C₅	1	12	yes	complemented
198	#936	C₂²×C₅	1	6	yes	complemented
199	D₄×Dic₃	C₂²×C₅	1	3	yes	complemented
200	D₄×Dic₃	C₂²×C₅	1	6	yes	complemented
201	C₄×#67	C₂²×C₅	1	6	yes	complemented
202	#924	C₂²×C₅	1	6	yes	complemented
203	#897	C₂²×C₅	1	6	yes	complemented
204	#893	C₂²×C₅	1	1	yes	characteristic
205	#893	C₂²×C₅	1	3	yes	complemented
206	#892	C₂²×C₅	1	3	yes	complemented
207	D₃×C₄⋊C₄	C₂²×C₅	1	3	yes	complemented
208	#883	C₂²×C₅	1	12	yes	complemented
209	#67⋊C₄	C₂²×C₅	1	6	yes	complemented
210	D₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	complemented
211	C₄×D₁₂	C₂²×C₅	1	3	yes	—
212	C₄×D₁₂	C₂²×C₅	1	3	yes	complemented
213	C₄²×D₃	C₂²×C₅	1	3	yes	complemented
214	#869	C₂²×C₅	1	3	yes	complemented
215	C₂⁴×C₅	—	3	6	no	—
216	C₅×#41	—	2	8	no	—
217	C₅×#41	—	3	8	no	—
218	C₅×#41	—	6	24	no	—
219	C₅×#41	—	6	24	no	—
220	C₂×C₅×Q₈	—	3	6	no	—
221	C₂×C₅×Q₈	—	6	8	no	—
222	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
223	C₂×C₅×D₄	—	3	6	no	—
224	C₂×C₅×D₄	—	3	12	no	—
225	C₂×C₅×D₄	—	3	1	no	—
226	C₂×C₅×D₄	—	3	3	no	—
227	C₂×C₅×D₄	—	6	24	no	—
228	C₂×C₅×D₄	—	6	12	no	—
229	C₂×C₅×D₄	C₂²×D₃	1	3	yes	—
230	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
231	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
232	C₂²×C₄×C₅	—	3	3	no	—
233	C₂²×C₄×C₅	—	3	6	no	—
234	C₂²×C₄×C₅	—	3	3	no	—
235	C₂²×C₄×C₅	—	3	6	no	—
236	C₂²×C₄×C₅	—	3	2	no	—
237	C₂²×C₄×C₅	—	3	6	no	—
238	C₂²×C₄×C₅	—	3	3	no	—
239	C₂²×C₄×C₅	—	6	24	no	—
240	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
241	C₅×C₄⋊C₄	—	3	3	no	—
242	C₅×C₄⋊C₄	—	3	6	no	—
243	C₅×C₄⋊C₄	—	3	3	no	—
244	C₅×C₄⋊C₄	—	3	6	no	—
245	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
246	C₅×C₄⋊C₄	C₂²×D₃	1	3	yes	—
247	C₅×C₂²⋊C₄	—	3	6	no	—
248	C₅×C₂²⋊C₄	—	3	12	no	—
249	C₅×C₂²⋊C₄	—	3	2	no	—
250	C₅×C₂²⋊C₄	—	3	6	no	—
251	C₅×C₂²⋊C₄	—	3	6	no	—
252	C₅×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
253	C₄²×C₅	—	3	1	no	—
254	C₄²×C₅	—	3	3	no	—
255	C₄²×C₅	—	3	3	no	—
256	C₄²×C₅	C₂²×D₃	1	3	yes	—
257	C₂²×#41	—	3	2	no	—
258	#550	C₅×D₃	1	1	yes	characteristic, complemented
259	D₄×Q₈	—	3	1	no	—
260	#548	—	3	2	no	—
261	#547	—	3	3	no	—
262	#546	—	3	6	no	—
263	D₄²	—	3	3	no	—
264	#532	—	3	3	no	—
265	#525	—	3	6	no	—
266	C₄×#41	—	3	1	no	—
267	C₂×C₄×D₄	—	3	3	no	—
268	C₂²×C₃×C₅	—	2	6	no	—
269	C₂²×C₃×C₅	—	2	6	no	—
270	C₂²×C₃×C₅	—	2	6	no	—
271	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
272	C₂×C₅×D₃	—	2	2	no	—
273	C₂×C₅×D₃	—	2	3	no	—
274	C₂×C₅×D₃	—	2	3	no	—
275	C₂×C₅×D₃	—	2	2	no	—
276	C₂×C₅×D₃	—	4	24	no	—
277	C₂×C₅×D₃	C₂²×D₄	1	6	yes	—
278	C₂×C₅×D₃	C₂×#41	1	4	yes	complemented
279	C₃×C₄×C₅	—	2	2	no	—
280	C₃×C₄×C₅	—	2	3	no	—
281	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
282	C₃×C₄×C₅	C₂×#41	1	2	yes	complemented
283	C₅×Dic₃	—	2	6	no	—
284	C₅×Dic₃	—	2	3	no	—
285	C₅×Dic₃	—	2	1	no	—
286	C₅×Dic₃	C₂²×D₄	1	2	yes	—
287	C₂³×D₃	C₂³×C₅	1	6	yes	—
288	C₃×#41	—	2	8	no	—
289	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₃×D₄	C₂³×C₅	1	3	yes	—
291	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
292	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
293	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
294	C₂×#67	C₂³×C₅	1	6	yes	—
295	C₂×#67	C₂³×C₅	1	12	yes	—
296	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
297	#239	C₅×D₄	1	8	yes	complemented
298	D₃×Q₈	—	2	8	no	—
299	#237	—	2	24	no	—
300	D₃×D₄	—	2	24	no	—
301	D₃×D₄	—	2	12	no	—
302	#235	—	2	24	no	—
303	C₂×D₁₂	C₂³×C₅	1	3	yes	—
304	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
305	C₂×C₄×D₃	—	2	24	no	—
306	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
307	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
308	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
309	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
310	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
311	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
312	C₂×Dic₆	C₂³×C₅	1	6	yes	—
313	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
314	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
315	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
316	C₃×C₄²	C₂³×C₅	1	3	yes	—
317	#217	C₂³×C₅	1	6	yes	—
318	#217	C₂³×C₅	1	12	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
320	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
321	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
322	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
323	C₄⋊Dic₃	C₂³×C₅	1	6	yes	—
324	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
325	Dic₃⋊C₄	C₂³×C₅	1	6	yes	—
326	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
327	C₄×Dic₃	C₂³×C₅	1	3	yes	—
328	C₄×Dic₃	C₂³×C₅	1	3	yes	—
329	C₂³×C₅	—	3	2	no	—
330	C₂³×C₅	—	3	3	no	—
331	C₂³×C₅	—	6	12	no	—
332	C₂³×C₅	—	6	12	no	—
333	C₂³×C₅	—	12	6	no	—
334	C₂³×C₅	C₂³×D₃	1	6	yes	—
335	C₅×Q₈	—	6	12	no	—
336	C₅×Q₈	D₃×D₄	1	4	yes	complemented
337	C₅×D₄	—	2	12	no	—
338	C₅×D₄	—	2	6	no	—
339	C₅×D₄	—	3	12	no	—
340	C₅×D₄	—	3	4	no	—
341	C₅×D₄	—	4	6	no	—
342	C₅×D₄	—	6	12	no	—
343	C₅×D₄	—	6	24	no	—
344	C₂×C₄×C₅	—	2	12	no	—
345	C₂×C₄×C₅	—	3	1	no	—
346	C₂×C₄×C₅	—	3	12	no	—
347	C₂×C₄×C₅	—	3	1	no	—
348	C₂×C₄×C₅	—	3	3	no	—
349	C₂×C₄×C₅	—	3	6	no	—
350	C₂×C₄×C₅	—	6	4	no	—
351	C₂×C₄×C₅	—	6	12	no	—
352	C₂×C₄×C₅	—	6	12	no	—
353	C₂×C₄×C₅	—	6	12	no	—
354	C₂×C₄×C₅	—	6	6	no	—
355	C₂×C₄×C₅	—	12	3	no	—
356	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
357	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
358	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
359	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
360	C₂×#41	—	3	1	no	—
361	C₂×#41	—	3	6	no	—
362	C₂×#41	—	3	6	no	—
363	C₂×#41	—	6	16	no	—
364	C₂×#41	C₂×C₅×D₃	1	2	yes	complemented
365	C₂²×Q₈	—	3	2	no	—
366	C₂²×D₄	—	3	3	no	—
367	C₂²×D₄	—	3	6	no	—
368	C₂³×C₄	—	3	6	no	—
369	C₄⋊Q₈	—	3	3	no	—
370	#127	C₂×C₅×D₃	1	3	yes	complemented
371	#124	—	3	6	no	—
372	#123	—	3	12	no	—
373	C₂²⋊Q₈	—	3	6	no	—
374	C₂²⋊Q₈	—	3	6	no	—
375	#121	—	3	6	no	—
376	#121	—	3	6	no	—
377	#121	—	3	6	no	—
378	#121	C₂×C₅×D₃	1	6	yes	complemented
379	#120	—	3	12	no	—
380	C₄×Q₈	—	3	1	no	—
381	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
382	C₄×D₄	—	3	3	no	—
383	C₄×D₄	—	3	6	no	—
384	C₄×D₄	—	3	6	no	—
385	C₄×D₄	—	3	1	no	—
386	C₄×D₄	—	3	3	no	—
387	C₄×D₄	—	3	6	no	—
388	C₄×D₄	—	3	3	no	—
389	C₄×D₄	—	3	3	no	—
390	C₄×D₄	C₂×C₅×D₃	1	3	yes	complemented
391	#117	—	3	3	no	—
392	C₂×C₄⋊C₄	—	3	3	no	—
393	C₂×C₂²⋊C₄	—	3	6	no	—
394	C₂×C₄²	—	3	3	no	—
395	C₂×C₃×C₅	—	4	6	no	—
396	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
397	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
398	C₂×C₃×C₅	#585	1	1	yes	characteristic
399	C₅×D₃	—	2	4	no	—
400	C₅×D₃	—	2	6	no	—
401	C₂³×C₃	C₂⁴×C₅	1	6	yes	—
402	C₂²×D₃	—	2	12	no	—
403	C₂²×D₃	—	2	12	no	—
404	C₂²×D₃	—	4	6	no	—
405	C₂²×D₃	C₂⁴×C₅	1	3	yes	—
406	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
407	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
408	C₃×D₄	—	2	12	no	—
409	C₃×D₄	—	2	6	no	—
410	C₃×D₄	—	4	6	no	—
411	C₂×C₃×C₄	—	2	12	no	—
412	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
413	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
415	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
416	#67	—	2	24	no	—
417	#67	—	2	12	no	—
418	C₂×Dic₃	—	2	12	no	—
419	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
420	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
421	C₂×Dic₃	C₂⁴×C₅	1	6	yes	—
422	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
423	D₁₂	C₂×C₅×D₄	1	12	yes	complemented
424	D₁₂	C₅×#41	1	4	yes	complemented
425	C₄×D₃	—	2	12	no	—
426	C₄×D₃	—	2	12	no	—
427	C₄×D₃	—	2	6	no	—
428	C₄×D₃	—	2	4	no	—
429	C₄×D₃	—	4	3	no	—
430	C₄×D₃	C₂×C₅×D₄	1	12	yes	complemented
431	Dic₆	—	2	12	no	—
432	C₂²×C₅	—	2	6	no	—
433	C₂²×C₅	—	2	6	no	—
434	C₂²×C₅	—	2	6	no	—
435	C₂²×C₅	—	3	6	no	—
436	C₂²×C₅	—	3	4	no	—
437	C₂²×C₅	—	6	2	no	—
438	C₂²×C₅	—	6	3	no	—
439	C₂²×C₅	—	6	3	no	—
440	C₂²×C₅	—	6	2	no	—
441	C₂²×C₅	—	12	24	no	—
442	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	3	no	—
445	C₄×C₅	—	3	2	no	—
446	C₄×C₅	—	6	6	no	—
447	C₄×C₅	—	6	3	no	—
448	C₄×C₅	—	6	1	no	—
449	C₄×C₅	C₂×D₃×D₄	1	6	yes	—
450	C₄×C₅	D₃×#41	1	2	yes	complemented
451	C₂⁴	—	3	6	no	—
452	#41	—	2	8	no	—
453	#41	—	3	8	no	—
454	#41	—	6	24	no	—
455	#41	—	6	24	no	—
456	C₂×Q₈	—	3	6	no	—
457	C₂×Q₈	—	6	8	no	—
458	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
459	C₂×D₄	—	3	6	no	—
460	C₂×D₄	—	3	12	no	—
461	C₂×D₄	—	3	1	no	—
462	C₂×D₄	—	3	3	no	—
463	C₂×D₄	—	6	24	no	—
464	C₂×D₄	—	6	12	no	—
465	C₂×D₄	C₂²×C₅×D₃	1	3	yes	—
466	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
467	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
468	C₂²×C₄	—	3	3	no	—
469	C₂²×C₄	—	3	6	no	—
470	C₂²×C₄	—	3	3	no	—
471	C₂²×C₄	—	3	6	no	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	—	3	6	no	—
474	C₂²×C₄	—	3	3	no	—
475	C₂²×C₄	—	6	24	no	—
476	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
477	C₄⋊C₄	—	3	3	no	—
478	C₄⋊C₄	—	3	6	no	—
479	C₄⋊C₄	—	3	3	no	—
480	C₄⋊C₄	—	3	6	no	—
481	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×C₅×D₃	1	3	yes	—
483	C₂²⋊C₄	—	3	6	no	—
484	C₂²⋊C₄	—	3	12	no	—
485	C₂²⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	6	no	—
487	C₂²⋊C₄	—	3	6	no	—
488	C₂²⋊C₄	C₂²×C₅×D₃	1	6	yes	—
489	C₄²	—	3	1	no	—
490	C₄²	—	3	3	no	—
491	C₄²	—	3	3	no	—
492	C₄²	C₂²×C₅×D₃	1	3	yes	—
493	C₃×C₅	D₄×#41	1	1	yes	characteristic, complemented, Hall
494	C₂²×C₃	—	2	6	no	—
495	C₂²×C₃	—	2	6	no	—
496	C₂²×C₃	—	2	6	no	—
497	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
498	C₂×D₃	—	2	2	no	—
499	C₂×D₃	—	2	3	no	—
500	C₂×D₃	—	2	3	no	—
501	C₂×D₃	—	2	2	no	—
502	C₂×D₃	—	4	24	no	—
503	C₂×D₃	C₂²×C₅×D₄	1	6	yes	—
504	C₂×D₃	C₂×C₅×#41	1	4	yes	complemented
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	3	no	—
507	C₃×C₄	C₂²×C₅×D₄	1	6	yes	—
508	C₃×C₄	C₂×C₅×#41	1	2	yes	complemented
509	Dic₃	—	2	6	no	—
510	Dic₃	—	2	3	no	—
511	Dic₃	—	2	1	no	—
512	Dic₃	C₂²×C₅×D₄	1	2	yes	—
513	C₂×C₅	—	4	6	no	—
514	C₂×C₅	—	6	4	no	—
515	C₂×C₅	—	6	6	no	—
516	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
517	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
518	C₂×C₅	#5966	1	1	yes	characteristic
519	C₂³	—	3	2	no	—
520	C₂³	—	3	3	no	—
521	C₂³	—	6	12	no	—
522	C₂³	—	6	12	no	—
523	C₂³	—	12	6	no	—
524	C₂³	C₂³×C₅×D₃	1	6	yes	—
525	Q₈	—	6	12	no	—
526	Q₈	C₅×D₃×D₄	1	4	yes	complemented
527	D₄	—	2	12	no	—
528	D₄	—	2	6	no	—
529	D₄	—	3	12	no	—
530	D₄	—	3	4	no	—
531	D₄	—	4	6	no	—
532	D₄	—	6	24	no	—
533	D₄	—	6	12	no	—
534	C₂×C₄	—	2	12	no	—
535	C₂×C₄	—	3	1	no	—
536	C₂×C₄	—	3	12	no	—
537	C₂×C₄	—	3	1	no	—
538	C₂×C₄	—	3	3	no	—
539	C₂×C₄	—	3	6	no	—
540	C₂×C₄	—	6	4	no	—
541	C₂×C₄	—	6	12	no	—
542	C₂×C₄	—	6	12	no	—
543	C₂×C₄	—	6	12	no	—
544	C₂×C₄	—	6	6	no	—
545	C₂×C₄	—	12	3	no	—
546	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
547	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
548	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
549	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
550	C₂×C₃	—	4	6	no	—
551	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
552	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
553	C₂×C₃	C₅×#585	1	1	yes	characteristic
554	D₃	—	2	4	no	—
555	D₃	—	2	6	no	—
556	C₅	#86766	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	2	6	no	—
558	C₂²	—	2	6	no	—
559	C₂²	—	2	6	no	—
560	C₂²	—	3	6	no	—
561	C₂²	—	3	4	no	—
562	C₂²	—	6	2	no	—
563	C₂²	—	6	3	no	—
564	C₂²	—	6	3	no	—
565	C₂²	—	6	2	no	—
566	C₂²	—	12	24	no	—
567	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	3	no	—
570	C₄	—	3	2	no	—
571	C₄	—	6	6	no	—
572	C₄	—	6	3	no	—
573	C₄	—	6	1	no	—
574	C₄	C₂×C₅×D₃×D₄	1	6	yes	—
575	C₄	C₅×D₃×#41	1	2	yes	complemented
576	C₃	C₅×D₄×#41	1	1	yes	characteristic, complemented, Sylow
577	C₂	—	4	6	no	—
578	C₂	—	6	4	no	—
579	C₂	—	6	6	no	—
580	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
581	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
582	C₂	C₅×#5966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#550	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#550	D₃
hypocenter	C₃	C₅×D₄×#41
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#550

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₃×C₅×#550	C₂	semidirect
3. C₅×#5831	C₂	semidirect
4. C₅×#5717	C₂	semidirect
5. C₅×#5716	C₂	semidirect
6. C₅×#5612	C₂	semidirect
7. C₅×#5606	C₂	semidirect
8. C₅×Q₈×D₁₂	C₂	semidirect
9. C₄×C₅×#239	C₂	semidirect
10. C₅×#5551	C₂	semidirect
11. C₄×C₅×D₃×D₄	C₂	semidirect
13. C₂×C₃×C₅×#41	C₂²	semidirect
16. C₂×C₅×D₃×Q₈	C₂²	semidirect
17. C₂×C₅×#237	C₂²	semidirect
19. C₂×C₅×D₃×D₄	C₂²	semidirect
20. C₂×C₅×#235	C₂²	semidirect
21. C₂²×C₄×C₅×D₃	C₂²	semidirect
22. C₃×C₅×#127	C₂²	semidirect
23. C₃×C₅×#121	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₅×#938	C₂²	semidirect
28. C₅×#938	C₂²	semidirect
29. C₅×#938	C₂²	semidirect
30. C₅×#937	C₂²	semidirect
31. C₅×#936	C₂²	semidirect
32. C₅×D₄×Dic₃	C₂²	semidirect
33. C₅×D₄×Dic₃	C₂²	semidirect
34. C₄×C₅×#67	C₂²	semidirect
35. C₅×#924	C₂²	semidirect
36. C₅×#897	C₂²	semidirect
38. C₅×#893	C₂²	semidirect
39. C₅×#892	C₂²	semidirect
40. C₅×D₃×C₄⋊C₄	C₂²	semidirect
41. C₅×#883	C₂²	semidirect
42. C₅×#67⋊C₄	C₂²	semidirect
43. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
45. C₄×C₅×D₁₂	C₂²	semidirect
46. C₄²×C₅×D₃	C₂²	semidirect
47. C₅×#869	C₂²	semidirect
48. #86766	C₅	direct (N × H)
50. C₅×#550	D₃	semidirect
70. C₅×#239	D₄	semidirect
102. C₂×D₃×#41	C₂×C₅	semidirect
103. C₃×#550	C₂×C₅	semidirect
104. #5831	C₂×C₅	semidirect
105. #5717	C₂×C₅	semidirect
106. #5716	C₂×C₅	semidirect
107. #5612	C₂×C₅	semidirect
108. #5606	C₂×C₅	semidirect
109. Q₈×D₁₂	C₂×C₅	semidirect
110. C₄×#239	C₂×C₅	semidirect
111. #5551	C₂×C₅	semidirect
112. C₄×D₃×D₄	C₂×C₅	semidirect
117. C₂×C₅×#41	C₂×D₃	semidirect
123. C₅×#127	C₂×D₃	semidirect
131. C₅×#121	C₂×D₃	semidirect
134. C₄×C₅×Q₈	C₂×D₃	semidirect
143. C₄×C₅×D₄	C₂×D₃	semidirect
155. C₃×C₅×Q₈	C₂×D₄	semidirect
171. C₅×D₁₂	C₂×D₄	semidirect
172. C₅×D₁₂	#41	semidirect
178. C₄×C₅×D₃	C₂×D₄	semidirect
180. C₂×C₃×#41	C₂²×C₅	semidirect
183. C₂×D₃×Q₈	C₂²×C₅	semidirect
184. C₂×#237	C₂²×C₅	semidirect
186. C₂×D₃×D₄	C₂²×C₅	semidirect
187. C₂×#235	C₂²×C₅	semidirect
188. C₂²×C₄×D₃	C₂²×C₅	semidirect
189. C₃×#127	C₂²×C₅	semidirect
190. C₃×#121	C₂²×C₅	semidirect
191. C₃×C₄×Q₈	C₂²×C₅	semidirect
192. C₃×C₄×D₄	C₂²×C₅	semidirect
193. Q₈×Dic₃	C₂²×C₅	semidirect
194. #938	C₂²×C₅	semidirect
195. #938	C₂²×C₅	semidirect
196. #938	C₂²×C₅	semidirect
197. #937	C₂²×C₅	semidirect
198. #936	C₂²×C₅	semidirect
199. D₄×Dic₃	C₂²×C₅	semidirect
200. D₄×Dic₃	C₂²×C₅	semidirect
201. C₄×#67	C₂²×C₅	semidirect
202. #924	C₂²×C₅	semidirect
203. #897	C₂²×C₅	semidirect
205. #893	C₂²×C₅	semidirect
206. #892	C₂²×C₅	semidirect
207. D₃×C₄⋊C₄	C₂²×C₅	semidirect
208. #883	C₂²×C₅	semidirect
209. #67⋊C₄	C₂²×C₅	semidirect
210. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
212. C₄×D₁₂	C₂²×C₅	semidirect
213. C₄²×D₃	C₂²×C₅	semidirect
214. #869	C₂²×C₅	semidirect
258. #550	C₅×D₃	semidirect
278. C₂×C₅×D₃	C₂×#41	semidirect
282. C₃×C₄×C₅	C₂×#41	semidirect
297. #239	C₅×D₄	semidirect
336. C₅×Q₈	D₃×D₄	semidirect
364. C₂×#41	C₂×C₅×D₃	semidirect
370. #127	C₂×C₅×D₃	semidirect
378. #121	C₂×C₅×D₃	semidirect
381. C₄×Q₈	C₂×C₅×D₃	semidirect
390. C₄×D₄	C₂×C₅×D₃	semidirect
407. C₃×Q₈	C₂×C₅×D₄	semidirect
423. D₁₂	C₂×C₅×D₄	semidirect
424. D₁₂	C₅×#41	semidirect
430. C₄×D₃	C₂×C₅×D₄	semidirect
450. C₄×C₅	D₃×#41	semidirect
493. C₃×C₅	D₄×#41	semidirect
504. C₂×D₃	C₂×C₅×#41	semidirect
508. C₃×C₄	C₂×C₅×#41	semidirect
526. Q₈	C₅×D₃×D₄	semidirect
556. C₅	#86766	direct (N × H)
575. C₄	C₅×D₃×#41	semidirect
576. C₃	C₅×D₄×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₃×C₅×#550	2
C₅×#5831	2
C₅×#5717	2
C₅×#5716	2
C₅×#5612	2
C₅×#5606	2
C₅×Q₈×D₁₂	2
C₄×C₅×#239	2
C₅×#5551	2
C₄×C₅×D₃×D₄	2
C₅×D₄×#41	3
#86766	5

Subgroups — C5×#86766 #14483054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86766 #14483054