Subgroups — #14419142

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	#11756339	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11750941	C₂	1	2	yes	maximal, complemented
5	#11750936	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750935	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750935	C₂	1	2	yes	maximal, complemented
8	#11750809	C₂	1	2	yes	maximal, complemented
9	#11750807	C₂	1	2	yes	maximal, complemented
10	#11750789	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611670	—	3	1	no	maximal, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	#91836	C₄	1	1	yes	characteristic
15	#91835	C₄	1	1	yes	characteristic
16	C₂×#6705	C₂²	1	2	yes	—
17	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₅	C₂²	1	2	yes	—
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	#91787	C₄	1	2	yes	—
21	#91784	C₄	1	1	yes	characteristic
22	#91783	C₄	1	2	yes	—
23	#91779	C₄	1	1	yes	characteristic
24	C₄×D₆₀	C₂²	1	1	yes	characteristic
25	C₄×D₆₀	C₂²	1	2	yes	—
26	#91761	C₂²	1	2	yes	—
27	C₄²×D₁₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₃×C₅×#97	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	#91104	C₂²	1	2	yes	—
33	#91104	C₂²	1	2	yes	—
34	#91104	C₂²	1	2	yes	—
35	#91099	C₂²	1	2	yes	—
36	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
37	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
38	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
40	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
41	C₄×C₃⋊#168	C₂²	1	2	yes	—
42	#79939	—	5	1	no	maximal, Hall
43	#65914	—	3	1	no	—
44	C₅×#446	D₃	1	1	yes	characteristic, complemented
45	Q₈×#168	—	3	1	no	—
46	#65129	—	3	2	no	—
47	#65124	—	3	1	no	—
48	#65123	—	3	1	no	—
49	#65123	—	3	2	no	—
50	#64997	—	3	2	no	—
51	#64995	—	3	2	no	—
52	#64977	—	3	1	no	—
53	C₄×C₈×D₅	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×D₆₀	C₂×C₄	1	2	yes	—
56	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
60	C₂×C₄×D₁₅	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	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	#6714	C₂×C₄	1	2	yes	—
73	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
74	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
75	#6712	C₂×C₄	1	2	yes	—
76	#6712	C₂×C₄	1	2	yes	—
77	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
80	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
81	C₂×C₃⋊#168	C₂³	1	2	yes	—
82	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
83	#6705	—	2	4	no	—
84	C₈×D₁₅	—	2	2	no	—
85	C₈×D₁₅	—	2	2	no	—
86	C₈×D₁₅	—	2	4	no	—
87	#5580	—	5	1	no	—
88	C₃×#446	D₅	1	1	yes	characteristic, complemented
89	Q₈×C₃⋊C₈	—	5	1	no	—
90	#4840	—	5	2	no	—
91	#4835	—	5	1	no	—
92	#4834	—	5	1	no	—
93	#4834	—	5	2	no	—
94	#4708	—	5	2	no	—
95	#4706	—	5	2	no	—
96	#4688	—	5	1	no	—
97	C₄×D₃×C₈	—	5	1	no	—
98	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
99	#4093	—	3	1	no	—
100	#4092	—	3	1	no	—
101	C₂×#676	—	3	2	no	—
102	C₂×C₈×D₅	—	3	1	no	—
103	C₂×C₈×D₅	—	3	2	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	#4044	—	3	2	no	—
106	#4041	—	3	1	no	—
107	#4040	—	3	2	no	—
108	#4036	—	3	1	no	—
109	C₄×D₂₀	—	3	1	no	—
110	C₄×D₂₀	—	3	2	no	—
111	#4018	—	3	2	no	—
112	C₄²×D₅	—	3	1	no	—
113	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
115	C₅×#97	C₂×D₃	1	2	yes	—
116	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
117	#3952	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3952	—	3	2	no	—
120	#3947	—	3	2	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	1	no	—
123	C₄⋊#168	—	3	1	no	—
124	C₄⋊#168	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	2	no	—
127	#2966	—	15	1	no	Sylow
128	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
129	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
140	D₆₀	—	2	4	no	—
141	D₆₀	—	2	2	no	—
142	C₄×D₁₅	—	2	2	no	—
143	C₄×D₁₅	—	2	2	no	—
144	C₄×D₁₅	—	2	1	no	—
145	C₄×D₁₅	—	2	1	no	—
146	C₄×D₁₅	—	2	2	no	—
147	C₄×D₁₅	—	2	2	no	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×C₅×C₈	#41	1	2	yes	—
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	—	2	2	no	—
153	C₃⋊#168	#41	1	2	yes	—
154	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
155	#947	—	5	1	no	—
156	#946	—	5	1	no	—
157	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
158	C₂×D₃×C₈	—	5	1	no	—
159	C₂×D₃×C₈	—	5	1	no	—
160	C₂×D₃×C₈	—	5	2	no	—
161	#898	—	5	2	no	—
162	#895	—	5	1	no	—
163	#894	—	5	2	no	—
164	#890	—	5	1	no	—
165	C₄×D₁₂	—	5	1	no	—
166	C₄×D₁₂	—	5	2	no	—
167	#872	—	5	2	no	—
168	C₄²×D₃	—	5	1	no	—
169	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
171	C₃×#97	C₂×D₅	1	2	yes	—
172	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
173	(C₂×D₃)⋊C₈	—	5	2	no	—
174	(C₂×D₃)⋊C₈	—	5	2	no	—
175	(C₂×D₃)⋊C₈	—	5	2	no	—
176	#815	—	5	2	no	—
177	C₈×Dic₃	—	5	1	no	—
178	C₈×Dic₃	—	5	1	no	—
179	C₄⋊(C₃⋊C₈)	—	5	1	no	—
180	C₄⋊(C₃⋊C₈)	—	5	2	no	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₄×C₃⋊C₈	—	5	2	no	—
183	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
184	C₂×D₂₀	—	3	2	no	—
185	C₂×D₂₀	—	3	1	no	—
186	C₂×C₄×D₅	—	3	1	no	—
187	C₂×C₄×D₅	—	3	1	no	—
188	C₂×C₄×D₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	2	no	—
190	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₄²×C₅	C₂²×D₃	1	2	yes	—
197	#685	—	3	2	no	—
198	#685	—	3	2	no	—
199	#685	—	3	2	no	—
200	#685	—	3	2	no	—
201	#685	—	3	2	no	—
202	C₄⋊Dic₅	—	3	2	no	—
203	C₄⋊Dic₅	—	3	1	no	—
204	#683	—	3	2	no	—
205	#683	—	3	2	no	—
206	C₄×Dic₅	—	3	1	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	1	no	—
209	C₂×#168	—	3	1	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	2	no	—
212	#676	—	6	4	no	—
213	C₈×D₅	—	6	2	no	—
214	C₈×D₅	—	6	4	no	—
215	C₈×D₅	—	6	2	no	—
216	#529	—	15	1	no	—
217	#446	D₁₅	1	1	yes	characteristic, complemented
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	—	15	1	no	—
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×D₁₅	—	2	1	no	—
229	C₂×D₁₅	—	2	1	no	—
230	C₂×D₁₅	—	2	2	no	—
231	C₂×D₁₅	—	2	2	no	—
232	C₂×D₁₅	—	2	2	no	—
233	C₂×D₁₅	#131	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	#131	1	2	yes	—
238	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	Dic₁₅	—	2	1	no	—
241	Dic₁₅	—	2	2	no	—
242	Dic₁₅	—	2	1	no	—
243	Dic₁₅	—	2	1	no	—
244	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
245	C₂×D₁₂	—	5	2	no	—
246	C₂×D₁₂	—	5	1	no	—
247	C₂×C₄×D₃	—	5	1	no	—
248	C₂×C₄×D₃	—	5	1	no	—
249	C₂×C₄×D₃	—	5	1	no	—
250	C₂×C₄×D₃	—	5	2	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	C₂²×D₅	1	2	yes	—
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	(C₂×D₃)⋊C₄	—	5	2	no	—
263	C₄⋊Dic₃	—	5	2	no	—
264	C₄⋊Dic₃	—	5	1	no	—
265	Dic₃⋊C₄	—	5	2	no	—
266	Dic₃⋊C₄	—	5	2	no	—
267	C₄×Dic₃	—	5	1	no	—
268	C₄×Dic₃	—	5	1	no	—
269	C₄×Dic₃	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	1	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	ΓL(1,𝔽₂₅)	—	10	4	no	—
274	D₃×C₈	—	10	2	no	—
275	D₃×C₈	—	10	4	no	—
276	D₃×C₈	—	10	2	no	—
277	C₂²×D₅	—	3	1	no	—
278	C₂²×D₅	—	3	2	no	—
279	C₅×Q₈	—	2	2	no	—
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
282	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
285	C₂×Dic₅	—	3	1	no	—
286	C₂×Dic₅	—	3	1	no	—
287	C₂×Dic₅	—	3	1	no	—
288	C₂×Dic₅	—	3	2	no	—
289	D₂₀	—	6	4	no	—
290	D₂₀	—	6	2	no	—
291	C₄×D₅	—	6	2	no	—
292	C₄×D₅	—	6	2	no	—
293	C₄×D₅	—	6	1	no	—
294	C₄×D₅	—	6	2	no	—
295	C₄×D₅	—	6	1	no	—
296	C₄×D₅	—	6	2	no	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	—	2	2	no	—
299	C₅×C₈	#239	1	2	yes	—
300	#168	—	3	2	no	—
301	#168	—	6	1	no	—
302	#168	—	6	2	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	C₂×D₁₅	1	1	yes	characteristic
314	C₄×D₄	—	15	2	no	—
315	C₄×D₄	—	15	1	no	—
316	#117	—	15	2	no	—
317	C₂×C₄²	—	15	1	no	—
318	C₄⋊C₈	—	15	1	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
321	C₄⋊C₈	C₂×D₁₅	1	2	yes	—
322	C₂²⋊C₈	—	15	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	—	15	2	no	—
325	#97	—	15	2	no	—
326	#97	C₂×D₁₅	1	2	yes	—
327	C₄×C₈	—	15	1	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	—	15	1	no	—
330	C₄×C₈	—	15	2	no	—
331	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
332	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	D₁₅	—	2	2	no	—
336	D₁₅	—	4	2	no	—
337	C₂²×D₃	—	5	1	no	—
338	C₂²×D₃	—	5	2	no	—
339	C₃×Q₈	—	2	2	no	—
340	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₂×Dic₃	—	5	1	no	—
346	C₂×Dic₃	—	5	1	no	—
347	C₂×Dic₃	—	5	1	no	—
348	C₂×Dic₃	—	5	2	no	—
349	D₁₂	—	10	4	no	—
350	D₁₂	—	10	2	no	—
351	C₄×D₃	—	10	2	no	—
352	C₄×D₃	—	10	1	no	—
353	C₄×D₃	—	10	2	no	—
354	C₄×D₃	—	10	1	no	—
355	C₄×D₃	—	10	2	no	—
356	C₄×D₃	—	10	2	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	2	2	no	—
359	C₃×C₈	#713	1	2	yes	—
360	C₃⋊C₈	—	5	2	no	—
361	C₃⋊C₈	—	10	1	no	—
362	C₃⋊C₈	—	10	2	no	—
363	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
364	C₂×D₅	—	3	2	no	—
365	C₂×D₅	—	6	1	no	—
366	C₂×D₅	—	6	1	no	—
367	C₂×D₅	—	6	2	no	—
368	C₂×D₅	—	6	2	no	—
369	C₂×D₅	—	6	2	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	#907	1	2	yes	—
374	C₄×C₅	C₂×#239	1	1	yes	characteristic
375	C₄×C₅	D₃×#41	1	1	yes	characteristic
376	Dic₅	—	6	1	no	—
377	Dic₅	—	6	1	no	—
378	Dic₅	—	6	1	no	—
379	Dic₅	—	6	2	no	—
380	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
381	C₂×D₄	—	15	2	no	—
382	C₂×D₄	—	15	1	no	—
383	C₂²×C₄	—	15	1	no	—
384	C₂²×C₄	—	15	1	no	—
385	C₂²×C₄	—	15	1	no	—
386	C₂²×C₄	—	15	2	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	15	1	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	15	2	no	—
391	C₂×C₈	—	30	2	no	—
392	C₂×C₈	—	30	4	no	—
393	C₂×C₈	—	30	2	no	—
394	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
395	C₂×C₈	C₂²×D₁₅	1	2	yes	—
396	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
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	C₄×D₁₅	1	1	yes	characteristic
402	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
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	1	no	—
409	C₄²	—	15	1	no	—
410	C₄²	—	15	1	no	—
411	C₄²	C₂²×D₁₅	1	1	yes	characteristic
412	C₄²	C₂²×D₁₅	1	2	yes	—
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
415	C₂×D₃	—	5	2	no	—
416	C₂×D₃	—	10	1	no	—
417	C₂×D₃	—	10	1	no	—
418	C₂×D₃	—	10	2	no	—
419	C₂×D₃	—	10	2	no	—
420	C₂×D₃	—	10	2	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	#4053	1	2	yes	—
425	C₃×C₄	C₂×#713	1	1	yes	characteristic
426	C₃×C₄	D₅×#41	1	1	yes	characteristic
427	Dic₃	—	10	1	no	—
428	Dic₃	—	10	1	no	—
429	Dic₃	—	10	1	no	—
430	Dic₃	—	10	2	no	—
431	C₂×C₅	C₄×#239	1	1	yes	characteristic
432	C₂×C₅	C₂×#907	1	1	yes	characteristic
433	C₂×C₅	D₃×#131	1	1	yes	characteristic
434	D₅	—	6	2	no	—
435	D₅	—	12	2	no	—
436	C₂³	—	15	1	no	—
437	C₂³	—	15	2	no	—
438	Q₈	—	2	2	no	—
439	D₄	—	30	4	no	—
440	D₄	—	30	2	no	—
441	C₂×C₄	—	15	1	no	—
442	C₂×C₄	—	15	1	no	—
443	C₂×C₄	—	15	1	no	—
444	C₂×C₄	—	15	2	no	—
445	C₂×C₄	—	30	2	no	—
446	C₂×C₄	—	30	2	no	—
447	C₂×C₄	—	30	1	no	—
448	C₂×C₄	—	30	2	no	—
449	C₂×C₄	—	30	1	no	—
450	C₂×C₄	—	30	2	no	—
451	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
453	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
454	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
455	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	15	2	no	—
459	C₈	—	30	1	no	—
460	C₈	—	30	2	no	—
461	C₈	#6821	1	2	yes	—
462	C₂×C₃	C₄×#713	1	1	yes	characteristic
463	C₂×C₃	C₂×#4053	1	1	yes	characteristic
464	C₂×C₃	D₅×#131	1	1	yes	characteristic
465	D₃	—	10	2	no	—
466	D₃	—	20	2	no	—
467	C₅	#79939	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	15	2	no	—
469	C₂²	—	30	1	no	—
470	C₂²	—	30	1	no	—
471	C₂²	—	30	2	no	—
472	C₂²	—	30	2	no	—
473	C₂²	—	30	2	no	—
474	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	30	1	no	—
479	C₄	—	30	2	no	—
480	C₄	—	30	1	no	—
481	C₄	—	30	1	no	—
482	C₄	#91796	1	2	yes	—
483	C₄	C₂×#6821	1	1	yes	characteristic
484	C₄	#41×D₁₅	1	1	yes	characteristic
485	C₃	#10611670	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	30	2	no	—
487	C₂	—	60	2	no	—
488	C₂	C₄×#6821	1	1	yes	characteristic
489	C₂	C₂×#91796	1	1	yes	characteristic
490	C₂	D₁₅×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#446	C₂
prime radical	#91784	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#446	D₁₅
hypocenter	C₃×C₅	#2966
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. Q₈×C₃⋊#168	C₂	semidirect
4. #11750941	C₂	semidirect
5. #11750936	C₂	semidirect
6. #11750935	C₂	semidirect
7. #11750935	C₂	semidirect
8. #11750809	C₂	semidirect
9. #11750807	C₂	semidirect
10. #11750789	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
44. C₅×#446	D₃	semidirect
88. C₃×#446	D₅	semidirect
217. #446	D₁₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#79939	semidirect
485. C₃	#10611670	semidirect

Maximal subgroups

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

subgroup	index
#11756339	2
C₃×C₅×#446	2
Q₈×C₃⋊#168	2
#11750941	2
#11750936	2
#11750935	2
#11750809	2
#11750807	2
#11750789	2
C₄×C₈×D₁₅	2
#10611670	3
#79939	5