Subgroups — #14418494

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756337	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747015	C₂	1	1	yes	maximal, characteristic
5	#11747001	C₂	1	2	yes	maximal
6	#11746982	C₂	1	2	yes	maximal
7	C₄×#6648	C₂	1	1	yes	maximal, characteristic
8	#11746864	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746855	C₂	1	2	yes	maximal, complemented
10	#11746855	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746852	C₂	1	2	yes	maximal, complemented
12	#10611648	—	3	1	no	maximal, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	#91835	C₄	1	1	yes	characteristic
15	#91833	C₄	1	1	yes	characteristic
16	#91786	C₄	1	1	yes	characteristic
17	#91785	C₄	1	2	yes	—
18	#91778	C₄	1	2	yes	—
19	#91777	C₄	1	1	yes	characteristic
20	#91761	C₂²	1	2	yes	—
21	C₄²×D₁₅	C₂²	1	1	yes	characteristic
22	C₄×Dic₃₀	C₂²	1	2	yes	—
23	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
24	C₂×#6651	C₂²	1	2	yes	—
25	C₂×#6648	C₂²	1	1	yes	characteristic
26	C₂×#6648	C₂²	1	1	yes	characteristic
27	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
28	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
33	C₃×#3935	C₂²	1	2	yes	—
34	C₃×C₄×#168	C₂²	1	1	yes	characteristic
35	#90983	C₂²	1	2	yes	—
36	#90983	C₂²	1	2	yes	—
37	#90983	C₂²	1	2	yes	—
38	#90954	C₂²	1	2	yes	—
39	#90951	C₂²	1	1	yes	characteristic
40	#90951	C₂²	1	1	yes	characteristic
41	#90951	C₂²	1	2	yes	—
42	#79958	—	5	1	no	maximal, Hall
43	#65912	—	3	1	no	—
44	C₅×C₈×Q₈	—	3	1	no	—
45	#65313	D₃	1	1	yes	characteristic, complemented
46	#65128	—	3	2	no	—
47	#65126	—	3	1	no	—
48	#65120	—	3	1	no	—
49	#65117	—	3	2	no	—
50	#64978	—	3	2	no	—
51	C₄×C₈×D₅	—	3	1	no	—
52	C₈×Dic₁₀	—	3	1	no	—
53	C₈×Dic₁₀	—	3	2	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
58	C₂×Dic₃₀	C₂×C₄	1	2	yes	—
59	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	#6714	C₂×C₄	1	2	yes	—
65	#6714	C₂×C₄	1	2	yes	—
66	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
67	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
68	#6712	C₂×C₄	1	2	yes	—
69	#6712	C₂×C₄	1	2	yes	—
70	#6712	C₂×C₄	1	2	yes	—
71	#6712	C₂×C₄	1	2	yes	—
72	#6712	C₂×C₄	1	2	yes	—
73	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
76	C₄×Dic₁₅	C₂³	1	2	yes	—
77	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
79	C₂×C₅×C₃⋊C₈	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	#6651	—	2	4	no	—
84	#6648	—	2	2	no	—
85	#6648	Q₈	1	4	yes	complemented
86	#5578	—	5	1	no	—
87	C₃×#446	—	5	1	no	—
88	Q₈×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
89	#4839	—	5	2	no	—
90	#4837	—	5	1	no	—
91	#4830	—	5	1	no	—
92	#4830	—	5	2	no	—
93	#4708	—	5	2	no	—
94	#4701	—	5	2	no	—
95	C₄×D₃×C₈	—	5	1	no	—
96	#4679	—	5	1	no	—
97	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
98	#4092	—	3	1	no	—
99	#4090	—	3	1	no	—
100	C₂×#676	—	3	2	no	—
101	C₂×C₈×D₅	—	3	1	no	—
102	C₂×C₈×D₅	—	3	1	no	—
103	#4043	—	3	1	no	—
104	#4042	—	3	2	no	—
105	#4035	—	3	2	no	—
106	#4034	—	3	1	no	—
107	#4018	—	3	2	no	—
108	C₄²×D₅	—	3	1	no	—
109	C₄×Dic₁₀	—	3	2	no	—
110	C₄×Dic₁₀	—	3	1	no	—
111	C₅×C₄⋊C₈	—	3	2	no	—
112	C₅×C₄⋊C₈	—	3	1	no	—
113	C₄×C₅×C₈	—	3	1	no	—
114	C₄×C₅×C₈	—	3	2	no	—
115	#3947	—	3	2	no	—
116	#3946	—	3	2	no	—
117	#3946	—	3	2	no	—
118	#3946	—	3	2	no	—
119	C₈×Dic₅	—	3	1	no	—
120	C₈×Dic₅	—	3	1	no	—
121	C₈×Dic₅	—	3	2	no	—
122	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
123	C₄⋊#168	C₂×D₃	1	2	yes	—
124	#3935	C₂×D₃	1	2	yes	—
125	C₄×#168	C₂×D₃	1	1	yes	characteristic
126	#2960	—	15	1	no	Sylow
127	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
137	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₁₅	—	2	2	no	—
140	C₄×D₁₅	—	2	2	no	—
141	C₄×D₁₅	C₂×Q₈	1	2	yes	—
142	C₄×D₁₅	#41	1	2	yes	—
143	Dic₃₀	—	2	2	no	—
144	Dic₃₀	—	2	4	no	—
145	C₃×#168	—	2	1	no	—
146	C₃×#168	—	2	2	no	—
147	C₃×#168	C₂×Q₈	1	2	yes	—
148	C₅×C₃⋊C₈	—	2	1	no	—
149	C₅×C₃⋊C₈	—	2	2	no	—
150	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
151	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
152	#946	—	5	1	no	—
153	#944	—	5	1	no	—
154	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
155	C₂×D₃×C₈	—	5	1	no	—
156	C₂×D₃×C₈	—	5	1	no	—
157	#897	—	5	1	no	—
158	#896	—	5	2	no	—
159	#889	—	5	2	no	—
160	#888	—	5	1	no	—
161	#872	—	5	2	no	—
162	C₄²×D₃	—	5	1	no	—
163	C₄×Dic₆	—	5	1	no	—
164	C₄×Dic₆	—	5	2	no	—
165	C₃×C₄⋊C₈	—	5	1	no	—
166	C₃×C₄⋊C₈	—	5	2	no	—
167	C₃×#97	—	5	2	no	—
168	C₃×C₄×C₈	—	5	1	no	—
169	#815	—	5	2	no	—
170	Dic₃⋊C₈	—	5	2	no	—
171	Dic₃⋊C₈	—	5	2	no	—
172	Dic₃⋊C₈	—	5	2	no	—
173	C₈×Dic₃	—	5	1	no	—
174	C₈×Dic₃	—	5	1	no	—
175	C₈×Dic₃	—	5	2	no	—
176	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
177	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
178	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
179	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	—
180	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
181	C₂×C₄×D₅	—	3	1	no	—
182	C₂×C₄×D₅	—	3	1	no	—
183	C₂×C₄×D₅	—	3	1	no	—
184	C₂×Dic₁₀	—	3	2	no	—
185	C₂×Dic₁₀	—	3	1	no	—
186	C₂×C₅×C₈	—	3	1	no	—
187	C₂×C₅×C₈	—	3	1	no	—
188	C₂×C₅×C₈	—	3	2	no	—
189	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
191	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
192	C₄²×C₅	C₂²×D₃	1	2	yes	—
193	#685	—	3	2	no	—
194	#685	—	3	2	no	—
195	C₄⋊Dic₅	—	3	1	no	—
196	C₄⋊Dic₅	—	3	2	no	—
197	#683	—	3	2	no	—
198	#683	—	3	2	no	—
199	#683	—	3	2	no	—
200	#683	—	3	2	no	—
201	#683	—	3	2	no	—
202	C₄×Dic₅	—	3	1	no	—
203	C₄×Dic₅	—	3	1	no	—
204	C₄×Dic₅	—	3	1	no	—
205	C₄×Dic₅	—	3	2	no	—
206	C₂×#168	C₂²×D₃	1	1	yes	characteristic
207	C₂×#168	C₂²×D₃	1	2	yes	—
208	C₂×#168	C₂²×D₃	1	1	yes	characteristic
209	#676	—	6	4	no	—
210	C₈×D₅	—	3	4	no	—
211	C₈×D₅	—	6	2	no	—
212	#533	—	15	1	no	—
213	#446	—	5	1	no	—
214	#446	—	15	1	no	—
215	#446	—	15	2	no	—
216	C₈×Q₈	—	3	1	no	—
217	C₈×Q₈	—	15	1	no	—
218	C₈×Q₈	—	15	2	no	—
219	#424	—	15	2	no	—
220	#423	—	15	1	no	—
221	#405	—	15	2	no	—
222	C₂×C₄×C₈	—	15	1	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂×D₁₅	—	2	1	no	—
225	C₂×D₁₅	—	2	1	no	—
226	C₂×D₁₅	C₄×Q₈	1	2	yes	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	#131	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	Dic₁₅	—	2	2	no	—
234	Dic₁₅	—	2	2	no	—
235	Dic₁₅	—	2	1	no	—
236	Dic₁₅	C₄×Q₈	1	2	yes	—
237	Dic₁₅	#131	1	2	yes	—
238	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
239	C₂×C₄×D₃	—	5	1	no	—
240	C₂×C₄×D₃	—	5	1	no	—
241	C₂×C₄×D₃	—	5	1	no	—
242	C₂×Dic₆	—	5	2	no	—
243	C₂×Dic₆	—	5	1	no	—
244	C₂×C₃×C₈	—	5	1	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	2	no	—
247	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
249	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
250	C₃×C₄²	C₂²×D₅	1	2	yes	—
251	(C₂×D₃)⋊C₄	—	5	2	no	—
252	(C₂×D₃)⋊C₄	—	5	2	no	—
253	C₄⋊Dic₃	—	5	1	no	—
254	C₄⋊Dic₃	—	5	2	no	—
255	Dic₃⋊C₄	—	5	2	no	—
256	Dic₃⋊C₄	—	5	2	no	—
257	Dic₃⋊C₄	—	5	2	no	—
258	Dic₃⋊C₄	—	5	2	no	—
259	Dic₃⋊C₄	—	5	2	no	—
260	C₄×Dic₃	—	5	1	no	—
261	C₄×Dic₃	—	5	1	no	—
262	C₄×Dic₃	—	5	1	no	—
263	C₄×Dic₃	—	5	2	no	—
264	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
265	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
266	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
267	ΓL(1,𝔽₂₅)	—	10	4	no	—
268	D₃×C₈	—	5	4	no	—
269	D₃×C₈	—	10	2	no	—
270	C₂²×D₅	—	3	1	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
274	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
275	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
277	C₂×Dic₅	—	3	1	no	—
278	C₂×Dic₅	—	3	1	no	—
279	C₂×Dic₅	—	3	1	no	—
280	C₂×Dic₅	—	3	2	no	—
281	C₂×Dic₅	—	3	2	no	—
282	C₄×D₅	—	3	2	no	—
283	C₄×D₅	—	3	2	no	—
284	C₄×D₅	—	6	2	no	—
285	C₄×D₅	—	6	2	no	—
286	Dic₁₀	—	6	4	no	—
287	Dic₁₀	—	6	2	no	—
288	C₅×C₈	—	3	2	no	—
289	C₅×C₈	—	6	1	no	—
290	C₅×C₈	—	6	2	no	—
291	#168	—	2	1	no	—
292	#168	—	2	2	no	—
293	#168	D₃×Q₈	1	2	yes	—
294	C₂×M₁₆	—	15	2	no	—
295	C₂²×C₈	—	15	1	no	—
296	C₂²×C₈	—	15	1	no	—
297	C₄⋊Q₈	—	15	1	no	—
298	C₄⋊Q₈	—	15	1	no	—
299	#125	—	15	2	no	—
300	C₂²⋊Q₈	—	15	1	no	—
301	C₂²⋊Q₈	—	15	2	no	—
302	C₂²⋊Q₈	—	15	1	no	—
303	C₄×Q₈	—	15	2	no	—
304	C₄×Q₈	—	15	1	no	—
305	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
306	#117	—	15	2	no	—
307	C₂×C₄²	—	15	1	no	—
308	C₄⋊C₈	—	3	1	no	—
309	C₄⋊C₈	—	3	2	no	—
310	C₄⋊C₈	—	5	1	no	—
311	C₄⋊C₈	—	5	2	no	—
312	C₄⋊C₈	—	15	2	no	—
313	C₄⋊C₈	—	15	2	no	—
314	C₄⋊C₈	—	15	2	no	—
315	#97	—	5	2	no	—
316	#97	—	15	2	no	—
317	C₄×C₈	—	3	1	no	—
318	C₄×C₈	—	3	2	no	—
319	C₄×C₈	—	5	1	no	—
320	C₄×C₈	—	15	1	no	—
321	C₄×C₈	—	15	1	no	—
322	C₄×C₈	—	15	2	no	—
323	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	D₁₅	—	2	2	no	—
327	C₂²×D₃	—	5	1	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
334	C₂×Dic₃	—	5	1	no	—
335	C₂×Dic₃	—	5	1	no	—
336	C₂×Dic₃	—	5	1	no	—
337	C₂×Dic₃	—	5	2	no	—
338	C₂×Dic₃	—	5	2	no	—
339	C₄×D₃	—	5	2	no	—
340	C₄×D₃	—	5	2	no	—
341	C₄×D₃	—	10	2	no	—
342	C₄×D₃	—	10	2	no	—
343	Dic₆	—	10	4	no	—
344	Dic₆	—	10	2	no	—
345	C₃×C₈	—	5	2	no	—
346	C₃×C₈	—	10	1	no	—
347	C₃×C₈	—	10	2	no	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	—	2	2	no	—
350	C₃⋊C₈	Q₈×D₅	1	2	yes	—
351	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₂×D₅	—	3	2	no	—
353	C₂×D₅	—	6	1	no	—
354	C₂×D₅	—	6	1	no	—
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	#907	1	2	yes	—
359	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
360	C₄×C₅	D₃×#41	1	1	yes	characteristic
361	Dic₅	—	3	2	no	—
362	Dic₅	—	3	2	no	—
363	Dic₅	—	6	2	no	—
364	Dic₅	—	6	1	no	—
365	Dic₅	—	6	2	no	—
366	C₂×Q₈	—	15	2	no	—
367	C₂×Q₈	—	15	1	no	—
368	C₂×Q₈	#1200	1	1	yes	characteristic
369	C₂²×C₄	—	15	1	no	—
370	C₂²×C₄	—	15	1	no	—
371	C₂²×C₄	—	15	1	no	—
372	M₁₆	—	30	4	no	—
373	C₂×C₈	—	3	1	no	—
374	C₂×C₈	—	3	1	no	—
375	C₂×C₈	—	3	2	no	—
376	C₂×C₈	—	5	1	no	—
377	C₂×C₈	—	5	1	no	—
378	C₂×C₈	—	5	2	no	—
379	C₂×C₈	—	15	4	no	—
380	C₂×C₈	—	30	2	no	—
381	C₄⋊C₄	—	15	2	no	—
382	C₄⋊C₄	—	15	2	no	—
383	C₄⋊C₄	—	15	2	no	—
384	C₄⋊C₄	—	15	2	no	—
385	C₄⋊C₄	—	15	2	no	—
386	C₄⋊C₄	—	15	2	no	—
387	C₄⋊C₄	—	15	1	no	—
388	C₄⋊C₄	#1200	1	2	yes	—
389	C₄⋊C₄	#1200	1	1	yes	characteristic
390	C₂²⋊C₄	—	15	2	no	—
391	C₂²⋊C₄	—	15	2	no	—
392	C₄²	—	15	1	no	—
393	C₄²	—	15	1	no	—
394	C₄²	—	15	1	no	—
395	C₄²	—	15	2	no	—
396	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
397	C₄²	C₂×D₃×D₅	1	2	yes	—
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
400	C₂×D₃	—	5	2	no	—
401	C₂×D₃	—	10	1	no	—
402	C₂×D₃	—	10	1	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	#4047	1	2	yes	—
407	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
408	C₃×C₄	D₅×#41	1	1	yes	characteristic
409	Dic₃	—	5	2	no	—
410	Dic₃	—	5	2	no	—
411	Dic₃	—	10	2	no	—
412	Dic₃	—	10	1	no	—
413	Dic₃	—	10	2	no	—
414	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
415	C₂×C₅	C₂×#907	1	1	yes	characteristic
416	C₂×C₅	D₃×#131	1	1	yes	characteristic
417	D₅	—	6	2	no	—
418	C₂³	—	15	1	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	30	4	no	—
421	Q₈	—	30	2	no	—
422	C₂×C₄	—	15	1	no	—
423	C₂×C₄	—	15	1	no	—
424	C₂×C₄	—	15	2	no	—
425	C₂×C₄	—	15	2	no	—
426	C₂×C₄	—	15	1	no	—
427	C₂×C₄	—	15	2	no	—
428	C₂×C₄	—	15	2	no	—
429	C₂×C₄	—	30	2	no	—
430	C₂×C₄	—	30	2	no	—
431	C₂×C₄	C₂×#1200	1	1	yes	characteristic
432	C₂×C₄	C₂×#1200	1	2	yes	—
433	C₂×C₄	C₂×#1200	1	2	yes	—
434	C₂×C₄	C₂×#1200	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
436	C₈	—	3	2	no	—
437	C₈	—	5	2	no	—
438	C₈	—	6	1	no	—
439	C₈	—	6	2	no	—
440	C₈	—	10	1	no	—
441	C₈	—	10	2	no	—
442	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
443	C₂×C₃	C₂×#4047	1	1	yes	characteristic
444	C₂×C₃	D₅×#131	1	1	yes	characteristic
445	D₃	—	10	2	no	—
446	C₅	#79958	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	15	2	no	—
448	C₂²	—	30	1	no	—
449	C₂²	—	30	1	no	—
450	C₂²	C₂²×#1200	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	15	2	no	—
455	C₄	—	15	2	no	—
456	C₄	—	30	2	no	—
457	C₄	—	30	1	no	—
458	C₄	—	30	2	no	—
459	C₄	#91291	1	2	yes	—
460	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
461	C₄	#92034	1	1	yes	characteristic
462	C₃	#10611648	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	30	2	no	—
464	C₂	C₂×#91291	1	1	yes	characteristic
465	C₂	Q₈×#1200	1	1	yes	characteristic
466	C₂	#11755299	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×Q₈	C₂²
prime radical	C₂²×D₁₅	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#2960
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₅×Q₈×C₃⋊C₈	C₂	semidirect
3. C₃×#65313	C₂	semidirect
8. #11746864	C₂	semidirect
9. #11746855	C₂	semidirect
10. #11746855	C₂	semidirect
11. #11746852	C₂	semidirect
45. #65313	D₃	semidirect
85. #6648	Q₈	semidirect
88. Q₈×C₃⋊C₈	D₅	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	#79958	semidirect
462. C₃	#10611648	semidirect

Maximal subgroups

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

subgroup	index
#11756337	2
C₅×Q₈×C₃⋊C₈	2
C₃×#65313	2
#11747015	2
#11747001	2
#11746982	2
C₄×#6648	2
#11746864	2
#11746855	2
#11746852	2
#10611648	3
#79958	5