Subgroups — #14417424

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6717	C₂	1	1	yes	maximal, characteristic
3	#11756280	C₂	1	1	yes	maximal, characteristic
4	#11751326	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751127	C₂	1	4	yes	maximal, complemented
6	C₄×#6717	C₂	1	4	yes	maximal, complemented
7	#11751102	C₂	1	1	yes	maximal, characteristic
8	#11751099	C₂	1	1	yes	maximal, characteristic, complemented
9	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614279	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×D₆₀	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
15	C₃×C₅×#117	—	2	2	no	—
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×#6717	C₄	1	8	yes	complemented
19	C₂×#6717	C₂²	1	2	yes	—
20	C₂×#6717	C₂²	1	2	yes	—
21	#91815	C₂²	1	1	yes	characteristic
22	C₂×#6710	C₂²	1	1	yes	characteristic
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	#91782	—	2	2	no	—
25	C₂²⋊C₄×D₁₅	—	2	2	no	—
26	C₄×D₆₀	C₂²	1	4	yes	—
27	#91119	C₂²	1	4	yes	complemented
28	#91093	C₂²	1	4	yes	—
29	#91092	C₂²	1	2	yes	complemented
30	#91091	C₂²	1	2	yes	complemented
31	#91087	C₂²	1	2	yes	complemented
32	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
33	#82548	—	5	1	no	maximal, Hall
34	C₅×#519	D₃	1	1	yes	characteristic, complemented
35	C₂²×#688	—	3	1	no	—
36	#65855	—	3	1	no	—
37	#65514	—	3	1	no	—
38	#65315	—	3	4	no	—
39	C₄×#688	—	3	4	no	—
40	#65290	—	3	1	no	—
41	#65287	—	3	1	no	—
42	#65286	—	3	1	no	—
43	C₂³×D₁₅	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂×D₆₀	—	2	1	no	—
51	C₂×D₆₀	—	2	2	no	—
52	C₂×D₆₀	C₂×C₄	1	4	yes	—
53	C₂×D₆₀	C₂³	1	2	yes	—
54	C₂×C₄×D₁₅	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	1	no	—
62	C₃×C₄²×C₅	C₂³	1	2	yes	—
63	#6719	—	2	1	no	—
64	#6717	C₂×C₄	1	8	yes	complemented
65	#6717	C₂×C₄	1	8	yes	complemented
66	#6714	—	2	4	no	—
67	C₄⋊Dic₁₅	C₂³	1	2	yes	—
68	C₄×Dic₁₅	—	2	1	no	—
69	#6710	—	2	2	no	—
70	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
71	C₂×C₃⋊#168	C₂³	1	2	yes	—
72	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
73	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
74	C₃×#519	D₅	1	1	yes	characteristic, complemented
75	C₂²×#215	—	5	1	no	—
76	#5521	—	5	1	no	—
77	#5225	—	5	1	no	—
78	#5026	—	5	4	no	—
79	C₄×#215	—	5	4	no	—
80	#5001	—	5	1	no	—
81	#4998	—	5	1	no	—
82	#4997	—	5	1	no	—
83	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×D₂₀	—	3	1	no	—
85	C₄×C₅×Q₈	—	2	2	no	—
86	C₄×C₅×Q₈	C₂×D₃	1	4	yes	complemented
87	C₅×#117	—	2	2	no	—
88	C₅×#117	C₂×D₃	1	1	yes	characteristic
89	C₅×#117	C₂×D₃	1	1	yes	characteristic
90	C₂×#688	—	3	8	no	—
91	C₂×#688	—	3	2	no	—
92	C₂×#688	—	3	2	no	—
93	#4072	—	3	1	no	—
94	C₂×#681	—	3	1	no	—
95	C₂²×#168	—	3	1	no	—
96	#4039	—	6	2	no	—
97	D₅×C₂²⋊C₄	—	6	2	no	—
98	C₄×D₂₀	—	3	4	no	—
99	#3967	—	3	4	no	—
100	#3941	—	3	4	no	—
101	#3940	—	3	2	no	—
102	#3939	—	3	2	no	—
103	#3935	—	3	2	no	—
104	C₄×#168	—	3	2	no	—
105	#2949	—	15	1	no	Sylow
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×D₁₅	—	2	2	no	—
108	C₂²×D₁₅	—	2	4	no	—
109	C₂²×D₁₅	—	8	2	no	—
110	C₃×C₅×Q₈	—	2	4	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×Dic₁₅	—	2	2	no	—
122	D₆₀	—	2	4	no	—
123	D₆₀	—	2	2	no	—
124	D₆₀	C₂²×C₄	1	4	yes	—
125	C₄×D₁₅	—	8	4	no	—
126	C₃⋊#168	—	2	2	no	—
127	C₃⋊#168	C₂²×C₄	1	2	yes	—
128	C₃⋊#168	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×D₁₂	—	5	1	no	—
131	C₃×C₄×Q₈	—	2	2	no	—
132	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
133	C₃×#117	—	2	2	no	—
134	C₃×#117	C₂×D₅	1	1	yes	characteristic
135	C₃×#117	C₂×D₅	1	1	yes	characteristic
136	C₂×#215	—	5	8	no	—
137	C₂×#215	—	5	2	no	—
138	C₂×#215	—	5	2	no	—
139	#926	—	5	1	no	—
140	C₂×#208	—	5	1	no	—
141	C₂²×C₃⋊C₈	—	5	1	no	—
142	#893	—	10	2	no	—
143	D₃×C₂²⋊C₄	—	10	2	no	—
144	C₄×D₁₂	—	5	4	no	—
145	#835	—	5	4	no	—
146	#809	—	5	4	no	—
147	#808	—	5	2	no	—
148	#807	—	5	2	no	—
149	#803	—	5	2	no	—
150	C₄×C₃⋊C₈	—	5	2	no	—
151	C₂³×D₅	—	6	1	no	—
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
155	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂×D₂₀	—	3	4	no	—
159	C₂×D₂₀	—	3	2	no	—
160	C₂×D₂₀	—	6	2	no	—
161	C₂×D₂₀	—	6	1	no	—
162	C₂×C₄×D₅	—	6	4	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	#67	1	2	yes	—
165	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	#67	1	2	yes	—
168	C₄²×C₅	—	2	4	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	C₂²×D₃	1	2	yes	—
171	C₂²⋊Dic₅	—	6	1	no	—
172	#688	—	3	8	no	—
173	#688	—	3	8	no	—
174	#685	—	6	4	no	—
175	C₄⋊Dic₅	—	3	2	no	—
176	C₄×Dic₅	—	6	1	no	—
177	#681	—	6	2	no	—
178	C₂×#168	—	3	4	no	—
179	C₂×#168	—	3	1	no	—
180	C₂×#168	—	3	1	no	—
181	C₂×#168	—	3	2	no	—
182	C₂²×SD₁₆	—	15	1	no	—
183	#519	D₁₅	1	1	yes	characteristic, complemented
184	#518	—	15	1	no	—
185	#440	—	15	4	no	—
186	C₄×SD₁₆	—	15	4	no	—
187	#427	—	15	1	no	—
188	#419	—	15	1	no	—
189	#418	—	15	1	no	—
190	#405	—	15	1	no	—
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×D₁₅	—	2	4	no	—
195	C₂×D₁₅	—	4	4	no	—
196	C₂×D₁₅	—	8	4	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	Dic₁₅	—	4	2	no	—
204	C₂³×D₃	—	10	1	no	—
205	C₂×C₃×Q₈	—	2	2	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
208	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₂×D₁₂	—	5	4	no	—
212	C₂×D₁₂	—	5	2	no	—
213	C₂×D₁₂	—	10	2	no	—
214	C₂×D₁₂	—	10	1	no	—
215	C₂×C₄×D₃	—	10	4	no	—
216	C₃×C₄⋊C₄	—	2	4	no	—
217	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
218	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
221	C₃×C₄²	—	2	4	no	—
222	C₃×C₄²	—	2	1	no	—
223	C₃×C₄²	C₂²×D₅	1	2	yes	—
224	#217	—	10	1	no	—
225	#215	—	5	8	no	—
226	#215	—	5	8	no	—
227	(C₂×D₃)⋊C₄	—	10	4	no	—
228	C₄⋊Dic₃	—	5	2	no	—
229	C₄×Dic₃	—	10	1	no	—
230	#208	—	10	2	no	—
231	C₂×C₃⋊C₈	—	5	4	no	—
232	C₂×C₃⋊C₈	—	5	1	no	—
233	C₂×C₃⋊C₈	—	5	1	no	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂³×C₅	C₂×#67	1	1	yes	characteristic
236	C₂²×D₅	—	6	2	no	—
237	C₂²×D₅	—	6	4	no	—
238	C₂²×D₅	—	24	2	no	—
239	C₅×Q₈	—	2	4	no	—
240	C₅×Q₈	—	2	2	no	—
241	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
246	C₂×C₄×C₅	#235	1	2	yes	—
247	C₂×C₄×C₅	C₂×#67	1	4	yes	—
248	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
250	C₂×Dic₅	—	6	2	no	—
251	D₂₀	—	3	4	no	—
252	D₂₀	—	6	4	no	—
253	D₂₀	—	6	2	no	—
254	C₄×D₅	—	24	4	no	—
255	#168	—	3	2	no	—
256	#168	—	3	2	no	—
257	#168	—	6	2	no	—
258	C₂²×Q₈	C₂×D₁₅	1	1	yes	characteristic
259	C₂²×D₄	—	15	1	no	—
260	C₂×SD₁₆	—	15	8	no	—
261	C₂×SD₁₆	—	15	2	no	—
262	C₂×SD₁₆	—	15	2	no	—
263	C₂×M₁₆	—	15	1	no	—
264	C₂²×C₈	—	15	1	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	C₂×D₁₅	1	4	yes	complemented
267	C₄×D₄	—	15	4	no	—
268	C₄×D₄	—	30	2	no	—
269	#117	—	2	2	no	—
270	#117	—	15	1	no	—
271	#117	C₂×D₁₅	1	1	yes	characteristic
272	#117	C₂×D₁₅	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	—	30	2	no	—
274	#107	—	15	2	no	—
275	#106	—	15	2	no	—
276	#103	—	15	4	no	—
277	#102	—	15	4	no	—
278	#97	—	15	2	no	—
279	C₄×C₈	—	15	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂×C₃×C₅	#577	1	2	yes	—
283	D₁₅	—	4	4	no	—
284	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
285	C₂²×D₃	—	10	2	no	—
286	C₂²×D₃	—	10	4	no	—
287	C₂²×D₃	—	40	2	no	—
288	C₃×Q₈	—	2	2	no	—
289	C₃×Q₈	—	2	4	no	—
290	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
295	C₂×C₃×C₄	#709	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
297	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
299	C₂×Dic₃	—	10	2	no	—
300	D₁₂	—	5	4	no	—
301	D₁₂	—	10	2	no	—
302	D₁₂	—	10	4	no	—
303	C₄×D₃	—	40	4	no	—
304	C₃⋊C₈	—	5	2	no	—
305	C₃⋊C₈	—	5	2	no	—
306	C₃⋊C₈	—	10	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	C₄×#67	1	2	yes	—
309	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
310	C₂×D₅	—	6	4	no	—
311	C₂×D₅	—	12	4	no	—
312	C₂×D₅	—	24	4	no	—
313	C₄×C₅	—	2	4	no	—
314	C₄×C₅	—	2	4	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	C₄×#67	1	2	yes	—
317	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
318	C₄×C₅	C₂×#235	1	1	yes	characteristic
319	Dic₅	—	12	2	no	—
320	C₂⁴	—	30	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₄×D₁₅	1	4	yes	complemented
324	C₂×Q₈	C₂²×D₁₅	1	2	yes	—
325	C₂×D₄	—	15	4	no	—
326	C₂×D₄	—	15	2	no	—
327	C₂×D₄	—	30	2	no	—
328	C₂×D₄	—	30	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	30	4	no	—
331	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
332	SD₁₆	—	15	8	no	—
333	SD₁₆	—	15	8	no	—
334	M₁₆	—	30	2	no	—
335	C₂×C₈	—	15	4	no	—
336	C₂×C₈	—	15	1	no	—
337	C₂×C₈	—	15	1	no	—
338	C₂×C₈	—	15	2	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	15	2	no	—
341	C₄⋊C₄	#1220	1	2	yes	—
342	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	30	1	no	—
345	C₂²⋊C₄	—	30	4	no	—
346	C₂²⋊C₄	#1220	1	2	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	30	1	no	—
350	C₄²	C₂²×D₁₅	1	2	yes	—
351	C₃×C₅	#2949	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
354	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
355	C₂×D₃	—	10	4	no	—
356	C₂×D₃	—	20	4	no	—
357	C₂×D₃	—	40	4	no	—
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
362	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
363	C₃×C₄	C₂×#709	1	1	yes	characteristic
364	Dic₃	—	20	2	no	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
367	C₂×C₅	#5837	1	2	yes	—
368	D₅	—	12	4	no	—
369	C₂³	—	30	2	no	—
370	C₂³	—	30	4	no	—
371	C₂³	—	120	2	no	—
372	C₂³	C₂×#1220	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	C₂×C₄×D₁₅	1	4	yes	—
376	D₄	—	15	4	no	—
377	D₄	—	30	4	no	—
378	D₄	—	30	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	30	2	no	—
383	C₂×C₄	—	120	4	no	—
384	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
385	C₂×C₄	#6817	1	2	yes	—
386	C₂×C₄	C₂×#1220	1	4	yes	—
387	C₂×C₄	C₂×#1220	1	1	yes	characteristic
388	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
389	C₈	—	15	2	no	—
390	C₈	—	15	2	no	—
391	C₈	—	30	2	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
394	C₂×C₃	#66171	1	2	yes	—
395	D₃	—	20	4	no	—
396	C₅	#82548	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	30	4	no	—
399	C₂²	—	60	4	no	—
400	C₂²	—	120	4	no	—
401	C₂²	C₄×#1220	1	2	yes	—
402	C₂²	C₂²×#1220	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	60	2	no	—
407	C₄	C₄×#1220	1	2	yes	—
408	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
409	C₄	C₂×#6817	1	1	yes	characteristic
410	C₃	#10614279	1	1	yes	characteristic, complemented, Sylow
411	C₂	—	2	2	no	—
412	C₂	—	60	4	no	—
413	C₂	C₂×C₄×#1220	1	1	yes	characteristic
414	C₂	#11756596	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×#1220
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₃×C₅×#519	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#519	D₁₅
hypocenter	C₃×C₅	#2949
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ #117 ◁ #519

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#519	C₂	semidirect
4. #11751326	C₂	semidirect
5. #11751127	C₂	semidirect
6. C₄×#6717	C₂	semidirect
8. #11751099	C₂	semidirect
9. #11751098	C₂	semidirect
14. C₃×C₄×C₅×Q₈	C₂²	semidirect
18. C₂×#6717	C₄	semidirect
27. #91119	C₂²	semidirect
29. #91092	C₂²	semidirect
30. #91091	C₂²	semidirect
31. #91087	C₂²	semidirect
32. C₄×C₃⋊#168	C₂²	semidirect
34. C₅×#519	D₃	semidirect
46. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
64. #6717	C₂×C₄	semidirect
65. #6717	C₂×C₄	semidirect
70. C₂×C₃⋊#168	C₂×C₄	semidirect
74. C₃×#519	D₅	semidirect
86. C₄×C₅×Q₈	C₂×D₃	semidirect
132. C₃×C₄×Q₈	C₂×D₅	semidirect
154. C₂×C₅×Q₈	C₄×D₃	semidirect
183. #519	D₁₅	semidirect
207. C₂×C₃×Q₈	C₄×D₅	semidirect
266. C₄×Q₈	C₂×D₁₅	semidirect
323. C₂×Q₈	C₄×D₁₅	semidirect
351. C₃×C₅	#2949	semidirect
396. C₅	#82548	semidirect
410. C₃	#10614279	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#519	2
C₂²×#6717	2
#11756280	2
#11751326	2
#11751127	2
C₄×#6717	2
#11751102	2
#11751099	2
#11751098	2
#10614279	3
#82548	5