Subgroups — #14301085

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6717	C₂	1	1	yes	maximal, characteristic
3	C₂×#91119	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91093	C₂	1	1	yes	maximal, characteristic
5	#11751040	C₂	1	1	yes	maximal, characteristic
6	#11746350	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746345	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602426	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×D₆₀	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	—	2	2	no	—
12	C₃×C₄×C₅×Q₈	—	2	2	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×#6717	—	2	2	no	—
18	C₂×#6717	—	2	2	no	—
19	C₂×#6717	C₄	1	4	yes	complemented
20	C₂×#6714	—	2	1	no	—
21	C₂×#6714	—	2	1	no	—
22	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	#91119	—	2	2	no	—
26	#91093	—	2	2	no	—
27	#71633	—	5	1	no	maximal, Hall
28	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
29	C₂²×#688	—	3	1	no	—
30	C₂×#3967	—	3	1	no	—
31	C₂×#3941	—	3	1	no	—
32	#65228	—	3	1	no	—
33	#64749	—	3	1	no	—
34	#64744	—	3	1	no	—
35	C₂³×D₁₅	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	—	2	1	no	—
38	C₂×C₃×C₅×Q₈	—	2	1	no	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
41	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₅	—	2	1	no	—
48	C₂×D₆₀	—	2	1	no	—
49	C₂×D₆₀	—	2	1	no	—
50	C₂×D₆₀	—	2	1	no	—
51	C₂×D₆₀	—	2	1	no	—
52	C₂×D₆₀	—	2	1	no	—
53	C₂×D₆₀	C₂×C₄	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
57	C₃×C₄²×C₅	—	2	4	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	#6717	—	2	8	no	—
61	#6714	—	4	2	no	—
62	#6714	—	4	2	no	—
63	C₄⋊Dic₁₅	—	2	1	no	—
64	C₄⋊Dic₁₅	—	2	1	no	—
65	C₂×C₃⋊#168	—	2	1	no	—
66	C₂×C₃⋊#168	—	2	1	no	—
67	C₂×C₃⋊#168	—	2	1	no	—
68	C₂×C₃⋊#168	—	2	1	no	—
69	C₂×C₃⋊#168	—	2	1	no	—
70	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
71	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic, complemented
72	C₂²×#215	—	5	1	no	—
73	C₂×#835	—	5	1	no	—
74	C₂×#809	—	5	1	no	—
75	#4939	—	5	1	no	—
76	#4529	—	5	1	no	—
77	#4524	—	5	1	no	—
78	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×D₂₀	—	3	1	no	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₄²×C₅	—	2	1	no	—
85	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
86	C₂×#688	—	3	4	no	—
87	C₂×#688	—	6	2	no	—
88	C₂×#688	—	6	2	no	—
89	C₂×#685	—	6	1	no	—
90	C₂×#685	—	6	1	no	—
91	C₂×C₄⋊Dic₅	—	3	1	no	—
92	C₂²×#168	—	3	1	no	—
93	C₂²×#168	—	3	1	no	—
94	#3967	—	6	2	no	—
95	#3941	—	6	2	no	—
96	#1880	—	15	1	no	Sylow
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×D₁₅	—	2	2	no	—
99	C₂²×D₁₅	—	4	1	no	—
100	C₂²×D₁₅	—	4	1	no	—
101	C₂²×D₁₅	—	4	1	no	—
102	C₂²×D₁₅	—	4	1	no	—
103	C₂²×D₁₅	—	4	1	no	—
104	C₂²×D₁₅	—	4	1	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	2	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	1	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	4	1	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	complemented
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
127	C₂×Dic₁₅	—	4	1	no	—
128	C₂×Dic₁₅	—	4	1	no	—
129	C₂×Dic₁₅	—	4	1	no	—
130	D₆₀	—	2	2	no	—
131	D₆₀	—	2	2	no	—
132	D₆₀	—	4	1	no	—
133	D₆₀	—	4	1	no	—
134	C₃⋊#168	—	2	2	no	—
135	C₃⋊#168	—	4	1	no	—
136	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
137	C₂²×D₁₂	—	5	1	no	—
138	C₃×C₄×Q₈	—	2	2	no	—
139	C₃×C₄×Q₈	—	2	2	no	—
140	C₂×C₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
142	C₂×C₃×C₄²	—	2	1	no	—
143	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
144	C₂×#215	—	5	4	no	—
145	C₂×#215	—	10	2	no	—
146	C₂×#215	—	10	2	no	—
147	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
148	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
149	C₂×C₄⋊Dic₃	—	5	1	no	—
150	C₂²×C₃⋊C₈	—	5	1	no	—
151	C₂²×C₃⋊C₈	—	5	1	no	—
152	#835	—	10	2	no	—
153	#809	—	10	2	no	—
154	C₂³×D₅	—	6	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	C₄×D₃	1	2	yes	—
159	C₂×C₅×Q₈	D₁₂	1	2	yes	—
160	C₂×C₅×Q₈	#67	1	2	yes	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	#67	1	1	yes	characteristic
164	C₂²×C₄×C₅	#67	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₂²×Dic₅	—	6	1	no	—
167	C₂×D₂₀	—	3	2	no	—
168	C₂×D₂₀	—	6	1	no	—
169	C₂×D₂₀	—	6	1	no	—
170	C₂×D₂₀	—	6	1	no	—
171	C₂×D₂₀	—	6	1	no	—
172	C₂×D₂₀	—	6	1	no	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	#67	1	2	yes	—
176	C₄²×C₅	—	2	4	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	#688	—	6	8	no	—
180	#685	—	12	2	no	—
181	#685	—	12	2	no	—
182	C₄⋊Dic₅	—	6	1	no	—
183	C₄⋊Dic₅	—	6	1	no	—
184	C₂×#168	—	3	2	no	—
185	C₂×#168	—	6	1	no	—
186	C₂×#168	—	6	1	no	—
187	C₂×#168	—	6	1	no	—
188	C₂×#168	—	6	1	no	—
189	C₂×#168	—	6	1	no	—
190	C₂²×SD₁₆	—	15	1	no	—
191	C₂×C₄×Q₈	D₁₅	1	1	yes	characteristic, complemented
192	C₂×#103	—	15	1	no	—
193	C₂×#102	—	15	1	no	—
194	#390	—	15	1	no	—
195	#340	—	15	1	no	—
196	#336	—	15	1	no	—
197	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	#120	1	1	yes	characteristic
199	C₂²×C₃×C₅	#121	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₃×C₅	#137	1	1	yes	characteristic
204	C₂×D₁₅	—	4	2	no	—
205	C₂×D₁₅	—	4	2	no	—
206	C₂×D₁₅	—	4	2	no	—
207	C₂×D₁₅	—	8	1	no	—
208	C₂×D₁₅	—	8	1	no	—
209	C₂×D₁₅	—	8	1	no	—
210	C₂×D₁₅	—	8	1	no	—
211	C₃×C₄×C₅	—	2	4	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	4	1	no	—
214	C₃×C₄×C₅	—	4	2	no	—
215	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
217	C₃×C₄×C₅	#121	1	1	yes	characteristic
218	C₃×C₄×C₅	#123	1	1	yes	characteristic
219	Dic₁₅	—	8	1	no	—
220	C₂³×D₃	—	10	1	no	—
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	—	2	1	no	—
223	C₂×C₃×Q₈	—	2	1	no	—
224	C₂×C₃×Q₈	C₄×D₅	1	2	yes	—
225	C₂×C₃×Q₈	D₂₀	1	2	yes	—
226	C₂×C₃×Q₈	C₂²⋊D₅	1	2	yes	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×Dic₃	—	10	1	no	—
233	C₂×D₁₂	—	5	2	no	—
234	C₂×D₁₂	—	10	1	no	—
235	C₂×D₁₂	—	10	1	no	—
236	C₂×D₁₂	—	10	1	no	—
237	C₂×D₁₂	—	10	1	no	—
238	C₂×D₁₂	—	10	1	no	—
239	C₃×C₄⋊C₄	—	2	4	no	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
242	C₃×C₄²	—	2	4	no	—
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	2	1	no	—
245	#215	—	10	8	no	—
246	(C₂×D₃)⋊C₄	—	20	2	no	—
247	(C₂×D₃)⋊C₄	—	20	2	no	—
248	C₄⋊Dic₃	—	10	1	no	—
249	C₄⋊Dic₃	—	10	1	no	—
250	C₂×C₃⋊C₈	—	5	2	no	—
251	C₂×C₃⋊C₈	—	10	1	no	—
252	C₂×C₃⋊C₈	—	10	1	no	—
253	C₂×C₃⋊C₈	—	10	1	no	—
254	C₂×C₃⋊C₈	—	10	1	no	—
255	C₂×C₃⋊C₈	—	10	1	no	—
256	C₂³×C₅	C₂×#67	1	1	yes	characteristic
257	C₂²×D₅	—	6	2	no	—
258	C₂²×D₅	—	12	1	no	—
259	C₂²×D₅	—	12	1	no	—
260	C₂²×D₅	—	12	1	no	—
261	C₂²×D₅	—	12	1	no	—
262	C₂²×D₅	—	12	1	no	—
263	C₂²×D₅	—	12	1	no	—
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	#215	1	2	yes	complemented
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
282	C₂×C₄×C₅	#235	1	1	yes	characteristic
283	C₂×C₄×C₅	#235	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
286	C₂×Dic₅	—	12	1	no	—
287	C₂×Dic₅	—	12	1	no	—
288	C₂×Dic₅	—	12	1	no	—
289	D₂₀	—	6	2	no	—
290	D₂₀	—	6	2	no	—
291	D₂₀	—	12	1	no	—
292	D₂₀	—	12	1	no	—
293	#168	—	6	2	no	—
294	#168	—	12	1	no	—
295	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic
296	C₂²×D₄	—	15	1	no	—
297	C₂×SD₁₆	—	15	4	no	—
298	C₂×SD₁₆	—	30	2	no	—
299	C₂×SD₁₆	—	30	2	no	—
300	C₂²×C₈	—	15	1	no	—
301	C₂²×C₈	—	15	1	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	15	1	no	—
306	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	30	1	no	—
308	C₂×C₂²⋊C₄	—	30	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
311	#103	—	30	2	no	—
312	#102	—	30	2	no	—
313	C₂×C₃×C₅	#386	1	1	yes	characteristic
314	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#440	1	1	yes	characteristic
316	C₂×C₃×C₅	#448	1	1	yes	characteristic
317	C₂×C₃×C₅	#449	1	1	yes	characteristic
318	C₂×C₃×C₅	#460	1	1	yes	characteristic
319	C₂×C₃×C₅	#464	1	1	yes	characteristic
320	D₁₅	—	8	2	no	—
321	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
322	C₂²×D₃	—	10	2	no	—
323	C₂²×D₃	—	20	1	no	—
324	C₂²×D₃	—	20	1	no	—
325	C₂²×D₃	—	20	1	no	—
326	C₂²×D₃	—	20	1	no	—
327	C₂²×D₃	—	20	1	no	—
328	C₂²×D₃	—	20	1	no	—
329	C₃×Q₈	—	2	2	no	—
330	C₃×Q₈	—	2	2	no	—
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	#685	1	4	yes	complemented
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	4	1	no	—
343	C₂×C₃×C₄	—	4	1	no	—
344	C₂×C₃×C₄	#688	1	2	yes	complemented
345	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
347	C₂×C₃×C₄	#709	1	1	yes	characteristic
348	C₂×C₃×C₄	#709	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
351	C₂×Dic₃	—	20	1	no	—
352	C₂×Dic₃	—	20	1	no	—
353	C₂×Dic₃	—	20	1	no	—
354	D₁₂	—	10	2	no	—
355	D₁₂	—	10	2	no	—
356	D₁₂	—	20	1	no	—
357	D₁₂	—	20	1	no	—
358	C₃⋊C₈	—	10	2	no	—
359	C₃⋊C₈	—	20	1	no	—
360	C₂²×C₅	C₄×#67	1	1	yes	characteristic
361	C₂²×C₅	#930	1	1	yes	characteristic
362	C₂²×C₅	C₂×#215	1	1	yes	characteristic
363	C₂²×C₅	#942	1	1	yes	characteristic
364	C₂²×C₅	#949	1	1	yes	characteristic
365	C₂²×C₅	#950	1	1	yes	characteristic
366	C₂²×C₅	#953	1	1	yes	characteristic
367	C₂×D₅	—	12	2	no	—
368	C₂×D₅	—	12	2	no	—
369	C₂×D₅	—	12	2	no	—
370	C₂×D₅	—	24	1	no	—
371	C₂×D₅	—	24	1	no	—
372	C₂×D₅	—	24	1	no	—
373	C₂×D₅	—	24	1	no	—
374	C₄×C₅	—	2	4	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
379	C₄×C₅	C₄×#67	1	1	yes	characteristic
380	C₄×C₅	#929	1	1	yes	characteristic
381	C₄×C₅	#930	1	1	yes	characteristic
382	Dic₅	—	24	1	no	—
383	C₂⁴	—	30	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	C₄×D₁₅	1	2	yes	—
388	C₂×Q₈	D₆₀	1	2	yes	—
389	C₂×Q₈	#1220	1	2	yes	—
390	C₂×D₄	—	15	2	no	—
391	C₂×D₄	—	30	1	no	—
392	C₂×D₄	—	30	1	no	—
393	C₂×D₄	—	30	1	no	—
394	C₂×D₄	—	30	1	no	—
395	C₂×D₄	—	30	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	30	1	no	—
399	C₂²×C₄	#1220	1	1	yes	characteristic
400	C₂²×C₄	#1220	1	1	yes	characteristic
401	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
402	SD₁₆	—	30	8	no	—
403	C₂×C₈	—	15	2	no	—
404	C₂×C₈	—	30	1	no	—
405	C₂×C₈	—	30	1	no	—
406	C₂×C₈	—	30	1	no	—
407	C₂×C₈	—	30	1	no	—
408	C₂×C₈	—	30	1	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	30	1	no	—
412	C₄⋊C₄	—	30	1	no	—
413	C₄⋊C₄	#1220	1	2	yes	—
414	C₂²⋊C₄	—	60	2	no	—
415	C₂²⋊C₄	—	60	2	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₃×C₅	#1880	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
421	C₂²×C₃	#4076	1	1	yes	characteristic
422	C₂²×C₃	C₂×#688	1	1	yes	characteristic
423	C₂²×C₃	#4088	1	1	yes	characteristic
424	C₂²×C₃	#4095	1	1	yes	characteristic
425	C₂²×C₃	#4096	1	1	yes	characteristic
426	C₂²×C₃	#4099	1	1	yes	characteristic
427	C₂×D₃	—	20	2	no	—
428	C₂×D₃	—	20	2	no	—
429	C₂×D₃	—	20	2	no	—
430	C₂×D₃	—	40	1	no	—
431	C₂×D₃	—	40	1	no	—
432	C₂×D₃	—	40	1	no	—
433	C₂×D₃	—	40	1	no	—
434	C₃×C₄	—	2	4	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	C₂×#685	1	1	yes	characteristic
439	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
440	C₃×C₄	#4075	1	1	yes	characteristic
441	C₃×C₄	#4076	1	1	yes	characteristic
442	Dic₃	—	40	1	no	—
443	C₂×C₅	C₄×#215	1	1	yes	characteristic
444	C₂×C₅	#5026	1	1	yes	characteristic
445	C₂×C₅	#5027	1	1	yes	characteristic
446	C₂×C₅	#5028	1	1	yes	characteristic
447	C₂×C₅	#5213	1	1	yes	characteristic
448	C₂×C₅	#5227	1	1	yes	characteristic
449	C₂×C₅	#5238	1	1	yes	characteristic
450	D₅	—	24	2	no	—
451	C₂³	—	30	2	no	—
452	C₂³	—	60	1	no	—
453	C₂³	—	60	1	no	—
454	C₂³	—	60	1	no	—
455	C₂³	—	60	1	no	—
456	C₂³	—	60	1	no	—
457	C₂³	—	60	1	no	—
458	C₂³	C₂×#1220	1	1	yes	characteristic
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	#6714	1	4	yes	complemented
463	D₄	—	30	2	no	—
464	D₄	—	30	2	no	—
465	D₄	—	60	1	no	—
466	D₄	—	60	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	60	1	no	—
479	C₂×C₄	—	60	1	no	—
480	C₂×C₄	—	60	1	no	—
481	C₂×C₄	#6717	1	2	yes	complemented
482	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
483	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
484	C₂×C₄	#6817	1	1	yes	characteristic
485	C₂×C₄	#6817	1	1	yes	characteristic
486	C₂×C₄	C₂×#1220	1	1	yes	characteristic
487	C₂×C₄	C₂×#1220	1	1	yes	characteristic
488	C₈	—	30	2	no	—
489	C₈	—	60	1	no	—
490	C₂×C₃	C₄×#688	1	1	yes	characteristic
491	C₂×C₃	#65315	1	1	yes	characteristic
492	C₂×C₃	#65316	1	1	yes	characteristic
493	C₂×C₃	#65317	1	1	yes	characteristic
494	C₂×C₃	#65502	1	1	yes	characteristic
495	C₂×C₃	#65516	1	1	yes	characteristic
496	C₂×C₃	#65527	1	1	yes	characteristic
497	D₃	—	40	2	no	—
498	C₅	#71633	1	1	yes	characteristic, complemented, Sylow
499	C₂²	—	60	2	no	—
500	C₂²	—	60	2	no	—
501	C₂²	—	60	2	no	—
502	C₂²	—	120	1	no	—
503	C₂²	—	120	1	no	—
504	C₂²	—	120	1	no	—
505	C₂²	—	120	1	no	—
506	C₂²	C₄×#1220	1	1	yes	characteristic
507	C₂²	#91819	1	1	yes	characteristic
508	C₂²	C₂×#6717	1	1	yes	characteristic
509	C₂²	#91831	1	1	yes	characteristic
510	C₂²	#91838	1	1	yes	characteristic
511	C₂²	#91839	1	1	yes	characteristic
512	C₂²	#91842	1	1	yes	characteristic
513	C₄	—	2	4	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	120	1	no	—
518	C₄	C₂×#6714	1	1	yes	characteristic
519	C₄	C₄×#1220	1	1	yes	characteristic
520	C₄	#91818	1	1	yes	characteristic
521	C₄	#91819	1	1	yes	characteristic
522	C₃	#10602426	1	1	yes	characteristic, complemented, Sylow
523	C₂	—	120	2	no	—
524	C₂	C₄×#6717	1	1	yes	characteristic
525	C₂	#11751127	1	1	yes	characteristic
526	C₂	#11751128	1	1	yes	characteristic
527	C₂	#11751129	1	1	yes	characteristic
528	C₂	#11751314	1	1	yes	characteristic
529	C₂	#11751328	1	1	yes	characteristic
530	C₂	#11751339	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1220
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄×Q₈	D₁₅
hypocenter	C₃×C₅	#1880
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₂×#91119	C₂	semidirect
6. #11746350	C₂	semidirect
7. #11746345	C₂	semidirect
19. C₂×#6717	C₄	semidirect
28. C₂×C₄×C₅×Q₈	D₃	semidirect
71. C₂×C₃×C₄×Q₈	D₅	semidirect
108. C₃×C₅×Q₈	C₂²⋊C₄	semidirect
120. C₂×C₃×C₄×C₅	SD₁₆	semidirect
191. C₂×C₄×Q₈	D₁₅	semidirect
267. C₅×Q₈	(C₂×D₃)⋊C₄	semidirect
279. C₂×C₄×C₅	#215	semidirect
332. C₃×Q₈	#685	semidirect
344. C₂×C₃×C₄	#688	semidirect
419. C₃×C₅	#1880	semidirect
462. Q₈	#6714	semidirect
481. C₂×C₄	#6717	semidirect
498. C₅	#71633	semidirect
522. C₃	#10602426	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×Q₈	2
C₂²×#6717	2
C₂×#91119	2
C₂×#91093	2
#11751040	2
#11746350	2
#11746345	2
#10602426	3
#71633	5