Subgroups — C₅×#86236 #14481514

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5828	C₂	1	2	yes	maximal, complemented
3	C₅×Dic₃×#41	C₂	1	2	yes	maximal, complemented
4	C₅×#5731	C₂	1	2	yes	maximal, complemented
5	C₅×#5719	C₂	1	2	yes	maximal, complemented
6	C₅×#5682	C₂	1	4	yes	maximal, complemented
7	C₅×#5617	C₂	1	4	yes	maximal, complemented
8	C₅×#5602	C₂	1	4	yes	maximal, complemented
9	C₅×#5538	C₂	1	8	yes	maximal, complemented
10	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3455	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#124	C₂²	1	2	yes	complemented
18	C₃×C₅×#121	C₂²	1	4	yes	—
19	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₅×#946	C₂²	1	4	yes	—
22	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
23	C₅×#939	C₂²	1	8	yes	—
24	C₅×#938	C₂²	1	4	yes	—
25	C₅×#937	C₂²	1	4	yes	—
26	C₅×#935	C₂²	1	4	yes	—
27	C₅×#935	C₂²	1	8	yes	complemented
28	C₅×D₄×Dic₃	C₂²	1	8	yes	—
29	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
30	C₄×C₅×#67	C₂²	1	8	yes	—
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₅×#926	C₂²	1	2	yes	—
33	C₅×#926	C₂²	1	4	yes	complemented
34	C₅×#924	C₂²	1	4	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
38	C₅×#898	C₂²	1	8	yes	—
39	C₅×#889	C₂²	1	8	yes	complemented
40	C₅×#886	C₂²	1	8	yes	—
41	C₅×#885	C₂²	1	8	yes	—
42	C₅×#879	C₂²	1	8	yes	complemented
43	C₅×#878	C₂²	1	8	yes	complemented
44	C₅×#872	C₂²	1	2	yes	—
45	C₅×#872	C₂²	1	2	yes	—
46	C₅×#872	C₂²	1	4	yes	—
47	C₅×#870	C₂²	1	2	yes	complemented
48	C₅×#869	C₂²	1	2	yes	complemented
49	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
50	#86236	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₅×#542	—	3	4	no	—
52	C₅×#541	—	3	2	no	—
53	C₅×#540	—	3	2	no	—
54	C₅×#539	—	3	4	no	—
55	C₅×#538	—	3	4	no	—
56	C₅×#533	—	3	1	no	—
57	C₅×#532	D₃	1	1	yes	characteristic, complemented
58	C₅×#529	—	3	8	no	—
59	C₅×#525	—	3	2	no	—
60	C₄×C₅×#41	—	3	2	no	—
61	C₂×C₅×#117	—	3	1	no	—
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₃×C₅×#41	—	2	8	no	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₅×#67	C₂³	1	8	yes	—
72	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₂²×C₅×Dic₃	C₂³	1	8	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
75	C₂×C₄×C₅×D₃	—	2	4	no	—
76	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
77	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
78	C₂×C₅×Dic₆	C₂³	1	4	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₃×C₄²×C₅	C₂³	1	2	yes	—
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#217	C₂³	1	8	yes	—
85	C₅×#217	C₂³	1	8	yes	—
86	C₅×#217	C₂³	1	4	yes	—
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
88	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
89	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
90	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
91	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
92	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
93	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
94	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
95	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
96	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
97	C₄×C₅×Dic₃	C₂³	1	4	yes	—
98	C₄×C₅×Dic₃	C₂³	1	2	yes	—
99	C₄×C₅×Dic₃	C₂³	1	2	yes	—
100	C₄×C₅×Dic₃	C₂³	1	8	yes	—
101	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
102	#5828	C₂×C₅	1	2	yes	complemented
103	Dic₃×#41	C₂×C₅	1	2	yes	complemented
104	#5731	C₂×C₅	1	2	yes	complemented
105	#5719	C₂×C₅	1	2	yes	complemented
106	#5682	C₂×C₅	1	4	yes	complemented
107	#5617	C₂×C₅	1	4	yes	complemented
108	#5602	C₂×C₅	1	4	yes	complemented
109	#5538	C₂×C₅	1	8	yes	complemented
110	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
111	#5470	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	C₂×D₃	1	2	yes	—
113	C₂³×C₄×C₅	—	3	1	no	—
114	C₅×C₄⋊Q₈	—	3	2	no	—
115	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
116	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
117	C₅×#126	—	3	8	no	—
118	C₅×#126	—	3	8	no	—
119	C₅×#125	—	3	8	no	—
120	C₅×#125	—	3	2	no	—
121	C₅×#124	—	3	8	no	—
122	C₅×#124	C₂×D₃	1	2	yes	complemented
123	C₅×#123	—	3	4	no	—
124	C₅×#123	—	3	8	no	—
125	C₅×#123	—	3	8	no	—
126	C₅×C₂²⋊Q₈	—	3	4	no	—
127	C₅×C₂²⋊Q₈	—	3	4	no	—
128	C₅×C₂²⋊Q₈	—	3	8	no	—
129	C₅×#121	—	3	4	no	—
130	C₅×#121	—	3	8	no	—
131	C₅×#121	C₂×D₃	1	4	yes	—
132	C₅×#120	—	3	4	no	—
133	C₄×C₅×Q₈	—	3	4	no	—
134	C₄×C₅×Q₈	—	3	4	no	—
135	C₄×C₅×D₄	—	3	8	no	—
136	C₄×C₅×D₄	—	3	4	no	—
137	C₄×C₅×D₄	—	3	8	no	—
138	C₄×C₅×D₄	C₂×D₃	1	4	yes	complemented
139	C₅×#117	—	3	2	no	—
140	C₅×#117	—	3	4	no	—
141	C₅×#117	—	3	4	no	—
142	C₅×#117	—	3	2	no	—
143	C₅×#117	—	3	2	no	—
144	C₂×C₅×C₄⋊C₄	—	3	2	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
146	C₂×C₄²×C₅	—	3	1	no	—
147	C₂×C₄²×C₅	—	3	4	no	—
148	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
149	#3455	—	3	1	no	Sylow
150	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
151	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
152	C₂²×C₅×D₃	—	2	2	no	—
153	C₂²×C₅×D₃	—	4	2	no	—
154	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
155	C₃×C₅×Q₈	—	2	4	no	—
156	C₃×C₅×D₄	—	2	8	no	—
157	C₃×C₅×D₄	—	2	4	no	—
158	C₃×C₅×D₄	—	4	4	no	—
159	C₂×C₃×C₄×C₅	—	2	8	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	#41	1	4	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₅×#67	—	4	8	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	4	8	no	—
170	C₂×C₅×Dic₃	—	4	2	no	—
171	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
174	C₄×C₅×D₃	—	2	4	no	—
175	C₄×C₅×D₃	—	2	4	no	—
176	C₅×Dic₆	—	4	4	no	—
177	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
178	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
179	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₃×#124	C₂²×C₅	1	2	yes	complemented
182	C₃×#121	C₂²×C₅	1	4	yes	—
183	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
184	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
185	#946	C₂²×C₅	1	4	yes	—
186	Q₈×Dic₃	C₂²×C₅	1	4	yes	complemented
187	#939	C₂²×C₅	1	8	yes	—
188	#938	C₂²×C₅	1	4	yes	—
189	#937	C₂²×C₅	1	4	yes	—
190	#935	C₂²×C₅	1	4	yes	—
191	#935	C₂²×C₅	1	8	yes	complemented
192	D₄×Dic₃	C₂²×C₅	1	8	yes	—
193	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
194	C₄×#67	C₂²×C₅	1	8	yes	—
195	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
196	#926	C₂²×C₅	1	2	yes	—
197	#926	C₂²×C₅	1	4	yes	complemented
198	#924	C₂²×C₅	1	4	yes	—
199	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
202	#898	C₂²×C₅	1	8	yes	—
203	#889	C₂²×C₅	1	8	yes	complemented
204	#886	C₂²×C₅	1	8	yes	—
205	#885	C₂²×C₅	1	8	yes	—
206	#879	C₂²×C₅	1	8	yes	complemented
207	#878	C₂²×C₅	1	8	yes	complemented
208	#872	C₂²×C₅	1	2	yes	—
209	#872	C₂²×C₅	1	2	yes	—
210	#872	C₂²×C₅	1	4	yes	—
211	#870	C₂²×C₅	1	2	yes	complemented
212	#869	C₂²×C₅	1	2	yes	complemented
213	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
214	C₂⁴×C₅	—	3	1	no	—
215	C₅×#41	—	2	8	no	—
216	C₂×C₅×Q₈	—	3	4	no	—
217	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
218	C₂×C₅×D₄	—	3	8	no	—
219	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
220	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
221	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	2	no	—
224	C₂²×C₄×C₅	—	3	8	no	—
225	C₂²×C₄×C₅	—	3	2	no	—
226	C₂²×C₄×C₅	—	3	2	no	—
227	C₂²×C₄×C₅	—	6	4	no	—
228	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
229	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₅×C₄⋊C₄	—	3	4	no	—
232	C₅×C₄⋊C₄	—	3	4	no	—
233	C₅×C₄⋊C₄	—	3	4	no	—
234	C₅×C₄⋊C₄	—	3	8	no	—
235	C₅×C₄⋊C₄	—	3	8	no	—
236	C₅×C₄⋊C₄	—	3	8	no	—
237	C₅×C₄⋊C₄	—	3	4	no	—
238	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
239	C₅×C₂²⋊C₄	—	3	4	no	—
240	C₅×C₂²⋊C₄	—	3	8	no	—
241	C₅×C₂²⋊C₄	—	3	8	no	—
242	C₅×C₂²⋊C₄	—	3	4	no	—
243	C₅×C₂²⋊C₄	—	3	4	no	—
244	C₅×C₂²⋊C₄	—	3	8	no	—
245	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
246	C₄²×C₅	—	3	2	no	—
247	C₄²×C₅	—	3	8	no	—
248	C₄²×C₅	—	3	2	no	—
249	C₄²×C₅	—	3	4	no	—
250	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
251	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
252	C₄²×C₅	C₂²×D₃	1	2	yes	—
253	#542	—	3	4	no	—
254	#541	—	3	2	no	—
255	#540	—	3	2	no	—
256	#539	—	3	4	no	—
257	#538	—	3	4	no	—
258	#533	—	3	1	no	—
259	#532	C₅×D₃	1	1	yes	characteristic, complemented
260	#529	—	3	8	no	—
261	#525	—	3	2	no	—
262	C₄×#41	—	3	2	no	—
263	C₂×#117	—	3	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	2	8	no	—
267	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
268	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
269	C₂×C₅×D₃	—	2	2	no	—
270	C₂×C₅×D₃	—	2	4	no	—
271	C₂×C₅×D₃	—	4	4	no	—
272	C₃×C₄×C₅	—	2	4	no	—
273	C₃×C₄×C₅	—	2	2	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	C₂×#41	1	2	yes	—
276	C₃×C₄×C₅	C₂×#41	1	2	yes	—
277	C₅×Dic₃	—	2	2	no	—
278	C₅×Dic₃	—	2	8	no	—
279	C₅×Dic₃	—	2	4	no	—
280	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
281	C₃×#41	—	2	8	no	—
282	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
283	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
284	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
285	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
286	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
287	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
288	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂×#67	C₂³×C₅	1	8	yes	—
290	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
291	C₂²×Dic₃	C₂³×C₅	1	8	yes	—
292	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
293	C₂×C₄×D₃	—	2	4	no	—
294	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
295	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
296	C₂×Dic₆	C₂³×C₅	1	4	yes	—
297	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
298	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
299	C₃×C₄²	C₂³×C₅	1	2	yes	—
300	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
301	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
302	#217	C₂³×C₅	1	8	yes	—
303	#217	C₂³×C₅	1	8	yes	—
304	#217	C₂³×C₅	1	4	yes	—
305	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
306	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
307	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
308	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
309	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
310	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
311	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
312	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
313	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
314	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
315	C₄×Dic₃	C₂³×C₅	1	4	yes	—
316	C₄×Dic₃	C₂³×C₅	1	2	yes	—
317	C₄×Dic₃	C₂³×C₅	1	2	yes	—
318	C₄×Dic₃	C₂³×C₅	1	8	yes	—
319	C₂³×C₅	—	3	2	no	—
320	C₂³×C₅	—	6	2	no	—
321	C₂³×C₅	—	12	2	no	—
322	C₂³×C₅	C₂³×D₃	1	4	yes	—
323	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
324	C₅×Q₈	—	2	4	no	—
325	C₅×Q₈	—	12	4	no	—
326	C₅×D₄	—	2	8	no	—
327	C₅×D₄	—	2	4	no	—
328	C₅×D₄	—	4	4	no	—
329	C₅×D₄	—	12	8	no	—
330	C₂×C₄×C₅	—	2	8	no	—
331	C₂×C₄×C₅	—	3	4	no	—
332	C₂×C₄×C₅	—	3	8	no	—
333	C₂×C₄×C₅	—	3	2	no	—
334	C₂×C₄×C₅	—	4	2	no	—
335	C₂×C₄×C₅	—	6	2	no	—
336	C₂×C₄×C₅	—	6	4	no	—
337	C₂×C₄×C₅	—	6	4	no	—
338	C₂×C₄×C₅	—	12	2	no	—
339	C₂×C₄×C₅	—	12	8	no	—
340	C₂×C₄×C₅	#237	1	4	yes	—
341	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
342	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
343	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
344	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
346	C₂×#41	C₂×C₅×D₃	1	2	yes	—
347	C₂³×C₄	—	3	1	no	—
348	C₄⋊Q₈	—	3	2	no	—
349	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
350	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
351	#126	—	3	8	no	—
352	#126	—	3	8	no	—
353	#125	—	3	8	no	—
354	#125	—	3	2	no	—
355	#124	—	3	8	no	—
356	#124	C₂×C₅×D₃	1	2	yes	complemented
357	#123	—	3	4	no	—
358	#123	—	3	8	no	—
359	#123	—	3	8	no	—
360	C₂²⋊Q₈	—	3	4	no	—
361	C₂²⋊Q₈	—	3	4	no	—
362	C₂²⋊Q₈	—	3	8	no	—
363	#121	—	3	4	no	—
364	#121	—	3	8	no	—
365	#121	C₂×C₅×D₃	1	4	yes	—
366	#120	—	3	4	no	—
367	C₄×Q₈	—	3	4	no	—
368	C₄×Q₈	—	3	4	no	—
369	C₄×D₄	—	3	8	no	—
370	C₄×D₄	—	3	4	no	—
371	C₄×D₄	—	3	8	no	—
372	C₄×D₄	C₂×C₅×D₃	1	4	yes	complemented
373	#117	—	3	2	no	—
374	#117	—	3	4	no	—
375	#117	—	3	4	no	—
376	#117	—	3	2	no	—
377	#117	—	3	2	no	—
378	C₂×C₄⋊C₄	—	3	2	no	—
379	C₂×C₂²⋊C₄	—	3	2	no	—
380	C₂×C₄²	—	3	1	no	—
381	C₂×C₄²	—	3	4	no	—
382	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
383	C₂×C₃×C₅	—	2	2	no	—
384	C₂×C₃×C₅	—	4	4	no	—
385	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
386	C₂×C₃×C₅	#585	1	2	yes	—
387	C₅×D₃	—	4	2	no	—
388	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
389	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
390	C₂²×D₃	—	2	2	no	—
391	C₂²×D₃	—	4	2	no	—
392	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
393	C₃×Q₈	—	2	4	no	—
394	C₃×D₄	—	2	8	no	—
395	C₃×D₄	—	2	4	no	—
396	C₃×D₄	—	4	4	no	—
397	C₂×C₃×C₄	—	2	8	no	—
398	C₂×C₃×C₄	—	4	2	no	—
399	C₂×C₃×C₄	C₅×#41	1	4	yes	—
400	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
401	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
402	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
403	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
405	#67	—	4	8	no	—
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	—	4	8	no	—
408	C₂×Dic₃	—	4	2	no	—
409	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
410	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
411	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
412	C₄×D₃	—	2	4	no	—
413	C₄×D₃	—	2	4	no	—
414	Dic₆	—	4	4	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	4	no	—
417	C₂²×C₅	—	2	8	no	—
418	C₂²×C₅	—	6	2	no	—
419	C₂²×C₅	—	6	4	no	—
420	C₂²×C₅	—	12	4	no	—
421	C₂²×C₅	C₂×#237	1	2	yes	—
422	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
423	C₄×C₅	—	2	4	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	6	2	no	—
427	C₄×C₅	—	6	4	no	—
428	C₄×C₅	—	6	8	no	—
429	C₄×C₅	C₂×#237	1	2	yes	—
430	C₄×C₅	C₂×#237	1	2	yes	—
431	C₂⁴	—	3	1	no	—
432	#41	—	2	8	no	—
433	C₂×Q₈	—	3	4	no	—
434	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
435	C₂×D₄	—	3	8	no	—
436	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
437	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
438	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
439	C₂²×C₄	—	3	1	no	—
440	C₂²×C₄	—	3	2	no	—
441	C₂²×C₄	—	3	8	no	—
442	C₂²×C₄	—	3	2	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	6	4	no	—
445	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
446	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
447	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
448	C₄⋊C₄	—	3	4	no	—
449	C₄⋊C₄	—	3	4	no	—
450	C₄⋊C₄	—	3	4	no	—
451	C₄⋊C₄	—	3	8	no	—
452	C₄⋊C₄	—	3	8	no	—
453	C₄⋊C₄	—	3	8	no	—
454	C₄⋊C₄	—	3	4	no	—
455	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
456	C₂²⋊C₄	—	3	4	no	—
457	C₂²⋊C₄	—	3	8	no	—
458	C₂²⋊C₄	—	3	8	no	—
459	C₂²⋊C₄	—	3	4	no	—
460	C₂²⋊C₄	—	3	4	no	—
461	C₂²⋊C₄	—	3	8	no	—
462	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
463	C₄²	—	3	2	no	—
464	C₄²	—	3	2	no	—
465	C₄²	—	3	4	no	—
466	C₄²	—	3	8	no	—
467	C₄²	C₂²×C₅×D₃	1	2	yes	—
468	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	4	no	—
473	C₂²×C₃	—	2	8	no	—
474	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
475	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
476	C₂×D₃	—	2	2	no	—
477	C₂×D₃	—	2	4	no	—
478	C₂×D₃	—	4	4	no	—
479	C₃×C₄	—	2	4	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	C₂×C₅×#41	1	2	yes	—
483	C₃×C₄	C₂×C₅×#41	1	2	yes	—
484	Dic₃	—	2	2	no	—
485	Dic₃	—	2	8	no	—
486	Dic₃	—	2	4	no	—
487	C₂×C₅	—	2	2	no	—
488	C₂×C₅	—	4	4	no	—
489	C₂×C₅	—	12	2	no	—
490	C₂×C₅	C₂²×#237	1	1	yes	characteristic
491	C₂×C₅	#5964	1	2	yes	—
492	C₂³	—	3	2	no	—
493	C₂³	—	6	2	no	—
494	C₂³	—	12	2	no	—
495	C₂³	C₂³×C₅×D₃	1	4	yes	—
496	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
497	Q₈	—	2	4	no	—
498	Q₈	—	12	4	no	—
499	D₄	—	2	8	no	—
500	D₄	—	2	4	no	—
501	D₄	—	4	4	no	—
502	D₄	—	12	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	3	4	no	—
505	C₂×C₄	—	3	8	no	—
506	C₂×C₄	—	3	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	6	2	no	—
509	C₂×C₄	—	6	4	no	—
510	C₂×C₄	—	6	4	no	—
511	C₂×C₄	—	12	2	no	—
512	C₂×C₄	—	12	8	no	—
513	C₂×C₄	C₅×#237	1	4	yes	—
514	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
515	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
516	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
517	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
518	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
519	C₂×C₃	—	2	2	no	—
520	C₂×C₃	—	4	4	no	—
521	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
522	C₂×C₃	C₅×#585	1	2	yes	—
523	D₃	—	4	2	no	—
524	C₅	#86236	1	1	yes	characteristic, direct product factor, Sylow
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	8	no	—
528	C₂²	—	6	2	no	—
529	C₂²	—	6	4	no	—
530	C₂²	—	12	4	no	—
531	C₂²	C₂×C₅×#237	1	2	yes	—
532	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	6	2	no	—
537	C₄	—	6	4	no	—
538	C₄	—	6	8	no	—
539	C₄	C₂×C₅×#237	1	2	yes	—
540	C₄	C₂×C₅×#237	1	2	yes	—
541	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
542	C₂	—	2	2	no	—
543	C₂	—	4	4	no	—
544	C₂	—	12	2	no	—
545	C₂	C₂²×C₅×#237	1	1	yes	characteristic
546	C₂	C₅×#5964	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#3455
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₅×#5828	C₂	semidirect
3. C₅×Dic₃×#41	C₂	semidirect
4. C₅×#5731	C₂	semidirect
5. C₅×#5719	C₂	semidirect
6. C₅×#5682	C₂	semidirect
7. C₅×#5617	C₂	semidirect
8. C₅×#5602	C₂	semidirect
9. C₅×#5538	C₂	semidirect
10. C₂×C₅×#872	C₂	semidirect
11. C₅×#5470	C₂	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
16. C₃×C₅×#127	C₂²	semidirect
17. C₃×C₅×#124	C₂²	semidirect
19. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₅×Q₈×Dic₃	C₂²	semidirect
27. C₅×#935	C₂²	semidirect
29. C₅×D₄×Dic₃	C₂²	semidirect
33. C₅×#926	C₂²	semidirect
37. C₂×C₄×C₅×Dic₃	C₂²	semidirect
39. C₅×#889	C₂²	semidirect
42. C₅×#879	C₂²	semidirect
43. C₅×#878	C₂²	semidirect
47. C₅×#870	C₂²	semidirect
48. C₅×#869	C₂²	semidirect
49. C₄×C₅×Dic₆	C₂²	semidirect
50. #86236	C₅	direct (N × H)
57. C₅×#532	D₃	semidirect
101. C₃×#532	C₂×C₅	semidirect
102. #5828	C₂×C₅	semidirect
103. Dic₃×#41	C₂×C₅	semidirect
104. #5731	C₂×C₅	semidirect
105. #5719	C₂×C₅	semidirect
106. #5682	C₂×C₅	semidirect
107. #5617	C₂×C₅	semidirect
108. #5602	C₂×C₅	semidirect
109. #5538	C₂×C₅	semidirect
110. C₂×#872	C₂×C₅	semidirect
111. #5470	C₂×C₅	semidirect
115. C₅×C₄⋊Q₈	C₂×D₃	semidirect
116. C₅×#127	C₂×D₃	semidirect
122. C₅×#124	C₂×D₃	semidirect
138. C₄×C₅×D₄	C₂×D₃	semidirect
179. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
180. C₃×#127	C₂²×C₅	semidirect
181. C₃×#124	C₂²×C₅	semidirect
183. C₃×C₄×D₄	C₂²×C₅	semidirect
186. Q₈×Dic₃	C₂²×C₅	semidirect
191. #935	C₂²×C₅	semidirect
193. D₄×Dic₃	C₂²×C₅	semidirect
197. #926	C₂²×C₅	semidirect
201. C₂×C₄×Dic₃	C₂²×C₅	semidirect
203. #889	C₂²×C₅	semidirect
206. #879	C₂²×C₅	semidirect
207. #878	C₂²×C₅	semidirect
211. #870	C₂²×C₅	semidirect
212. #869	C₂²×C₅	semidirect
213. C₄×Dic₆	C₂²×C₅	semidirect
259. #532	C₅×D₃	semidirect
349. C₄⋊Q₈	C₂×C₅×D₃	semidirect
350. #127	C₂×C₅×D₃	semidirect
356. #124	C₂×C₅×D₃	semidirect
372. C₄×D₄	C₂×C₅×D₃	semidirect
470. C₃×C₅	#3455	semidirect
524. C₅	#86236	direct (N × H)
541. C₃	C₅×#3455	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₅×#5828	2
C₅×Dic₃×#41	2
C₅×#5731	2
C₅×#5719	2
C₅×#5682	2
C₅×#5617	2
C₅×#5602	2
C₅×#5538	2
C₂×C₅×#872	2
C₅×#5470	2
C₅×#3455	3
#86236	5

Subgroups — C5×#86236 #14481514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86236 #14481514