Subgroups — #14430233

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6817	C₂	1	1	yes	maximal, characteristic
2	#11756229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751214	C₂	1	2	yes	maximal
5	#11751207	C₂	1	2	yes	maximal, complemented
6	#11750952	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750951	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750948	C₂	1	2	yes	maximal, complemented
9	#11750947	C₂	1	1	yes	maximal, characteristic, complemented
10	#11750943	C₂	1	1	yes	maximal, characteristic, complemented
11	#11750930	C₂	1	2	yes	maximal, complemented
12	#10610756	—	3	1	no	maximal, Hall
13	C₂×#6817	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₄×#1220	—	2	1	no	—
17	C₄×#1220	—	2	1	no	—
18	#91815	C₂²	1	1	yes	characteristic
19	#91815	C₂²	1	2	yes	—
20	#91813	—	2	1	no	—
21	#91813	—	2	1	no	—
22	C₄×D₆₀	C₂²	1	1	yes	characteristic
23	C₄×D₆₀	C₂²	1	1	yes	characteristic
24	#91761	—	2	1	no	—
25	C₄²×D₁₅	—	2	1	no	—
26	#91759	C₂²	1	2	yes	—
27	#91758	C₂²	1	1	yes	characteristic
28	#91758	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₀	—	2	1	no	—
30	C₄×Dic₃₀	—	2	1	no	—
31	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
32	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	#91105	C₂²	1	2	yes	—
37	#91105	C₂²	1	2	yes	—
38	#91102	C₂²	1	2	yes	—
39	#91102	C₂²	1	2	yes	—
40	#91101	C₂²	1	2	yes	—
41	#91101	C₂²	1	2	yes	—
42	#91100	C₂²	1	2	yes	—
43	#91100	C₂²	1	2	yes	—
44	#79025	—	5	1	no	maximal, Hall
45	C₄×#709	—	3	1	no	—
46	#65804	—	3	1	no	—
47	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
48	#65402	—	3	2	no	—
49	#65395	—	3	2	no	—
50	#65140	—	3	1	no	—
51	#65139	—	3	1	no	—
52	#65136	—	3	2	no	—
53	#65135	—	3	1	no	—
54	#65131	—	3	1	no	—
55	#65118	—	3	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×#1220	—	2	1	no	—
60	#6817	—	2	2	no	—
61	#6817	Q₈	1	4	yes	complemented
62	C₂×D₆₀	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₁₅	—	2	1	no	—
64	C₂×C₄×D₁₅	—	2	1	no	—
65	C₂×C₄×D₁₅	—	2	1	no	—
66	C₂×Dic₃₀	—	2	1	no	—
67	C₂×Dic₃₀	—	2	1	no	—
68	C₂×Dic₃₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	#6719	—	2	2	no	—
77	#6719	—	2	1	no	—
78	#6714	—	2	1	no	—
79	#6714	—	2	1	no	—
80	C₄⋊Dic₁₅	—	2	1	no	—
81	C₄⋊Dic₁₅	—	2	1	no	—
82	C₄⋊Dic₁₅	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₅	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₁₅	C₂³	1	2	yes	—
85	C₄⋊Dic₁₅	C₂³	1	2	yes	—
86	#6712	—	2	2	no	—
87	#6712	—	2	2	no	—
88	#6712	—	2	1	no	—
89	#6712	—	2	1	no	—
90	C₄×Dic₁₅	—	2	2	no	—
91	C₄×Dic₁₅	—	2	1	no	—
92	C₄×Dic₁₅	—	2	1	no	—
93	C₄×Dic₁₅	—	2	1	no	—
94	C₄×#235	—	5	1	no	—
95	#5470	—	5	1	no	—
96	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
97	#5113	—	5	2	no	—
98	#5106	—	5	2	no	—
99	#4851	—	5	1	no	—
100	#4850	—	5	1	no	—
101	#4847	—	5	2	no	—
102	#4846	—	5	1	no	—
103	#4842	—	5	1	no	—
104	#4829	—	5	2	no	—
105	C₂×#709	—	3	1	no	—
106	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
107	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
108	C₄×C₂²⋊D₅	—	6	1	no	—
109	C₄×C₂²⋊D₅	—	6	1	no	—
110	#4072	—	3	2	no	—
111	#4072	—	3	1	no	—
112	#4070	—	6	1	no	—
113	#4070	—	6	1	no	—
114	C₄×D₂₀	—	3	1	no	—
115	C₄×D₂₀	—	3	1	no	—
116	#4018	—	6	1	no	—
117	C₄²×D₅	—	6	1	no	—
118	#4016	—	3	2	no	—
119	#4015	—	3	1	no	—
120	#4015	—	3	1	no	—
121	C₄×Dic₁₀	—	3	1	no	—
122	C₄×Dic₁₀	—	3	1	no	—
123	C₄×Dic₁₀	—	6	1	no	—
124	C₄×Dic₁₀	—	6	1	no	—
125	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
126	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
127	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
128	#3953	—	3	2	no	—
129	#3953	—	3	2	no	—
130	#3950	—	3	2	no	—
131	#3950	—	3	2	no	—
132	#3949	—	3	2	no	—
133	#3949	—	3	2	no	—
134	#3948	—	3	2	no	—
135	#3948	—	3	2	no	—
136	#3076	—	15	1	no	Sylow
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₁₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	4	1	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	#1220	—	2	4	no	—
150	C₂×Dic₁₅	—	2	1	no	—
151	C₂×Dic₁₅	—	2	1	no	—
152	C₂×Dic₁₅	—	2	1	no	—
153	C₂×Dic₁₅	—	2	2	no	—
154	C₂×Dic₁₅	—	2	2	no	—
155	D₆₀	—	2	1	no	—
156	D₆₀	C₂×Q₈	1	2	yes	—
157	C₄×D₁₅	—	2	4	no	—
158	C₄×D₁₅	—	4	2	no	—
159	C₄×D₁₅	—	4	2	no	—
160	Dic₃₀	—	2	1	no	—
161	Dic₃₀	—	4	2	no	—
162	Dic₃₀	—	4	2	no	—
163	Dic₃₀	C₂×Q₈	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₂×#235	—	5	1	no	—
167	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
168	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
169	C₄×#67	—	10	1	no	—
170	C₄×#67	—	10	1	no	—
171	#926	—	5	2	no	—
172	#926	—	5	1	no	—
173	#924	—	10	1	no	—
174	#924	—	10	1	no	—
175	C₄×D₁₂	—	5	1	no	—
176	C₄×D₁₂	—	5	1	no	—
177	#872	—	10	1	no	—
178	C₄²×D₃	—	10	1	no	—
179	#870	—	5	2	no	—
180	#869	—	5	1	no	—
181	#869	—	5	1	no	—
182	C₄×Dic₆	—	5	1	no	—
183	C₄×Dic₆	—	5	1	no	—
184	C₄×Dic₆	—	10	1	no	—
185	C₄×Dic₆	—	10	1	no	—
186	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
187	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
188	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
189	#821	—	5	2	no	—
190	#821	—	5	2	no	—
191	#818	—	5	2	no	—
192	#818	—	5	2	no	—
193	#817	—	5	2	no	—
194	#817	—	5	2	no	—
195	#816	—	5	2	no	—
196	#816	—	5	2	no	—
197	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
198	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	—	6	1	no	—
201	#709	—	3	4	no	—
202	#709	—	6	2	no	—
203	C₂×D₂₀	—	3	1	no	—
204	C₂×C₄×D₅	—	6	1	no	—
205	C₂×C₄×D₅	—	6	1	no	—
206	C₂×C₄×D₅	—	6	1	no	—
207	C₂×Dic₁₀	—	3	1	no	—
208	C₂×Dic₁₀	—	6	1	no	—
209	C₂×Dic₁₀	—	6	1	no	—
210	C₂×C₅×C₈	—	2	4	no	—
211	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
212	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
213	C₄²×C₅	D₁₂	1	1	yes	characteristic
214	C₄²×C₅	D₁₂	1	1	yes	characteristic
215	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₂²⋊Dic₅	—	6	2	no	—
218	C₂²⋊Dic₅	—	6	1	no	—
219	#685	—	6	1	no	—
220	#685	—	6	1	no	—
221	C₄⋊Dic₅	—	3	2	no	—
222	C₄⋊Dic₅	—	3	2	no	—
223	C₄⋊Dic₅	—	3	1	no	—
224	C₄⋊Dic₅	—	3	1	no	—
225	C₄⋊Dic₅	—	6	1	no	—
226	C₄⋊Dic₅	—	6	1	no	—
227	#683	—	6	1	no	—
228	#683	—	6	1	no	—
229	#683	—	6	2	no	—
230	#683	—	6	2	no	—
231	C₄×Dic₅	—	6	1	no	—
232	C₄×Dic₅	—	6	1	no	—
233	C₄×Dic₅	—	6	2	no	—
234	C₄×Dic₅	—	6	1	no	—
235	#533	—	15	1	no	—
236	C₄×#41	—	15	1	no	—
237	#479	—	15	2	no	—
238	#478	—	15	2	no	—
239	#477	—	15	1	no	—
240	#476	—	15	1	no	—
241	#475	—	15	1	no	—
242	#474	—	15	1	no	—
243	#427	—	15	2	no	—
244	C₂×C₄⋊C₈	D₁₅	1	1	yes	characteristic, complemented
245	#416	—	15	2	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×D₁₅	—	2	2	no	—
251	C₂×D₁₅	—	4	1	no	—
252	C₂×D₁₅	—	4	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
257	C₃×C₄×C₅	#135	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	Dic₁₅	—	2	2	no	—
261	Dic₁₅	—	4	2	no	—
262	Dic₁₅	—	4	1	no	—
263	Dic₁₅	—	4	2	no	—
264	Dic₁₅	—	4	1	no	—
265	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
266	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
268	C₂×#67	—	10	1	no	—
269	#235	—	5	4	no	—
270	#235	—	10	2	no	—
271	C₂×D₁₂	—	5	1	no	—
272	C₂×C₄×D₃	—	10	1	no	—
273	C₂×C₄×D₃	—	10	1	no	—
274	C₂×C₄×D₃	—	10	1	no	—
275	C₂×Dic₆	—	5	1	no	—
276	C₂×Dic₆	—	10	1	no	—
277	C₂×Dic₆	—	10	1	no	—
278	C₂×C₃×C₈	—	2	4	no	—
279	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
280	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
281	C₃×C₄²	D₂₀	1	1	yes	characteristic
282	C₃×C₄²	D₂₀	1	1	yes	characteristic
283	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
284	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
285	#217	—	10	2	no	—
286	#217	—	10	1	no	—
287	(C₂×D₃)⋊C₄	—	10	1	no	—
288	(C₂×D₃)⋊C₄	—	10	1	no	—
289	C₄⋊Dic₃	—	5	2	no	—
290	C₄⋊Dic₃	—	5	2	no	—
291	C₄⋊Dic₃	—	5	1	no	—
292	C₄⋊Dic₃	—	5	1	no	—
293	C₄⋊Dic₃	—	10	1	no	—
294	C₄⋊Dic₃	—	10	1	no	—
295	Dic₃⋊C₄	—	10	1	no	—
296	Dic₃⋊C₄	—	10	1	no	—
297	Dic₃⋊C₄	—	10	2	no	—
298	Dic₃⋊C₄	—	10	2	no	—
299	C₄×Dic₃	—	10	1	no	—
300	C₄×Dic₃	—	10	1	no	—
301	C₄×Dic₃	—	10	2	no	—
302	C₄×Dic₃	—	10	1	no	—
303	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
304	C₂²×D₅	—	6	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
312	C₂×C₄×C₅	#237	1	2	yes	—
313	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
314	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
315	C₂²⋊D₅	—	6	4	no	—
316	C₂×Dic₅	—	6	1	no	—
317	C₂×Dic₅	—	6	1	no	—
318	C₂×Dic₅	—	6	1	no	—
319	C₂×Dic₅	—	6	2	no	—
320	C₂×Dic₅	—	6	2	no	—
321	D₂₀	—	3	2	no	—
322	D₂₀	—	6	1	no	—
323	C₄×D₅	—	6	4	no	—
324	C₄×D₅	—	12	2	no	—
325	C₄×D₅	—	12	2	no	—
326	Dic₁₀	—	3	2	no	—
327	Dic₁₀	—	6	1	no	—
328	Dic₁₀	—	12	2	no	—
329	Dic₁₀	—	12	2	no	—
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₂×#41	—	15	1	no	—
333	C₂²×C₈	C₂×D₁₅	1	2	yes	—
334	C₄⋊Q₈	—	15	1	no	—
335	C₄⋊Q₈	—	15	1	no	—
336	#125	—	15	2	no	—
337	C₂²⋊Q₈	—	30	1	no	—
338	C₂²⋊Q₈	—	30	1	no	—
339	C₄×Q₈	—	15	1	no	—
340	C₄×Q₈	—	15	1	no	—
341	C₄×Q₈	—	30	1	no	—
342	C₄×Q₈	—	30	1	no	—
343	C₄×D₄	—	15	1	no	—
344	C₄×D₄	—	15	1	no	—
345	C₄×D₄	—	30	1	no	—
346	C₄×D₄	—	30	1	no	—
347	#117	—	15	1	no	—
348	#117	—	15	2	no	—
349	#117	—	30	1	no	—
350	C₂×C₄²	—	30	1	no	—
351	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
352	#107	—	15	2	no	—
353	#107	—	15	2	no	—
354	#106	—	15	2	no	—
355	#106	—	15	2	no	—
356	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
357	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
358	C₄⋊C₈	C₂×D₁₅	1	2	yes	—
359	#103	—	15	2	no	—
360	#103	—	15	2	no	—
361	#102	—	15	2	no	—
362	#102	—	15	2	no	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	D₁₅	—	4	2	no	—
368	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
369	C₂²×D₃	—	10	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	1	no	—
372	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
377	C₂×C₃×C₄	#711	1	2	yes	—
378	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
379	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
380	#67	—	10	4	no	—
381	C₂×Dic₃	—	10	1	no	—
382	C₂×Dic₃	—	10	1	no	—
383	C₂×Dic₃	—	10	1	no	—
384	C₂×Dic₃	—	10	2	no	—
385	C₂×Dic₃	—	10	2	no	—
386	D₁₂	—	5	2	no	—
387	D₁₂	—	10	1	no	—
388	C₄×D₃	—	10	4	no	—
389	C₄×D₃	—	20	2	no	—
390	C₄×D₃	—	20	2	no	—
391	Dic₆	—	5	2	no	—
392	Dic₆	—	10	1	no	—
393	Dic₆	—	20	2	no	—
394	Dic₆	—	20	2	no	—
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	2	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	#897	1	2	yes	—
400	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
401	C₂×D₅	—	6	2	no	—
402	C₂×D₅	—	12	1	no	—
403	C₂×D₅	—	12	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	#897	1	2	yes	—
408	C₄×C₅	#904	1	2	yes	—
409	C₄×C₅	C₂×#237	1	1	yes	characteristic
410	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
411	Dic₅	—	6	2	no	—
412	Dic₅	—	12	2	no	—
413	Dic₅	—	12	1	no	—
414	Dic₅	—	12	2	no	—
415	Dic₅	—	12	1	no	—
416	#41	—	15	4	no	—
417	#41	—	30	2	no	—
418	C₂×Q₈	—	15	1	no	—
419	C₂×Q₈	—	30	1	no	—
420	C₂×Q₈	—	30	1	no	—
421	C₂×D₄	—	15	1	no	—
422	C₂×D₄	—	30	1	no	—
423	C₂²×C₄	—	30	1	no	—
424	C₂²×C₄	—	30	1	no	—
425	C₂²×C₄	—	30	1	no	—
426	C₂²×C₄	D₆₀	1	1	yes	characteristic
427	C₂²×C₄	D₆₀	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	C₂²×D₁₅	1	2	yes	—
431	C₂×C₈	C₂²×D₁₅	1	2	yes	—
432	C₄⋊C₄	—	15	2	no	—
433	C₄⋊C₄	—	15	2	no	—
434	C₄⋊C₄	—	15	1	no	—
435	C₄⋊C₄	—	15	1	no	—
436	C₄⋊C₄	—	30	1	no	—
437	C₄⋊C₄	—	30	1	no	—
438	C₄⋊C₄	—	30	2	no	—
439	C₄⋊C₄	—	30	2	no	—
440	C₄⋊C₄	—	30	1	no	—
441	C₄⋊C₄	—	30	1	no	—
442	C₂²⋊C₄	—	30	1	no	—
443	C₂²⋊C₄	—	30	2	no	—
444	C₂²⋊C₄	—	30	1	no	—
445	C₂²⋊C₄	—	30	1	no	—
446	C₄²	—	30	1	no	—
447	C₄²	—	30	1	no	—
448	C₄²	—	30	1	no	—
449	C₄²	—	30	2	no	—
450	C₄²	D₆₀	1	1	yes	characteristic
451	C₄²	D₆₀	1	1	yes	characteristic
452	C₄²	C₂²×D₁₅	1	1	yes	characteristic
453	C₄²	C₂²×D₁₅	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	#4043	1	2	yes	—
458	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
459	C₂×D₃	—	10	2	no	—
460	C₂×D₃	—	20	1	no	—
461	C₂×D₃	—	20	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	#4043	1	2	yes	—
466	C₃×C₄	#4050	1	2	yes	—
467	C₃×C₄	C₂×#711	1	1	yes	characteristic
468	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
469	Dic₃	—	10	2	no	—
470	Dic₃	—	20	2	no	—
471	Dic₃	—	20	1	no	—
472	Dic₃	—	20	2	no	—
473	Dic₃	—	20	1	no	—
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	C₂×#897	1	1	yes	characteristic
476	C₂×C₅	C₂×#904	1	1	yes	characteristic
477	C₂×C₅	#5748	1	1	yes	characteristic
478	D₅	—	12	2	no	—
479	C₂³	—	30	1	no	—
480	C₂³	C₂×D₆₀	1	1	yes	characteristic
481	Q₈	—	15	2	no	—
482	Q₈	—	30	1	no	—
483	Q₈	—	60	2	no	—
484	Q₈	—	60	2	no	—
485	D₄	—	15	2	no	—
486	D₄	—	30	4	no	—
487	D₄	—	30	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	30	1	no	—
491	C₂×C₄	—	30	4	no	—
492	C₂×C₄	—	30	1	no	—
493	C₂×C₄	—	30	1	no	—
494	C₂×C₄	—	30	2	no	—
495	C₂×C₄	—	30	2	no	—
496	C₂×C₄	—	60	2	no	—
497	C₂×C₄	—	60	2	no	—
498	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
499	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
500	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
501	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
502	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
503	C₂×C₄	#6819	1	2	yes	—
504	C₂×C₄	Q₈×D₁₅	1	2	yes	—
505	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	C₂×#4043	1	1	yes	characteristic
510	C₂×C₃	C₂×#4050	1	1	yes	characteristic
511	C₂×C₃	#66082	1	1	yes	characteristic
512	D₃	—	20	2	no	—
513	C₅	#79025	1	1	yes	characteristic, complemented, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	30	2	no	—
517	C₂²	—	60	1	no	—
518	C₂²	—	60	1	no	—
519	C₂²	#91786	1	2	yes	—
520	C₂²	C₂²×D₆₀	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	30	2	no	—
525	C₄	—	60	1	no	—
526	C₄	—	60	2	no	—
527	C₄	—	60	1	no	—
528	C₄	—	60	2	no	—
529	C₄	#91786	1	2	yes	—
530	C₄	#91793	1	2	yes	—
531	C₄	C₂×#6819	1	1	yes	characteristic
532	C₄	C₂×Q₈×D₁₅	1	1	yes	characteristic
533	C₃	#10610756	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	60	2	no	—
536	C₂	C₂×#91786	1	1	yes	characteristic
537	C₂	C₂×#91793	1	1	yes	characteristic
538	C₂	#11756507	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×#6817	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₅
hypocenter	C₃×C₅	#3076
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11756229	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. #11751207	C₂	semidirect
6. #11750952	C₂	semidirect
7. #11750951	C₂	semidirect
8. #11750948	C₂	semidirect
9. #11750947	C₂	semidirect
10. #11750943	C₂	semidirect
11. #11750930	C₂	semidirect
47. C₂×C₅×C₄⋊C₈	D₃	semidirect
61. #6817	Q₈	semidirect
96. C₂×C₃×C₄⋊C₈	D₅	semidirect
244. C₂×C₄⋊C₈	D₁₅	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	#79025	semidirect
533. C₃	#10610756	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6817	2
#11756229	2
C₂×C₃×C₅×C₄⋊C₈	2
#11751214	2
#11751207	2
#11750952	2
#11750951	2
#11750948	2
#11750947	2
#11750943	2
#11750930	2
#10610756	3
#79025	5