Subgroups — #14415450

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×#91837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6710	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751335	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91114	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751113	C₂	1	2	yes	maximal, complemented
7	#11751112	C₂	1	2	yes	maximal, complemented
8	#11751112	C₂	1	2	yes	maximal, complemented
9	D₄×C₃⋊#168	C₂	1	2	yes	maximal, complemented
10	#11751100	C₂	1	1	yes	maximal, characteristic, complemented
11	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614649	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#123	C₄	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₃×C₅×#121	C₄	1	1	yes	characteristic
19	C₃×C₅×#121	C₄	1	1	yes	characteristic
20	C₃×C₅×#120	C₄	1	2	yes	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	#91837	—	2	4	no	—
25	C₂×#6710	—	2	4	no	—
26	C₂×#6710	C₂²	1	1	yes	characteristic
27	C₂×#6710	C₂²	1	2	yes	—
28	C₂×#6710	C₂²	1	1	yes	characteristic
29	C₂×#6710	C₂²	1	2	yes	complemented
30	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
32	C₂²×C₃⋊#168	C₂²	1	2	yes	—
33	C₂²×C₃⋊#168	C₂²	1	2	yes	complemented
34	#91114	C₂²	1	1	yes	characteristic
35	#91114	C₂²	1	1	yes	characteristic
36	#91114	C₂²	1	1	yes	characteristic
37	#91114	C₂²	1	1	yes	characteristic
38	#91114	C₂²	1	2	yes	complemented
39	#91114	C₂²	1	2	yes	complemented
40	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
41	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
42	#91087	C₂²	1	2	yes	complemented
43	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
44	#82918	—	5	1	no	maximal, Hall
45	C₅×#525	D₃	1	1	yes	characteristic
46	C₂×#4094	—	3	1	no	—
47	C₂²×#681	—	3	1	no	—
48	#65523	—	3	1	no	—
49	C₂×C₂²⋊#168	—	3	1	no	—
50	#65301	—	3	2	no	—
51	#65300	—	3	2	no	—
52	#65300	—	3	2	no	—
53	D₄×#168	—	3	2	no	—
54	#65288	—	3	1	no	—
55	#65286	—	3	1	no	—
56	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
62	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₃×C₄²×C₅	C₂³	1	2	yes	—
83	#6710	—	2	2	no	—
84	#6710	—	2	4	no	—
85	#6710	—	2	4	no	—
86	#6710	D₄	1	4	yes	complemented
87	C₂×C₃⋊#168	—	2	2	no	—
88	C₂×C₃⋊#168	—	2	2	no	—
89	C₂×C₃⋊#168	—	2	4	no	—
90	C₂×C₃⋊#168	—	2	4	no	—
91	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
92	C₂×C₃⋊#168	C₂³	1	2	yes	—
93	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
94	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
95	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
96	C₂×C₃⋊#168	C₂³	1	2	yes	—
97	C₃×#525	D₅	1	1	yes	characteristic
98	C₂×#948	—	5	1	no	—
99	C₂²×#208	—	5	1	no	—
100	#5234	—	5	1	no	—
101	C₂×#830	—	5	1	no	—
102	#5012	—	5	2	no	—
103	#5011	—	5	2	no	—
104	#5011	—	5	2	no	—
105	D₄×C₃⋊C₈	—	5	2	no	—
106	#4999	—	5	1	no	—
107	#4997	—	5	1	no	—
108	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
110	C₅×#123	Dic₃	1	2	yes	—
111	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
112	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
113	C₅×#121	Dic₃	1	1	yes	characteristic
114	C₅×#121	Dic₃	1	1	yes	characteristic
115	C₅×#120	Dic₃	1	2	yes	—
116	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
117	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
118	C₅×#117	C₂×D₃	1	1	yes	characteristic
119	#4094	—	6	4	no	—
120	C₂×#681	—	3	1	no	—
121	C₂×#681	—	3	1	no	—
122	C₂×#681	—	3	2	no	—
123	C₂×#681	—	3	2	no	—
124	C₂×#681	—	6	4	no	—
125	C₂²×#168	—	3	1	no	—
126	C₂²×#168	—	3	1	no	—
127	C₂²×#168	—	3	2	no	—
128	C₂²×#168	—	3	2	no	—
129	C₂²⋊#168	—	3	1	no	—
130	C₂²⋊#168	—	3	2	no	—
131	C₂²⋊#168	—	3	1	no	—
132	C₂²⋊#168	—	3	1	no	—
133	C₂²⋊#168	—	3	2	no	—
134	C₂²⋊#168	—	3	1	no	—
135	C₄⋊#168	—	3	2	no	—
136	C₄⋊#168	—	3	2	no	—
137	#3935	—	3	2	no	—
138	C₄×#168	—	3	2	no	—
139	#2933	—	15	1	no	Sylow
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	4	1	no	—
143	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
145	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×D₄	—	2	4	no	—
149	C₃×C₅×D₄	—	2	4	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	1	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
168	C₂×C₃×C₄×C₅	#41	1	2	yes	—
169	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₃⋊#168	—	2	1	no	—
171	C₃⋊#168	—	2	1	no	—
172	C₃⋊#168	—	2	2	no	—
173	C₃⋊#168	—	2	1	no	—
174	C₃⋊#168	—	2	1	no	—
175	C₃⋊#168	C₂×D₄	1	4	yes	—
176	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
178	C₃×#123	Dic₅	1	2	yes	—
179	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
180	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
181	C₃×#121	Dic₅	1	1	yes	characteristic
182	C₃×#121	Dic₅	1	1	yes	characteristic
183	C₃×#120	Dic₅	1	2	yes	—
184	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
185	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
186	C₃×#117	C₂×D₅	1	1	yes	characteristic
187	#948	—	10	4	no	—
188	C₂×#208	—	5	1	no	—
189	C₂×#208	—	5	1	no	—
190	C₂×#208	—	5	2	no	—
191	C₂×#208	—	5	2	no	—
192	C₂×#208	—	10	4	no	—
193	C₂²×C₃⋊C₈	—	5	1	no	—
194	C₂²×C₃⋊C₈	—	5	1	no	—
195	C₂²×C₃⋊C₈	—	5	2	no	—
196	C₂²×C₃⋊C₈	—	5	2	no	—
197	#830	—	5	1	no	—
198	#830	—	5	1	no	—
199	#830	—	5	1	no	—
200	#830	—	5	1	no	—
201	#830	—	5	2	no	—
202	#830	—	5	2	no	—
203	C₄⋊(C₃⋊C₈)	—	5	2	no	—
204	C₄⋊(C₃⋊C₈)	—	5	2	no	—
205	#803	—	5	2	no	—
206	C₄×C₃⋊C₈	—	5	2	no	—
207	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
208	C₅×#41	—	2	2	no	—
209	C₅×#41	—	2	2	no	—
210	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
211	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
212	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
213	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
214	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	2	no	—
217	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
225	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
227	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
228	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
229	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
230	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
231	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
232	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
233	C₄²×C₅	C₂²×D₃	1	2	yes	—
234	#681	—	3	4	no	—
235	#681	—	6	4	no	—
236	#681	—	6	4	no	—
237	#681	—	6	2	no	—
238	C₂×#168	—	3	2	no	—
239	C₂×#168	—	3	1	no	—
240	C₂×#168	—	3	1	no	—
241	C₂×#168	—	3	1	no	—
242	C₂×#168	—	3	2	no	—
243	C₂×#168	—	3	1	no	—
244	C₂×#168	—	6	4	no	—
245	C₂×#168	—	6	4	no	—
246	C₂×#168	—	6	2	no	—
247	C₂×#168	—	6	2	no	—
248	C₂×#131	—	15	1	no	—
249	C₂²×M₁₆	—	15	1	no	—
250	#525	D₁₅	1	1	yes	characteristic
251	#436	—	15	2	no	—
252	#435	—	15	2	no	—
253	#435	—	15	2	no	—
254	C₈×D₄	—	15	2	no	—
255	#424	—	15	1	no	—
256	#408	—	15	1	no	—
257	C₂×C₂²⋊C₈	—	15	1	no	—
258	#405	—	15	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	1	no	—
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	4	no	—
270	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
271	C₂²×C₃×C₅	#131	1	2	yes	complemented
272	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	1	no	—
275	C₃×C₄×C₅	—	2	2	no	—
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
279	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
282	C₃×#41	—	2	2	no	—
283	C₃×#41	—	2	2	no	—
284	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
285	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
286	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
287	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
288	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
299	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
300	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
301	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
302	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
303	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
304	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
305	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
306	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
307	C₃×C₄²	C₂²×D₅	1	2	yes	—
308	#208	—	5	4	no	—
309	#208	—	10	4	no	—
310	#208	—	10	4	no	—
311	#208	—	10	2	no	—
312	C₂×C₃⋊C₈	—	5	2	no	—
313	C₂×C₃⋊C₈	—	5	1	no	—
314	C₂×C₃⋊C₈	—	5	1	no	—
315	C₂×C₃⋊C₈	—	5	1	no	—
316	C₂×C₃⋊C₈	—	5	2	no	—
317	C₂×C₃⋊C₈	—	5	1	no	—
318	C₂×C₃⋊C₈	—	10	4	no	—
319	C₂×C₃⋊C₈	—	10	4	no	—
320	C₂×C₃⋊C₈	—	10	2	no	—
321	C₂×C₃⋊C₈	—	10	2	no	—
322	C₂³×C₅	—	2	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	4	1	no	—
325	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
326	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
327	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
328	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
329	C₅×Q₈	—	2	2	no	—
330	C₅×D₄	—	2	4	no	—
331	C₅×D₄	—	2	4	no	—
332	C₅×D₄	—	2	2	no	—
333	C₅×D₄	—	4	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
344	C₂×C₄×C₅	#237	1	2	yes	—
345	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
346	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
347	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
350	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
352	#168	—	3	4	no	—
353	#168	—	6	1	no	—
354	#168	—	6	2	no	—
355	#168	—	6	1	no	—
356	#168	—	6	1	no	—
357	#168	—	6	1	no	—
358	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
359	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
360	#131	—	30	4	no	—
361	C₂×M₁₆	—	15	1	no	—
362	C₂×M₁₆	—	15	1	no	—
363	C₂×M₁₆	—	15	2	no	—
364	C₂×M₁₆	—	15	2	no	—
365	C₂×M₁₆	—	30	4	no	—
366	C₂²×C₈	—	15	2	no	—
367	C₂²×C₈	—	15	1	no	—
368	C₂²×C₈	—	15	2	no	—
369	C₂²×C₈	—	15	1	no	—
370	#123	Dic₁₅	1	2	yes	—
371	C₂²⋊Q₈	Dic₁₅	1	1	yes	characteristic
372	C₂²⋊Q₈	Dic₁₅	1	1	yes	characteristic
373	#121	Dic₁₅	1	1	yes	characteristic
374	#121	Dic₁₅	1	1	yes	characteristic
375	#120	Dic₁₅	1	2	yes	—
376	C₄×D₄	C₂×D₁₅	1	2	yes	—
377	C₄×D₄	C₂×D₁₅	1	2	yes	—
378	#117	C₂×D₁₅	1	1	yes	characteristic
379	C₄⋊C₈	—	15	2	no	—
380	C₄⋊C₈	—	15	2	no	—
381	C₂²⋊C₈	—	15	1	no	—
382	C₂²⋊C₈	—	15	1	no	—
383	C₂²⋊C₈	—	15	1	no	—
384	C₂²⋊C₈	—	15	1	no	—
385	C₂²⋊C₈	—	15	2	no	—
386	C₂²⋊C₈	—	15	2	no	—
387	#97	—	15	2	no	—
388	C₄×C₈	—	15	2	no	—
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	—	2	2	no	—
391	C₂×C₃×C₅	—	4	2	no	—
392	C₂×C₃×C₅	—	4	1	no	—
393	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
394	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
395	C₂×C₃×C₅	#568	1	1	yes	characteristic
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	—	4	1	no	—
399	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
400	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
401	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
402	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
403	C₃×Q₈	—	2	2	no	—
404	C₃×D₄	—	2	4	no	—
405	C₃×D₄	—	2	4	no	—
406	C₃×D₄	—	2	2	no	—
407	C₃×D₄	—	4	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
418	C₂×C₃×C₄	#711	1	2	yes	—
419	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
420	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
421	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
424	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
426	C₃⋊C₈	—	5	4	no	—
427	C₃⋊C₈	—	10	1	no	—
428	C₃⋊C₈	—	10	2	no	—
429	C₃⋊C₈	—	10	1	no	—
430	C₃⋊C₈	—	10	1	no	—
431	C₃⋊C₈	—	10	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	1	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	2	1	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	4	4	no	—
443	C₂²×C₅	D₄×Dic₃	1	2	yes	—
444	C₂²×C₅	#948	1	2	yes	complemented
445	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	D₄×Dic₃	1	2	yes	—
452	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
453	C₄×C₅	C₂×#237	1	1	yes	characteristic
454	C₂⁴	C₂×Dic₁₅	1	1	yes	characteristic
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	C₂×Q₈	C₂×Dic₁₅	1	1	yes	characteristic
458	C₂×D₄	C₂×Dic₁₅	1	2	yes	—
459	C₂×D₄	C₂×Dic₁₅	1	2	yes	—
460	C₂×D₄	C₂×Dic₁₅	1	1	yes	characteristic
461	C₂×D₄	C₂×Dic₁₅	1	2	yes	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	C₂×Dic₁₅	1	1	yes	characteristic
465	C₂²×C₄	C₂×Dic₁₅	1	1	yes	characteristic
466	C₂²×C₄	C₂×Dic₁₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
469	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
470	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
471	M₁₆	—	15	4	no	—
472	M₁₆	—	30	4	no	—
473	M₁₆	—	30	4	no	—
474	M₁₆	—	30	2	no	—
475	C₂×C₈	—	15	2	no	—
476	C₂×C₈	—	15	1	no	—
477	C₂×C₈	—	15	1	no	—
478	C₂×C₈	—	15	1	no	—
479	C₂×C₈	—	15	1	no	—
480	C₂×C₈	—	15	2	no	—
481	C₂×C₈	—	30	4	no	—
482	C₂×C₈	—	30	4	no	—
483	C₂×C₈	—	30	2	no	—
484	C₂×C₈	—	30	2	no	—
485	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
486	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
487	C₄⋊C₄	C₂×Dic₁₅	1	2	yes	—
488	C₄⋊C₄	C₂×Dic₁₅	1	2	yes	—
489	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
490	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
491	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
492	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
493	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
494	C₄²	C₂²×D₁₅	1	2	yes	—
495	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	4	4	no	—
507	C₂²×C₃	D₄×Dic₅	1	2	yes	—
508	C₂²×C₃	#4094	1	2	yes	complemented
509	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	D₄×Dic₅	1	2	yes	—
516	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
517	C₃×C₄	C₂×#711	1	1	yes	characteristic
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	2	2	no	—
520	C₂×C₅	—	4	1	no	—
521	C₂×C₅	—	4	2	no	—
522	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
523	C₂×C₅	C₂×#948	1	1	yes	characteristic
524	C₂×C₅	#5819	1	1	yes	characteristic
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
529	C₂³	C₂²×Dic₁₅	1	2	yes	—
530	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
531	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	4	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	D₄×D₁₅	1	2	yes	—
547	C₂×C₄	#6819	1	2	yes	—
548	C₂×C₄	C₂²×Dic₁₅	1	2	yes	—
549	C₂×C₄	C₂²×Dic₁₅	1	2	yes	—
550	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
551	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
552	C₂×C₄	C₂²×Dic₁₅	1	2	yes	—
553	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
555	C₈	—	15	4	no	—
556	C₈	—	30	1	no	—
557	C₈	—	30	2	no	—
558	C₈	—	30	1	no	—
559	C₈	—	30	1	no	—
560	C₈	—	30	1	no	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	4	2	no	—
565	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
566	C₂×C₃	C₂×#4094	1	1	yes	characteristic
567	C₂×C₃	#66153	1	1	yes	characteristic
568	C₅	#82918	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	D₄×Dic₁₅	1	2	yes	—
581	C₂²	#91837	1	2	yes	complemented
582	C₂²	C₂³×Dic₁₅	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	D₄×Dic₁₅	1	2	yes	—
589	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
590	C₄	C₂×#6819	1	1	yes	characteristic
591	C₃	#10614649	1	1	yes	characteristic, complemented, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	4	2	no	—
596	C₂	C₂×D₄×Dic₁₅	1	1	yes	characteristic
597	C₂	C₂×#91837	1	1	yes	characteristic
598	C₂	#11756578	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting, prime radical	C₃×C₅×#525	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#525	D₁₅
hypocenter	C₃×C₅	#2933
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
2. C₂×#91837	C₂	semidirect
3. C₂²×#6710	C₂	semidirect
4. #11751335	C₂	semidirect
5. C₂×#91114	C₂	semidirect
6. #11751113	C₂	semidirect
7. #11751112	C₂	semidirect
8. #11751112	C₂	semidirect
9. D₄×C₃⋊#168	C₂	semidirect
10. #11751100	C₂	semidirect
11. #11751098	C₂	semidirect
29. C₂×#6710	C₂²	semidirect
33. C₂²×C₃⋊#168	C₂²	semidirect
38. #91114	C₂²	semidirect
39. #91114	C₂²	semidirect
40. C₄⋊(C₃⋊#168)	C₂²	semidirect
41. C₄⋊(C₃⋊#168)	C₂²	semidirect
42. #91087	C₂²	semidirect
43. C₄×C₃⋊#168	C₂²	semidirect
86. #6710	D₄	semidirect
271. C₂²×C₃×C₅	#131	semidirect
444. C₂²×C₅	#948	semidirect
495. C₃×C₅	#2933	semidirect
508. C₂²×C₃	#4094	semidirect
568. C₅	#82918	semidirect
581. C₂²	#91837	semidirect
591. C₃	#10614649	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#525	2
C₂×#91837	2
C₂²×#6710	2
#11751335	2
C₂×#91114	2
#11751113	2
#11751112	2
D₄×C₃⋊#168	2
#11751100	2
#11751098	2
#10614649	3
#82918	5