Subgroups — #14419127

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756238	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11750939	C₂	1	1	yes	maximal, characteristic, complemented
5	#11750935	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750932	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750931	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750831	C₂	1	2	yes	maximal, complemented
9	#11750826	C₂	1	2	yes	maximal, complemented
10	#11750810	C₂	1	2	yes	maximal, complemented
11	#11750809	C₂	1	2	yes	maximal, complemented
12	#10611056	—	3	1	no	maximal, Hall
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	#91819	C₄	1	1	yes	characteristic
15	#91818	C₄	1	2	yes	—
16	C₄×#1220	C₂²	1	2	yes	—
17	#91813	C₄	1	1	yes	characteristic
18	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	C₂×#6705	C₂²	1	2	yes	—
21	C₂×C₈×D₁₅	C₂²	1	2	yes	—
22	#91765	C₄	1	2	yes	—
23	#91764	C₄	1	1	yes	characteristic
24	C₄×D₆₀	C₂²	1	1	yes	characteristic
25	#91761	C₂²	1	2	yes	—
26	#91759	C₄	1	1	yes	characteristic
27	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	#91104	C₂²	1	2	yes	—
33	#91104	C₂²	1	2	yes	—
34	#91099	C₂²	1	2	yes	—
35	#91098	C₂²	1	2	yes	—
36	#91098	C₂²	1	2	yes	—
37	C₈×Dic₁₅	C₂²	1	2	yes	—
38	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
39	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
40	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
42	#79325	—	5	1	no	maximal, Hall
43	#65813	—	3	1	no	—
44	C₅×#432	D₃	1	1	yes	characteristic, complemented
45	C₂×C₄×#168	—	3	1	no	—
46	#65127	—	3	1	no	—
47	#65123	—	3	1	no	—
48	#65120	—	3	1	no	—
49	#65119	—	3	1	no	—
50	#65019	—	3	2	no	—
51	#65014	—	3	2	no	—
52	#64998	—	3	2	no	—
53	#64997	—	3	2	no	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×#1220	C₂×C₄	1	2	yes	—
58	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂³	1	2	yes	—
60	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	#6719	C₂×C₄	1	2	yes	—
68	#6714	C₂×C₄	1	2	yes	—
69	#6714	C₂×C₄	1	2	yes	—
70	#6714	C₂×C₄	1	2	yes	—
71	#6714	C₂×C₄	1	2	yes	—
72	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
73	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	#6712	C₂×C₄	1	2	yes	—
75	#6712	C₂×C₄	1	2	yes	—
76	#6712	C₂×C₄	1	2	yes	—
77	#6712	C₂×C₄	1	2	yes	—
78	C₄×Dic₁₅	C₂³	1	2	yes	—
79	C₂×C₃⋊#168	—	2	2	no	—
80	C₂×C₃⋊#168	—	2	2	no	—
81	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
83	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
84	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
85	#6705	—	2	4	no	—
86	C₈×D₁₅	—	2	4	no	—
87	#5479	—	5	1	no	—
88	C₃×#432	D₅	1	1	yes	characteristic, complemented
89	C₂×C₄×C₃⋊C₈	—	5	1	no	—
90	#4838	—	5	1	no	—
91	#4834	—	5	1	no	—
92	#4831	—	5	1	no	—
93	#4830	—	5	1	no	—
94	#4730	—	5	2	no	—
95	#67⋊C₈	—	5	2	no	—
96	#4709	—	5	2	no	—
97	#4708	—	5	2	no	—
98	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
99	#4076	—	3	1	no	—
100	#4075	—	3	2	no	—
101	C₄×C₂²⋊D₅	—	3	2	no	—
102	#4070	—	3	1	no	—
103	C₂²×#168	—	3	1	no	—
104	C₂²×#168	—	3	1	no	—
105	C₂×#676	—	3	2	no	—
106	C₂×C₈×D₅	—	3	2	no	—
107	#4022	—	3	2	no	—
108	#4021	—	3	1	no	—
109	C₄×D₂₀	—	3	1	no	—
110	#4018	—	3	2	no	—
111	#4016	—	3	1	no	—
112	C₄×Dic₁₀	—	3	1	no	—
113	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
116	C₅×#97	C₂×D₃	1	2	yes	—
117	#3952	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3947	—	3	2	no	—
120	#3946	—	3	2	no	—
121	#3946	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₄×#168	—	3	1	no	—
124	C₄×#168	—	3	1	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	1	no	—
127	#2966	—	15	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	#1220	—	2	4	no	—
141	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
142	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
143	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
144	D₆₀	—	2	2	no	—
145	C₄×D₁₅	—	2	2	no	—
146	C₄×D₁₅	—	2	2	no	—
147	Dic₃₀	—	2	2	no	—
148	C₃×C₅×C₈	—	2	2	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃⋊#168	—	2	1	no	—
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	#41	1	2	yes	—
153	C₃⋊#168	#41	1	2	yes	—
154	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
155	#930	—	5	1	no	—
156	#929	—	5	2	no	—
157	C₄×#67	—	5	2	no	—
158	#924	—	5	1	no	—
159	C₂²×C₃⋊C₈	—	5	1	no	—
160	C₂²×C₃⋊C₈	—	5	1	no	—
161	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
162	C₂×D₃×C₈	—	5	2	no	—
163	#876	—	5	2	no	—
164	#875	—	5	1	no	—
165	C₄×D₁₂	—	5	1	no	—
166	#872	—	5	2	no	—
167	#870	—	5	1	no	—
168	C₄×Dic₆	—	5	1	no	—
169	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
171	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
172	C₃×#97	C₂×D₅	1	2	yes	—
173	(C₂×D₃)⋊C₈	—	5	2	no	—
174	(C₂×D₃)⋊C₈	—	5	2	no	—
175	#815	—	5	2	no	—
176	Dic₃⋊C₈	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	C₈×Dic₃	—	5	2	no	—
179	C₄×C₃⋊C₈	—	5	1	no	—
180	C₄×C₃⋊C₈	—	5	1	no	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
186	C₂×C₂²⋊D₅	—	3	2	no	—
187	C₂×D₂₀	—	3	1	no	—
188	C₂×C₄×D₅	—	3	2	no	—
189	C₂×Dic₁₀	—	3	1	no	—
190	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
191	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
192	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
193	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
194	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²⋊Dic₅	—	3	2	no	—
197	#685	—	3	2	no	—
198	#685	—	3	2	no	—
199	#685	—	3	2	no	—
200	#685	—	3	2	no	—
201	C₄⋊Dic₅	—	3	1	no	—
202	C₄⋊Dic₅	—	3	1	no	—
203	#683	—	3	2	no	—
204	#683	—	3	2	no	—
205	#683	—	3	2	no	—
206	#683	—	3	2	no	—
207	C₄×Dic₅	—	3	2	no	—
208	C₂×#168	—	3	1	no	—
209	C₂×#168	—	3	1	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	—	6	2	no	—
213	C₂×#168	—	6	2	no	—
214	#676	—	6	4	no	—
215	C₈×D₅	—	6	4	no	—
216	#529	—	15	1	no	—
217	#446	—	15	1	no	—
218	C₈×Q₈	—	15	1	no	—
219	#436	—	15	1	no	—
220	#435	—	15	2	no	—
221	C₈×D₄	—	15	1	no	—
222	C₈×D₄	—	15	2	no	—
223	#433	—	15	2	no	—
224	#432	D₁₅	1	1	yes	characteristic, complemented
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	#131	1	2	yes	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×D₁₅	—	2	2	no	—
232	C₂×D₁₅	—	2	2	no	—
233	C₂×D₁₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	#131	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	Dic₁₅	—	2	2	no	—
242	Dic₁₅	—	2	2	no	—
243	Dic₁₅	—	2	2	no	—
244	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂×#67	—	5	2	no	—
248	C₂×D₁₂	—	5	1	no	—
249	C₂×C₄×D₃	—	5	2	no	—
250	C₂×Dic₆	—	5	1	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
252	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
253	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
254	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
255	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	#217	—	5	2	no	—
258	(C₂×D₃)⋊C₄	—	5	2	no	—
259	(C₂×D₃)⋊C₄	—	5	2	no	—
260	(C₂×D₃)⋊C₄	—	5	2	no	—
261	(C₂×D₃)⋊C₄	—	5	2	no	—
262	C₄⋊Dic₃	—	5	1	no	—
263	C₄⋊Dic₃	—	5	1	no	—
264	Dic₃⋊C₄	—	5	2	no	—
265	Dic₃⋊C₄	—	5	2	no	—
266	Dic₃⋊C₄	—	5	2	no	—
267	Dic₃⋊C₄	—	5	2	no	—
268	C₄×Dic₃	—	5	2	no	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	1	no	—
272	C₂×C₃⋊C₈	—	5	1	no	—
273	C₂×C₃⋊C₈	—	10	2	no	—
274	C₂×C₃⋊C₈	—	10	2	no	—
275	ΓL(1,𝔽₂₅)	—	10	4	no	—
276	D₃×C₈	—	10	4	no	—
277	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
278	C₂²×D₅	—	3	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	6	4	no	—
290	C₂×Dic₅	—	3	2	no	—
291	C₂×Dic₅	—	3	2	no	—
292	C₂×Dic₅	—	3	2	no	—
293	D₂₀	—	6	2	no	—
294	C₄×D₅	—	6	2	no	—
295	C₄×D₅	—	6	2	no	—
296	Dic₁₀	—	6	2	no	—
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	2	2	no	—
299	#168	—	3	2	no	—
300	#168	—	3	2	no	—
301	#168	—	6	1	no	—
302	#168	—	6	1	no	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	15	1	no	—
305	C₂²×C₈	—	15	1	no	—
306	C₂²×C₈	—	15	2	no	—
307	#126	—	15	2	no	—
308	#125	—	15	1	no	—
309	#124	—	15	1	no	—
310	#123	—	15	2	no	—
311	C₂²⋊Q₈	—	15	1	no	—
312	#121	—	15	1	no	—
313	C₄×Q₈	—	15	1	no	—
314	C₄×D₄	—	15	2	no	—
315	C₄×D₄	—	15	1	no	—
316	#117	—	15	2	no	—
317	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
318	C₄⋊C₈	—	15	2	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
321	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
322	C₂²⋊C₈	—	15	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	C₂×D₁₅	1	2	yes	—
325	#97	—	15	2	no	—
326	#97	C₂×D₁₅	1	2	yes	—
327	C₄×C₈	—	15	2	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	—	15	1	no	—
330	C₄×C₈	—	15	1	no	—
331	C₄×C₈	—	15	1	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	D₁₅	—	4	2	no	—
337	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂²×D₃	—	5	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
349	#67	—	10	4	no	—
350	C₂×Dic₃	—	5	2	no	—
351	C₂×Dic₃	—	5	2	no	—
352	C₂×Dic₃	—	5	2	no	—
353	D₁₂	—	10	2	no	—
354	C₄×D₃	—	10	2	no	—
355	C₄×D₃	—	10	2	no	—
356	Dic₆	—	10	2	no	—
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	2	2	no	—
359	C₃⋊C₈	—	5	2	no	—
360	C₃⋊C₈	—	5	2	no	—
361	C₃⋊C₈	—	10	1	no	—
362	C₃⋊C₈	—	10	1	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	#907	1	2	yes	—
366	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
367	C₂×D₅	—	6	2	no	—
368	C₂×D₅	—	6	2	no	—
369	C₂×D₅	—	6	2	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	#907	1	2	yes	—
375	C₄×C₅	D₃×#41	1	1	yes	characteristic
376	C₄×C₅	D₃×#41	1	1	yes	characteristic
377	Dic₅	—	6	2	no	—
378	Dic₅	—	6	2	no	—
379	Dic₅	—	6	2	no	—
380	C₂×Q₈	—	15	1	no	—
381	C₂×D₄	—	15	2	no	—
382	C₂×D₄	—	15	1	no	—
383	C₂²×C₄	—	15	2	no	—
384	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
385	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	15	1	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	15	1	no	—
391	C₂×C₈	—	15	1	no	—
392	C₂×C₈	—	30	4	no	—
393	C₂×C₈	—	30	2	no	—
394	C₂×C₈	—	30	2	no	—
395	C₂×C₈	C₂²×D₁₅	1	2	yes	—
396	C₂×C₈	C₂²×D₁₅	1	2	yes	—
397	C₄⋊C₄	—	15	2	no	—
398	C₄⋊C₄	—	15	2	no	—
399	C₄⋊C₄	—	15	1	no	—
400	C₄⋊C₄	—	15	2	no	—
401	C₄⋊C₄	—	15	1	no	—
402	C₄⋊C₄	—	15	2	no	—
403	C₂²⋊C₄	—	15	2	no	—
404	C₂²⋊C₄	—	15	2	no	—
405	C₂²⋊C₄	—	15	2	no	—
406	C₂²⋊C₄	—	15	2	no	—
407	C₂²⋊C₄	—	15	2	no	—
408	C₄²	—	15	2	no	—
409	C₄²	C₄×D₁₅	1	1	yes	characteristic
410	C₄²	C₄×D₁₅	1	1	yes	characteristic
411	C₄²	C₂²×D₁₅	1	1	yes	characteristic
412	C₄²	C₂²×D₁₅	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	#4053	1	2	yes	—
417	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
418	C₂×D₃	—	10	2	no	—
419	C₂×D₃	—	10	2	no	—
420	C₂×D₃	—	10	2	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	#4053	1	2	yes	—
426	C₃×C₄	D₅×#41	1	1	yes	characteristic
427	C₃×C₄	D₅×#41	1	1	yes	characteristic
428	Dic₃	—	10	2	no	—
429	Dic₃	—	10	2	no	—
430	Dic₃	—	10	2	no	—
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	#5522	1	1	yes	characteristic
433	C₂×C₅	C₂×#907	1	1	yes	characteristic
434	C₂×C₅	C₂×#907	1	1	yes	characteristic
435	D₅	—	12	2	no	—
436	C₂³	—	15	2	no	—
437	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
438	Q₈	—	30	2	no	—
439	D₄	—	30	4	no	—
440	D₄	—	30	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	15	2	no	—
446	C₂×C₄	—	15	2	no	—
447	C₂×C₄	—	15	2	no	—
448	C₂×C₄	—	30	2	no	—
449	C₂×C₄	—	30	2	no	—
450	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
455	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	15	2	no	—
459	C₈	—	15	2	no	—
460	C₈	—	30	1	no	—
461	C₈	—	30	1	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	#65856	1	1	yes	characteristic
464	C₂×C₃	C₂×#4053	1	1	yes	characteristic
465	C₂×C₃	C₂×#4053	1	1	yes	characteristic
466	D₃	—	20	2	no	—
467	C₅	#79325	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	30	2	no	—
471	C₂²	—	30	2	no	—
472	C₂²	—	30	2	no	—
473	C₂²	#91796	1	2	yes	—
474	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	30	2	no	—
480	C₄	—	30	2	no	—
481	C₄	—	30	2	no	—
482	C₄	#91796	1	2	yes	—
483	C₄	#41×D₁₅	1	1	yes	characteristic
484	C₄	#41×D₁₅	1	1	yes	characteristic
485	C₃	#10611056	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	60	2	no	—
488	C₂	#11756281	1	1	yes	characteristic
489	C₂	C₂×#91796	1	1	yes	characteristic
490	C₂	C₂×#91796	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#432	C₂
prime radical	#91819	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#432	D₁₅
hypocenter	C₃×C₅	#2966
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#432	C₂	semidirect
3. C₂×C₄×C₃⋊#168	C₂	semidirect
4. #11750939	C₂	semidirect
5. #11750935	C₂	semidirect
6. #11750932	C₂	semidirect
7. #11750931	C₂	semidirect
8. #11750831	C₂	semidirect
9. #11750826	C₂	semidirect
10. #11750810	C₂	semidirect
11. #11750809	C₂	semidirect
44. C₅×#432	D₃	semidirect
88. C₃×#432	D₅	semidirect
224. #432	D₁₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#79325	semidirect
485. C₃	#10611056	semidirect

Maximal subgroups

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

subgroup	index
#11756238	2
C₃×C₅×#432	2
C₂×C₄×C₃⋊#168	2
#11750939	2
#11750935	2
#11750932	2
#11750931	2
#11750831	2
#11750826	2
#11750810	2
#11750809	2
#10611056	3
#79325	5