Subgroups — C₅×D₃×#562 #14495272

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5700	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5684	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#124	C₂	1	2	yes	maximal, complemented
6	C₅×#5667	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#123	C₂	1	4	yes	maximal, complemented
8	C₅×#5647	C₂	1	4	yes	maximal, complemented
9	C₅×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
10	C₅×#5621	C₂	1	4	yes	maximal, complemented
11	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
12	C₂×C₅×#562	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
15	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#124	C₂²	1	2	yes	complemented
19	C₃×C₅×#123	C₂²	1	4	yes	complemented
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
21	C₃×C₅×#121	C₂²	1	4	yes	complemented
22	C₅×#947	C₂²	1	2	yes	complemented
23	C₅×#946	C₂²	1	4	yes	complemented
24	C₅×#939	C₂²	1	4	yes	complemented
25	C₅×#939	C₂²	1	4	yes	complemented
26	C₅×#938	C₂²	1	4	yes	complemented
27	C₅×#936	C₂²	1	2	yes	complemented
28	C₅×#935	C₂²	1	4	yes	complemented
29	C₅×#930	C₂²	1	4	yes	complemented
30	C₅×#929	C₂²	1	4	yes	complemented
31	C₅×#924	C₂²	1	4	yes	complemented
32	C₅×#897	C₂²	1	4	yes	complemented
33	C₅×#896	C₂²	1	4	yes	complemented
34	C₅×#896	C₂²	1	4	yes	complemented
35	C₅×#895	C₂²	1	4	yes	complemented
36	C₅×#894	C₂²	1	4	yes	complemented
37	C₅×#894	C₂²	1	4	yes	complemented
38	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
40	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
41	C₅×#890	C₂²	1	2	yes	complemented
42	C₅×#889	C₂²	1	4	yes	complemented
43	C₅×#886	C₂²	1	4	yes	complemented
44	C₅×#885	C₂²	1	4	yes	complemented
45	C₅×#885	C₂²	1	4	yes	complemented
46	C₅×#884	C₂²	1	4	yes	complemented
47	C₅×#884	C₂²	1	4	yes	complemented
48	C₅×#883	C₂²	1	4	yes	complemented
49	C₅×#883	C₂²	1	4	yes	complemented
50	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
51	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₅×#878	C₂²	1	4	yes	complemented
54	C₅×#878	C₂²	1	4	yes	complemented
55	C₅×#875	C₂²	1	2	yes	complemented
56	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
57	C₅×#870	C₂²	1	1	yes	characteristic, complemented
58	D₃×#562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
59	C₅×#562	—	3	1	no	—
60	C₅×#562	—	3	2	no	—
61	C₅×#562	—	3	4	no	—
62	C₅×#562	—	3	4	no	—
63	C₅×#562	—	3	4	no	—
64	C₅×#562	D₃	1	1	yes	characteristic, direct product factor
65	C₂×C₅×#125	—	3	1	no	—
66	C₂×C₅×#124	—	3	2	no	—
67	C₂×C₅×#123	—	3	4	no	—
68	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
69	C₂×C₅×#121	—	3	4	no	—
70	C₂³×C₅×D₃	C₂³	1	4	yes	—
71	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
73	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
75	C₂×C₅×#67	C₂³	1	4	yes	—
76	C₂×C₅×#67	C₂³	1	4	yes	—
77	C₂×C₅×#67	C₂³	1	4	yes	—
78	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
79	C₅×D₃×Q₈	—	4	4	no	—
80	C₅×D₃×D₄	—	4	8	no	—
81	C₅×D₃×D₄	—	4	4	no	—
82	C₂×C₅×D₁₂	C₂³	1	2	yes	—
83	C₂×C₅×D₁₂	C₂³	1	4	yes	—
84	C₂×C₄×C₅×D₃	—	4	8	no	—
85	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
87	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
88	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
89	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
90	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
91	C₂×C₅×Dic₆	C₂³	1	2	yes	—
92	C₂×C₅×Dic₆	C₂³	1	4	yes	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#217	C₂³	1	4	yes	—
101	C₅×#217	C₂³	1	4	yes	—
102	C₅×#217	C₂³	1	4	yes	—
103	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
104	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
105	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
106	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
107	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
108	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
109	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
110	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
111	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
112	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
113	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
114	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
115	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
116	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
117	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
118	C₄×C₅×Dic₃	C₂³	1	2	yes	—
119	C₃×#562	C₂×C₅	1	1	yes	characteristic, complemented
120	#5700	C₂×C₅	1	1	yes	characteristic, complemented
121	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
122	#5684	C₂×C₅	1	2	yes	complemented
123	D₃×#124	C₂×C₅	1	2	yes	complemented
124	#5667	C₂×C₅	1	4	yes	complemented
125	D₃×#123	C₂×C₅	1	4	yes	complemented
126	#5647	C₂×C₅	1	4	yes	complemented
127	D₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
128	#5621	C₂×C₅	1	4	yes	complemented
129	D₃×#121	C₂×C₅	1	4	yes	complemented
130	C₂²×C₅×Q₈	—	3	2	no	—
131	C₂²×C₅×D₄	—	3	4	no	—
132	C₂²×C₅×D₄	—	3	2	no	—
133	C₂³×C₄×C₅	—	3	4	no	—
134	C₅×#125	—	3	4	no	—
135	C₅×#125	—	3	2	no	—
136	C₅×#125	—	3	1	no	—
137	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
138	C₅×#124	—	3	2	no	—
139	C₅×#124	—	3	2	no	—
140	C₅×#124	—	3	4	no	—
141	C₅×#124	—	3	4	no	—
142	C₅×#124	—	3	2	no	—
143	C₅×#124	C₂×D₃	1	2	yes	complemented
144	C₅×#123	—	3	4	no	—
145	C₅×#123	—	3	4	no	—
146	C₅×#123	—	3	4	no	—
147	C₅×#123	—	3	4	no	—
148	C₅×#123	—	3	4	no	—
149	C₅×#123	—	3	4	no	—
150	C₅×#123	—	3	4	no	—
151	C₅×#123	C₂×D₃	1	4	yes	complemented
152	C₅×C₂²⋊Q₈	—	3	4	no	—
153	C₅×C₂²⋊Q₈	—	3	4	no	—
154	C₅×C₂²⋊Q₈	—	3	4	no	—
155	C₅×C₂²⋊Q₈	—	3	4	no	—
156	C₅×C₂²⋊Q₈	—	3	4	no	—
157	C₅×C₂²⋊Q₈	—	3	4	no	—
158	C₅×C₂²⋊Q₈	—	3	4	no	—
159	C₅×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
160	C₅×#121	—	3	4	no	—
161	C₅×#121	—	3	4	no	—
162	C₅×#121	—	3	4	no	—
163	C₅×#121	—	3	4	no	—
164	C₅×#121	—	3	4	no	—
165	C₅×#121	—	3	4	no	—
166	C₅×#121	—	3	4	no	—
167	C₅×#121	C₂×D₃	1	4	yes	complemented
168	C₂×C₅×C₄⋊C₄	—	3	4	no	—
169	C₂×C₅×C₄⋊C₄	—	3	4	no	—
170	C₂×C₅×C₄⋊C₄	—	3	2	no	—
171	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
172	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
173	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
174	C₂×C₄²×C₅	—	3	1	no	—
175	C₂×#562	—	3	1	no	Sylow
176	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
177	C₂²×C₅×D₃	—	2	8	no	—
178	C₂²×C₅×D₃	—	2	8	no	—
179	C₂²×C₅×D₃	—	2	8	no	—
180	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
181	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
182	C₃×C₅×Q₈	—	4	2	no	—
183	C₃×C₅×D₄	—	4	2	no	—
184	C₃×C₅×D₄	—	4	4	no	—
185	C₂×C₃×C₄×C₅	—	4	4	no	—
186	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
187	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
189	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
190	C₅×#67	—	4	4	no	—
191	C₅×#67	—	4	4	no	—
192	C₅×#67	—	4	4	no	—
193	C₂×C₅×Dic₃	—	4	4	no	—
194	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
196	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
197	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
198	C₅×D₁₂	—	4	2	no	—
199	C₅×D₁₂	—	4	4	no	—
200	C₄×C₅×D₃	—	2	8	no	—
201	C₄×C₅×D₃	—	2	8	no	—
202	C₄×C₅×D₃	—	2	4	no	—
203	C₄×C₅×D₃	—	2	2	no	—
204	C₄×C₅×D₃	—	4	4	no	—
205	C₄×C₅×D₃	—	4	4	no	—
206	C₅×Dic₆	—	4	2	no	—
207	C₅×Dic₆	—	4	4	no	—
208	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
209	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
210	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
211	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
212	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
213	C₃×#124	C₂²×C₅	1	2	yes	complemented
214	C₃×#123	C₂²×C₅	1	4	yes	complemented
215	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
216	C₃×#121	C₂²×C₅	1	4	yes	complemented
217	#947	C₂²×C₅	1	2	yes	complemented
218	#946	C₂²×C₅	1	4	yes	complemented
219	#939	C₂²×C₅	1	4	yes	complemented
220	#939	C₂²×C₅	1	4	yes	complemented
221	#938	C₂²×C₅	1	4	yes	complemented
222	#936	C₂²×C₅	1	2	yes	complemented
223	#935	C₂²×C₅	1	4	yes	complemented
224	#930	C₂²×C₅	1	4	yes	complemented
225	#929	C₂²×C₅	1	4	yes	complemented
226	#924	C₂²×C₅	1	4	yes	complemented
227	#897	C₂²×C₅	1	4	yes	complemented
228	#896	C₂²×C₅	1	4	yes	complemented
229	#896	C₂²×C₅	1	4	yes	complemented
230	#895	C₂²×C₅	1	4	yes	complemented
231	#894	C₂²×C₅	1	4	yes	complemented
232	#894	C₂²×C₅	1	4	yes	complemented
233	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
234	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
235	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
236	#890	C₂²×C₅	1	2	yes	complemented
237	#889	C₂²×C₅	1	4	yes	complemented
238	#886	C₂²×C₅	1	4	yes	complemented
239	#885	C₂²×C₅	1	4	yes	complemented
240	#885	C₂²×C₅	1	4	yes	complemented
241	#884	C₂²×C₅	1	4	yes	complemented
242	#884	C₂²×C₅	1	4	yes	complemented
243	#883	C₂²×C₅	1	4	yes	complemented
244	#883	C₂²×C₅	1	4	yes	complemented
245	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
246	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
247	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
248	#878	C₂²×C₅	1	4	yes	complemented
249	#878	C₂²×C₅	1	4	yes	complemented
250	#875	C₂²×C₅	1	2	yes	complemented
251	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
252	#870	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂⁴×C₅	—	3	4	no	—
254	C₂×C₅×Q₈	—	3	4	no	—
255	C₂×C₅×Q₈	—	3	2	no	—
256	C₂×C₅×Q₈	—	12	4	no	—
257	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
258	C₂×C₅×D₄	—	3	4	no	—
259	C₂×C₅×D₄	—	3	4	no	—
260	C₂×C₅×D₄	—	3	4	no	—
261	C₂×C₅×D₄	—	3	4	no	—
262	C₂×C₅×D₄	—	3	2	no	—
263	C₂×C₅×D₄	—	12	8	no	—
264	C₂×C₅×D₄	—	12	4	no	—
265	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
266	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
267	C₂²×C₄×C₅	—	3	4	no	—
268	C₂²×C₄×C₅	—	3	1	no	—
269	C₂²×C₄×C₅	—	3	2	no	—
270	C₂²×C₄×C₅	—	3	4	no	—
271	C₂²×C₄×C₅	—	3	4	no	—
272	C₂²×C₄×C₅	—	3	4	no	—
273	C₂²×C₄×C₅	—	3	4	no	—
274	C₂²×C₄×C₅	—	12	8	no	—
275	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
276	C₅×C₄⋊C₄	—	3	4	no	—
277	C₅×C₄⋊C₄	—	3	4	no	—
278	C₅×C₄⋊C₄	—	3	4	no	—
279	C₅×C₄⋊C₄	—	3	4	no	—
280	C₅×C₄⋊C₄	—	3	4	no	—
281	C₅×C₄⋊C₄	—	3	4	no	—
282	C₅×C₄⋊C₄	—	3	4	no	—
283	C₅×C₄⋊C₄	—	3	2	no	—
284	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
285	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
286	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
287	C₅×C₂²⋊C₄	—	3	4	no	—
288	C₅×C₂²⋊C₄	—	3	4	no	—
289	C₅×C₂²⋊C₄	—	3	4	no	—
290	C₅×C₂²⋊C₄	—	3	4	no	—
291	C₅×C₂²⋊C₄	—	3	4	no	—
292	C₅×C₂²⋊C₄	—	3	4	no	—
293	C₅×C₂²⋊C₄	—	3	4	no	—
294	C₅×C₂²⋊C₄	—	3	4	no	—
295	C₅×C₂²⋊C₄	—	3	4	no	—
296	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
297	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
298	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
299	C₄²×C₅	—	3	2	no	—
300	C₄²×C₅	—	3	1	no	—
301	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
302	#562	—	3	1	no	—
303	#562	—	3	2	no	—
304	#562	—	3	4	no	—
305	#562	—	3	4	no	—
306	#562	—	3	4	no	—
307	#562	C₅×D₃	1	1	yes	characteristic, direct product factor
308	C₂×#125	—	3	1	no	—
309	C₂×#124	—	3	2	no	—
310	C₂×#123	—	3	4	no	—
311	C₂×C₂²⋊Q₈	—	3	4	no	—
312	C₂×#121	—	3	4	no	—
313	C₂²×C₃×C₅	—	2	4	no	—
314	C₂²×C₃×C₅	—	2	4	no	—
315	C₂²×C₃×C₅	—	2	4	no	—
316	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
317	C₂×C₅×D₃	—	2	4	no	—
318	C₂×C₅×D₃	—	2	4	no	—
319	C₂×C₅×D₃	—	2	4	no	—
320	C₂×C₅×D₃	—	4	16	no	—
321	C₂×C₅×D₃	H(5,𝔽₂)	1	4	yes	—
322	C₂×C₅×D₃	2₋¹⁺⁴	1	2	yes	—
323	C₃×C₄×C₅	—	2	4	no	—
324	C₃×C₄×C₅	—	2	2	no	—
325	C₃×C₄×C₅	—	2	4	no	—
326	C₃×C₄×C₅	—	2	1	no	—
327	C₅×Dic₃	—	2	4	no	—
328	C₅×Dic₃	—	2	2	no	—
329	C₅×Dic₃	—	2	4	no	—
330	C₅×Dic₃	—	2	1	no	—
331	C₂³×D₃	C₂³×C₅	1	4	yes	—
332	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
333	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
334	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
335	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
336	C₂×#67	C₂³×C₅	1	4	yes	—
337	C₂×#67	C₂³×C₅	1	4	yes	—
338	C₂×#67	C₂³×C₅	1	4	yes	—
339	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
340	D₃×Q₈	—	4	4	no	—
341	D₃×D₄	—	4	8	no	—
342	D₃×D₄	—	4	4	no	—
343	C₂×D₁₂	C₂³×C₅	1	2	yes	—
344	C₂×D₁₂	C₂³×C₅	1	4	yes	—
345	C₂×C₄×D₃	—	4	8	no	—
346	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
348	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
349	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
350	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
351	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
352	C₂×Dic₆	C₂³×C₅	1	2	yes	—
353	C₂×Dic₆	C₂³×C₅	1	4	yes	—
354	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
355	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
356	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
357	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
358	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
359	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
360	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
361	#217	C₂³×C₅	1	4	yes	—
362	#217	C₂³×C₅	1	4	yes	—
363	#217	C₂³×C₅	1	4	yes	—
364	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
365	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
366	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
367	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
368	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
369	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
370	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
371	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
372	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
373	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
374	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
375	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
376	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
377	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
378	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₄×Dic₃	C₂³×C₅	1	2	yes	—
380	C₂³×C₅	—	3	1	no	—
381	C₂³×C₅	—	3	4	no	—
382	C₂³×C₅	—	6	8	no	—
383	C₂³×C₅	—	6	8	no	—
384	C₂³×C₅	—	6	8	no	—
385	C₂³×C₅	C₂³×D₃	1	4	yes	—
386	C₅×Q₈	—	4	2	no	—
387	C₅×Q₈	—	12	4	no	—
388	C₅×Q₈	—	12	2	no	—
389	C₅×D₄	—	4	4	no	—
390	C₅×D₄	—	4	2	no	—
391	C₅×D₄	—	12	4	no	—
392	C₅×D₄	—	12	2	no	—
393	C₅×D₄	—	12	4	no	—
394	C₅×D₄	—	12	4	no	—
395	C₅×D₄	—	12	4	no	—
396	C₂×C₄×C₅	—	3	1	no	—
397	C₂×C₄×C₅	—	3	2	no	—
398	C₂×C₄×C₅	—	3	4	no	—
399	C₂×C₄×C₅	—	3	4	no	—
400	C₂×C₄×C₅	—	4	4	no	—
401	C₂×C₄×C₅	—	6	2	no	—
402	C₂×C₄×C₅	—	6	8	no	—
403	C₂×C₄×C₅	—	6	8	no	—
404	C₂×C₄×C₅	—	6	4	no	—
405	C₂×C₄×C₅	—	12	4	no	—
406	C₂×C₄×C₅	—	12	4	no	—
407	C₂×C₄×C₅	—	12	4	no	—
408	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
409	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
410	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
411	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
412	C₂²×Q₈	—	3	2	no	—
413	C₂²×D₄	—	3	4	no	—
414	C₂²×D₄	—	3	2	no	—
415	C₂³×C₄	—	3	4	no	—
416	#125	—	3	4	no	—
417	#125	—	3	2	no	—
418	#125	—	3	1	no	—
419	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
420	#124	—	3	2	no	—
421	#124	—	3	2	no	—
422	#124	—	3	4	no	—
423	#124	—	3	4	no	—
424	#124	—	3	2	no	—
425	#124	C₂×C₅×D₃	1	2	yes	complemented
426	#123	—	3	4	no	—
427	#123	—	3	4	no	—
428	#123	—	3	4	no	—
429	#123	—	3	4	no	—
430	#123	—	3	4	no	—
431	#123	—	3	4	no	—
432	#123	—	3	4	no	—
433	#123	C₂×C₅×D₃	1	4	yes	complemented
434	C₂²⋊Q₈	—	3	4	no	—
435	C₂²⋊Q₈	—	3	4	no	—
436	C₂²⋊Q₈	—	3	4	no	—
437	C₂²⋊Q₈	—	3	4	no	—
438	C₂²⋊Q₈	—	3	4	no	—
439	C₂²⋊Q₈	—	3	4	no	—
440	C₂²⋊Q₈	—	3	4	no	—
441	C₂²⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
442	#121	—	3	4	no	—
443	#121	—	3	4	no	—
444	#121	—	3	4	no	—
445	#121	—	3	4	no	—
446	#121	—	3	4	no	—
447	#121	—	3	4	no	—
448	#121	—	3	4	no	—
449	#121	C₂×C₅×D₃	1	4	yes	complemented
450	C₂×C₄⋊C₄	—	3	4	no	—
451	C₂×C₄⋊C₄	—	3	4	no	—
452	C₂×C₄⋊C₄	—	3	2	no	—
453	C₂×C₂²⋊C₄	—	3	4	no	—
454	C₂×C₂²⋊C₄	—	3	4	no	—
455	C₂×C₂²⋊C₄	—	3	4	no	—
456	C₂×C₄²	—	3	1	no	—
457	C₂×C₃×C₅	—	4	4	no	—
458	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
459	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
460	C₅×D₃	—	4	4	no	—
461	C₅×D₃	#562	1	4	yes	direct product factor
462	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
463	C₂²×D₃	—	2	8	no	—
464	C₂²×D₃	—	2	8	no	—
465	C₂²×D₃	—	2	8	no	—
466	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
467	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
468	C₃×Q₈	—	4	2	no	—
469	C₃×D₄	—	4	2	no	—
470	C₃×D₄	—	4	4	no	—
471	C₂×C₃×C₄	—	4	4	no	—
472	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
473	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
474	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
475	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
476	#67	—	4	4	no	—
477	#67	—	4	4	no	—
478	#67	—	4	4	no	—
479	C₂×Dic₃	—	4	4	no	—
480	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
481	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
482	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
483	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
484	D₁₂	—	4	2	no	—
485	D₁₂	—	4	4	no	—
486	C₄×D₃	—	2	8	no	—
487	C₄×D₃	—	2	8	no	—
488	C₄×D₃	—	2	4	no	—
489	C₄×D₃	—	2	2	no	—
490	C₄×D₃	—	4	4	no	—
491	C₄×D₃	—	4	4	no	—
492	Dic₆	—	4	2	no	—
493	Dic₆	—	4	4	no	—
494	C₂²×C₅	—	2	4	no	—
495	C₂²×C₅	—	2	4	no	—
496	C₂²×C₅	—	2	4	no	—
497	C₂²×C₅	—	3	4	no	—
498	C₂²×C₅	—	3	2	no	—
499	C₂²×C₅	—	6	4	no	—
500	C₂²×C₅	—	6	4	no	—
501	C₂²×C₅	—	6	4	no	—
502	C₂²×C₅	—	12	16	no	—
503	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
504	C₄×C₅	—	2	4	no	—
505	C₄×C₅	—	2	4	no	—
506	C₄×C₅	—	2	2	no	—
507	C₄×C₅	—	2	1	no	—
508	C₄×C₅	—	6	4	no	—
509	C₄×C₅	—	6	4	no	—
510	C₄×C₅	—	6	2	no	—
511	C₄×C₅	—	6	1	no	—
512	C₂⁴	—	3	4	no	—
513	C₂×Q₈	—	3	4	no	—
514	C₂×Q₈	—	3	2	no	—
515	C₂×Q₈	—	12	4	no	—
516	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
517	C₂×D₄	—	3	4	no	—
518	C₂×D₄	—	3	4	no	—
519	C₂×D₄	—	3	4	no	—
520	C₂×D₄	—	3	4	no	—
521	C₂×D₄	—	3	2	no	—
522	C₂×D₄	—	12	8	no	—
523	C₂×D₄	—	12	4	no	—
524	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
525	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
526	C₂²×C₄	—	3	4	no	—
527	C₂²×C₄	—	3	1	no	—
528	C₂²×C₄	—	3	2	no	—
529	C₂²×C₄	—	3	4	no	—
530	C₂²×C₄	—	3	4	no	—
531	C₂²×C₄	—	3	4	no	—
532	C₂²×C₄	—	3	4	no	—
533	C₂²×C₄	—	12	8	no	—
534	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
535	C₄⋊C₄	—	3	4	no	—
536	C₄⋊C₄	—	3	4	no	—
537	C₄⋊C₄	—	3	4	no	—
538	C₄⋊C₄	—	3	4	no	—
539	C₄⋊C₄	—	3	4	no	—
540	C₄⋊C₄	—	3	4	no	—
541	C₄⋊C₄	—	3	4	no	—
542	C₄⋊C₄	—	3	2	no	—
543	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
544	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
545	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
546	C₂²⋊C₄	—	3	4	no	—
547	C₂²⋊C₄	—	3	4	no	—
548	C₂²⋊C₄	—	3	4	no	—
549	C₂²⋊C₄	—	3	4	no	—
550	C₂²⋊C₄	—	3	4	no	—
551	C₂²⋊C₄	—	3	4	no	—
552	C₂²⋊C₄	—	3	4	no	—
553	C₂²⋊C₄	—	3	4	no	—
554	C₂²⋊C₄	—	3	4	no	—
555	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
556	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
557	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
558	C₄²	—	3	2	no	—
559	C₄²	—	3	1	no	—
560	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
561	C₃×C₅	C₂×#562	1	1	yes	characteristic, complemented, Hall
562	C₂²×C₃	—	2	4	no	—
563	C₂²×C₃	—	2	4	no	—
564	C₂²×C₃	—	2	4	no	—
565	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
566	C₂×D₃	—	2	4	no	—
567	C₂×D₃	—	2	4	no	—
568	C₂×D₃	—	2	4	no	—
569	C₂×D₃	—	4	16	no	—
570	C₂×D₃	C₅×H(5,𝔽₂)	1	4	yes	—
571	C₂×D₃	C₅×2₋¹⁺⁴	1	2	yes	—
572	C₃×C₄	—	2	4	no	—
573	C₃×C₄	—	2	2	no	—
574	C₃×C₄	—	2	4	no	—
575	C₃×C₄	—	2	1	no	—
576	Dic₃	—	2	4	no	—
577	Dic₃	—	2	2	no	—
578	Dic₃	—	2	4	no	—
579	Dic₃	—	2	1	no	—
580	C₂×C₅	—	3	4	no	—
581	C₂×C₅	—	4	4	no	—
582	C₂×C₅	—	12	4	no	—
583	C₂×C₅	D₃×H(5,𝔽₂)	1	2	yes	—
584	C₂×C₅	D₃×2₋¹⁺⁴	1	1	yes	characteristic
585	C₂³	—	3	1	no	—
586	C₂³	—	3	4	no	—
587	C₂³	—	6	8	no	—
588	C₂³	—	6	8	no	—
589	C₂³	—	6	8	no	—
590	C₂³	C₂³×C₅×D₃	1	4	yes	—
591	Q₈	—	4	2	no	—
592	Q₈	—	12	4	no	—
593	Q₈	—	12	2	no	—
594	D₄	—	4	4	no	—
595	D₄	—	4	2	no	—
596	D₄	—	12	4	no	—
597	D₄	—	12	2	no	—
598	D₄	—	12	4	no	—
599	D₄	—	12	4	no	—
600	D₄	—	12	4	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	2	no	—
603	C₂×C₄	—	3	4	no	—
604	C₂×C₄	—	3	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	6	8	no	—
607	C₂×C₄	—	6	8	no	—
608	C₂×C₄	—	6	4	no	—
609	C₂×C₄	—	6	2	no	—
610	C₂×C₄	—	12	4	no	—
611	C₂×C₄	—	12	4	no	—
612	C₂×C₄	—	12	4	no	—
613	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
615	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
616	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
617	C₂×C₃	—	4	4	no	—
618	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
619	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
620	D₃	—	4	4	no	—
621	D₃	C₅×#562	1	4	yes	direct product factor
622	C₅	D₃×#562	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	3	4	no	—
627	C₂²	—	3	2	no	—
628	C₂²	—	6	4	no	—
629	C₂²	—	6	4	no	—
630	C₂²	—	6	4	no	—
631	C₂²	—	12	16	no	—
632	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
633	C₄	—	2	4	no	—
634	C₄	—	2	4	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	6	4	no	—
638	C₄	—	6	4	no	—
639	C₄	—	6	2	no	—
640	C₄	—	6	1	no	—
641	C₃	C₂×C₅×#562	1	1	yes	characteristic, complemented, Sylow
642	C₂	—	3	4	no	—
643	C₂	—	4	4	no	—
644	C₂	—	12	4	no	—
645	C₂	C₅×D₃×H(5,𝔽₂)	1	2	yes	—
646	C₂	C₅×D₃×2₋¹⁺⁴	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×#562	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#562	D₃
hypocenter	C₃	C₂×C₅×#562
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#562

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#562	C₂	semidirect
2. C₅×#5700	C₂	semidirect
3. C₅×D₃×#125	C₂	semidirect
4. C₅×#5684	C₂	semidirect
5. C₅×D₃×#124	C₂	semidirect
6. C₅×#5667	C₂	semidirect
7. C₅×D₃×#123	C₂	semidirect
8. C₅×#5647	C₂	semidirect
9. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₅×#5621	C₂	semidirect
11. C₅×D₃×#121	C₂	semidirect
17. C₃×C₅×#125	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
19. C₃×C₅×#123	C₂²	semidirect
20. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
21. C₃×C₅×#121	C₂²	semidirect
22. C₅×#947	C₂²	semidirect
23. C₅×#946	C₂²	semidirect
24. C₅×#939	C₂²	semidirect
25. C₅×#939	C₂²	semidirect
26. C₅×#938	C₂²	semidirect
27. C₅×#936	C₂²	semidirect
28. C₅×#935	C₂²	semidirect
29. C₅×#930	C₂²	semidirect
30. C₅×#929	C₂²	semidirect
31. C₅×#924	C₂²	semidirect
32. C₅×#897	C₂²	semidirect
33. C₅×#896	C₂²	semidirect
34. C₅×#896	C₂²	semidirect
35. C₅×#895	C₂²	semidirect
36. C₅×#894	C₂²	semidirect
37. C₅×#894	C₂²	semidirect
41. C₅×#890	C₂²	semidirect
42. C₅×#889	C₂²	semidirect
43. C₅×#886	C₂²	semidirect
44. C₅×#885	C₂²	semidirect
45. C₅×#885	C₂²	semidirect
46. C₅×#884	C₂²	semidirect
47. C₅×#884	C₂²	semidirect
48. C₅×#883	C₂²	semidirect
49. C₅×#883	C₂²	semidirect
53. C₅×#878	C₂²	semidirect
54. C₅×#878	C₂²	semidirect
55. C₅×#875	C₂²	semidirect
57. C₅×#870	C₂²	semidirect
58. D₃×#562	C₅	direct (N × H)
64. C₅×#562	D₃	direct (N × H)
119. C₃×#562	C₂×C₅	semidirect
120. #5700	C₂×C₅	semidirect
121. D₃×#125	C₂×C₅	semidirect
122. #5684	C₂×C₅	semidirect
123. D₃×#124	C₂×C₅	semidirect
124. #5667	C₂×C₅	semidirect
125. D₃×#123	C₂×C₅	semidirect
126. #5647	C₂×C₅	semidirect
127. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
128. #5621	C₂×C₅	semidirect
129. D₃×#121	C₂×C₅	semidirect
137. C₅×#125	C₂×D₃	semidirect
143. C₅×#124	C₂×D₃	semidirect
151. C₅×#123	C₂×D₃	semidirect
159. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
167. C₅×#121	C₂×D₃	semidirect
212. C₃×#125	C₂²×C₅	semidirect
213. C₃×#124	C₂²×C₅	semidirect
214. C₃×#123	C₂²×C₅	semidirect
215. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
216. C₃×#121	C₂²×C₅	semidirect
217. #947	C₂²×C₅	semidirect
218. #946	C₂²×C₅	semidirect
219. #939	C₂²×C₅	semidirect
220. #939	C₂²×C₅	semidirect
221. #938	C₂²×C₅	semidirect
222. #936	C₂²×C₅	semidirect
223. #935	C₂²×C₅	semidirect
224. #930	C₂²×C₅	semidirect
225. #929	C₂²×C₅	semidirect
226. #924	C₂²×C₅	semidirect
227. #897	C₂²×C₅	semidirect
228. #896	C₂²×C₅	semidirect
229. #896	C₂²×C₅	semidirect
230. #895	C₂²×C₅	semidirect
231. #894	C₂²×C₅	semidirect
232. #894	C₂²×C₅	semidirect
236. #890	C₂²×C₅	semidirect
237. #889	C₂²×C₅	semidirect
238. #886	C₂²×C₅	semidirect
239. #885	C₂²×C₅	semidirect
240. #885	C₂²×C₅	semidirect
241. #884	C₂²×C₅	semidirect
242. #884	C₂²×C₅	semidirect
243. #883	C₂²×C₅	semidirect
244. #883	C₂²×C₅	semidirect
248. #878	C₂²×C₅	semidirect
249. #878	C₂²×C₅	semidirect
250. #875	C₂²×C₅	semidirect
252. #870	C₂²×C₅	semidirect
307. #562	C₅×D₃	direct (N × H)
419. #125	C₂×C₅×D₃	semidirect
425. #124	C₂×C₅×D₃	semidirect
433. #123	C₂×C₅×D₃	semidirect
441. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
449. #121	C₂×C₅×D₃	semidirect
461. C₅×D₃	#562	direct (N × H)
561. C₃×C₅	C₂×#562	semidirect
621. D₃	C₅×#562	direct (N × H)
622. C₅	D₃×#562	direct (N × H)
641. C₃	C₂×C₅×#562	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#562	2
C₅×#5700	2
C₅×D₃×#125	2
C₅×#5684	2
C₅×D₃×#124	2
C₅×#5667	2
C₅×D₃×#123	2
C₅×#5647	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5621	2
C₅×D₃×#121	2
C₂×C₅×#562	3
D₃×#562	5

Subgroups — C5×D3×#562 #14495272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#562 #14495272