Subgroups — #11754041

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6771	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#91292	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
7	D₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	#91268	C₂	1	2	yes	maximal, complemented
9	#91267	C₂	1	2	yes	maximal, complemented
10	#91266	C₂	1	2	yes	maximal, complemented
11	#91265	C₂	1	2	yes	maximal, complemented
12	#66079	—	3	1	no	maximal, Hall
13	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×#1204	C₄	1	1	yes	characteristic
17	C₂×#1203	C₄	1	1	yes	characteristic
18	C₂×#1202	C₄	1	1	yes	characteristic
19	C₂×#1201	C₄	1	1	yes	characteristic
20	#6771	C₄	1	1	yes	characteristic
21	#6771	C₄	1	1	yes	characteristic
22	#6771	C₄	1	1	yes	characteristic
23	#6771	C₄	1	1	yes	characteristic
24	#6771	C₂²	1	1	yes	characteristic
25	#6771	C₂²	1	1	yes	characteristic
26	#6771	C₂²	1	1	yes	characteristic
27	#6771	C₂²	1	1	yes	characteristic
28	C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
29	#6710	C₂²	1	1	yes	characteristic
30	#6705	C₂²	1	2	yes	complemented
31	C₈×D₁₅	C₂²	1	2	yes	complemented
32	C₅×#208	C₂²	1	1	yes	characteristic
33	C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
34	C₅×D₃×C₈	C₂²	1	2	yes	complemented
35	C₃×#681	C₂²	1	1	yes	characteristic
36	C₃×#676	C₂²	1	2	yes	complemented
37	C₃×C₈×D₅	C₂²	1	2	yes	complemented
38	#6651	C₂²	1	2	yes	complemented
39	#6650	C₂²	1	2	yes	complemented
40	#6649	C₂²	1	2	yes	complemented
41	#6648	C₂²	1	2	yes	complemented
42	D₃×#168	C₂²	1	2	yes	complemented
43	D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
44	#5745	—	5	1	no	maximal, Hall
45	C₂×#709	—	3	1	no	—
46	C₂×C₅×M₁₆	—	3	1	no	—
47	C₂×#681	—	3	1	no	—
48	#4053	—	3	2	no	—
49	#4053	—	3	2	no	—
50	D₅×M₁₆	—	3	1	no	—
51	D₅×M₁₆	—	3	1	no	—
52	D₅×M₁₆	—	3	1	no	—
53	D₅×M₁₆	D₃	1	1	yes	characteristic, complemented
54	#4047	—	3	2	no	—
55	#4047	—	3	2	no	—
56	C₂²×D₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×Dic₁₅	C₂×C₄	1	1	yes	characteristic
61	C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
62	C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₅	C₂³	1	1	yes	characteristic
64	C₄×D₁₅	C₂³	1	1	yes	characteristic
65	C₂×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
67	C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
72	C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄×D₅	C₂³	1	1	yes	characteristic
74	C₃×C₄×D₅	C₂³	1	1	yes	characteristic
75	#1204	C₂×C₄	1	1	yes	characteristic
76	#1204	C₂×C₄	1	1	yes	characteristic
77	#1204	C₂×C₄	1	1	yes	characteristic
78	#1204	C₂×C₄	1	1	yes	characteristic
79	#1203	C₂×C₄	1	1	yes	characteristic
80	#1203	C₂×C₄	1	1	yes	characteristic
81	#1203	C₂×C₄	1	1	yes	characteristic
82	#1203	C₂×C₄	1	1	yes	characteristic
83	#1202	C₂×C₄	1	1	yes	characteristic
84	#1202	C₂×C₄	1	1	yes	characteristic
85	#1202	C₂×C₄	1	1	yes	characteristic
86	#1202	C₂×C₄	1	1	yes	characteristic
87	#1201	C₂×C₄	1	1	yes	characteristic
88	#1201	C₂×C₄	1	1	yes	characteristic
89	#1201	C₂×C₄	1	1	yes	characteristic
90	#1201	C₂×C₄	1	1	yes	characteristic
91	C₃×C₅×C₈	C₂³	1	2	yes	—
92	C₃⋊#168	C₂³	1	2	yes	—
93	C₃×#168	C₂³	1	2	yes	—
94	C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	C₂×#235	—	5	1	no	—
96	C₂×C₃×M₁₆	—	5	1	no	—
97	C₂×#208	—	5	1	no	—
98	#907	—	5	2	no	—
99	#907	—	5	2	no	—
100	D₃×M₁₆	—	5	1	no	—
101	D₃×M₁₆	—	5	1	no	—
102	D₃×M₁₆	—	5	1	no	—
103	D₃×M₁₆	D₅	1	1	yes	characteristic, complemented
104	#901	—	5	2	no	—
105	#901	—	5	2	no	—
106	C₂²×C₄×C₅	—	3	1	no	—
107	C₂×C₂²⋊D₅	—	3	1	no	—
108	C₂×C₂²⋊D₅	—	3	1	no	—
109	#709	—	3	1	no	—
110	#709	—	3	1	no	—
111	#709	—	3	1	no	—
112	#709	—	3	1	no	—
113	#709	—	3	1	no	—
114	#709	—	3	1	no	—
115	#709	—	3	1	no	—
116	#709	—	3	1	no	—
117	C₂×D₂₀	—	3	1	no	—
118	C₂×C₄×D₅	—	3	1	no	—
119	C₂×C₄×D₅	C₂×D₃	1	1	yes	characteristic
120	C₂×Dic₁₀	—	3	1	no	—
121	C₅×M₁₆	—	3	1	no	—
122	C₅×M₁₆	—	3	2	no	—
123	C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
124	C₂×C₅×C₈	—	3	2	no	—
125	#681	—	3	1	no	—
126	#681	—	3	2	no	—
127	#681	C₂×D₃	1	1	yes	characteristic
128	C₂×#168	—	3	2	no	—
129	#676	—	3	2	no	—
130	#676	—	3	2	no	—
131	#676	—	3	2	no	—
132	#676	C₂×D₃	1	2	yes	complemented
133	C₈×D₅	—	3	2	no	—
134	C₈×D₅	—	3	2	no	—
135	C₈×D₅	—	3	2	no	—
136	C₈×D₅	C₂×D₃	1	2	yes	complemented
137	#568	—	15	1	no	Sylow
138	C₂²×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₁₅	—	4	1	no	—
140	C₂×D₁₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×D₁₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×D₃	—	4	1	no	—
143	C₂×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×D₅	—	4	1	no	—
146	C₂×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
148	C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	Dic₁₅	C₂²×C₄	1	1	yes	characteristic
151	Dic₁₅	C₂²×C₄	1	1	yes	characteristic
152	C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
155	C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	—	5	1	no	—
157	C₂×#67	—	5	1	no	—
158	C₂×#67	—	5	1	no	—
159	#235	—	5	1	no	—
160	#235	—	5	1	no	—
161	#235	—	5	1	no	—
162	#235	—	5	1	no	—
163	#235	—	5	1	no	—
164	#235	—	5	1	no	—
165	#235	—	5	1	no	—
166	#235	—	5	1	no	—
167	C₂×D₁₂	—	5	1	no	—
168	C₂×C₄×D₃	—	5	1	no	—
169	C₂×C₄×D₃	C₂×D₅	1	1	yes	characteristic
170	C₂×Dic₆	—	5	1	no	—
171	C₃×M₁₆	—	5	1	no	—
172	C₃×M₁₆	—	5	2	no	—
173	C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
174	C₂×C₃×C₈	—	5	2	no	—
175	#208	—	5	1	no	—
176	#208	—	5	2	no	—
177	#208	C₂×D₅	1	1	yes	characteristic
178	C₂×C₃⋊C₈	—	5	2	no	—
179	ΓL(1,𝔽₂₅)	—	5	2	no	—
180	ΓL(1,𝔽₂₅)	—	5	2	no	—
181	ΓL(1,𝔽₂₅)	—	5	2	no	—
182	ΓL(1,𝔽₂₅)	C₂×D₅	1	2	yes	complemented
183	D₃×C₈	—	5	2	no	—
184	D₃×C₈	—	5	2	no	—
185	D₃×C₈	—	5	2	no	—
186	D₃×C₈	C₂×D₅	1	2	yes	complemented
187	C₂³×C₅	—	3	1	no	—
188	C₂²×D₅	—	3	1	no	—
189	C₂²×D₅	C₄×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	—	3	1	no	—
191	C₂×C₄×C₅	—	3	1	no	—
192	C₂×C₄×C₅	—	3	1	no	—
193	C₂×C₄×C₅	—	3	1	no	—
194	C₂×C₄×C₅	—	3	1	no	—
195	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²⋊D₅	—	3	1	no	—
197	C₂²⋊D₅	—	3	1	no	—
198	C₂²⋊D₅	—	3	1	no	—
199	C₂²⋊D₅	—	3	1	no	—
200	C₂²⋊D₅	—	3	1	no	—
201	C₂²⋊D₅	—	3	1	no	—
202	C₂²⋊D₅	—	3	1	no	—
203	C₂²⋊D₅	—	3	1	no	—
204	C₂×Dic₅	—	3	1	no	—
205	C₂×Dic₅	C₄×D₃	1	1	yes	characteristic
206	D₂₀	—	3	1	no	—
207	D₂₀	—	3	1	no	—
208	D₂₀	—	3	1	no	—
209	D₂₀	—	3	1	no	—
210	C₄×D₅	—	3	1	no	—
211	C₄×D₅	—	3	1	no	—
212	C₄×D₅	—	3	1	no	—
213	C₄×D₅	—	3	1	no	—
214	C₄×D₅	C₄×D₃	1	1	yes	characteristic
215	C₄×D₅	C₄×D₃	1	1	yes	characteristic
216	C₄×D₅	C₂²×D₃	1	1	yes	characteristic
217	C₄×D₅	C₂²×D₃	1	1	yes	characteristic
218	Dic₁₀	—	3	1	no	—
219	Dic₁₀	—	3	1	no	—
220	Dic₁₀	—	3	1	no	—
221	Dic₁₀	—	3	1	no	—
222	C₅×C₈	—	3	2	no	—
223	C₅×C₈	C₂²×D₃	1	2	yes	—
224	#168	—	3	2	no	—
225	#168	C₂²×D₃	1	2	yes	—
226	C₂×#41	—	15	1	no	—
227	#131	—	15	2	no	—
228	#131	—	15	2	no	—
229	#131	—	15	2	no	—
230	#131	—	15	2	no	—
231	C₂×M₁₆	—	3	1	no	—
232	C₂×M₁₆	—	5	1	no	—
233	C₂×M₁₆	—	15	1	no	—
234	C₂×M₁₆	—	15	1	no	—
235	C₂×M₁₆	—	15	1	no	—
236	C₂×M₁₆	—	15	1	no	—
237	C₂×C₃×C₅	—	2	1	no	—
238	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
239	D₁₅	—	2	1	no	—
240	D₁₅	—	2	1	no	—
241	C₃×D₅	—	2	1	no	—
242	C₃×D₅	—	2	1	no	—
243	C₅×D₃	—	2	1	no	—
244	C₅×D₃	—	2	1	no	—
245	C₂³×C₃	—	5	1	no	—
246	C₂²×D₃	—	5	1	no	—
247	C₂²×D₃	C₄×D₅	1	1	yes	characteristic
248	C₂×C₃×C₄	—	5	1	no	—
249	C₂×C₃×C₄	—	5	1	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	#67	—	5	1	no	—
255	#67	—	5	1	no	—
256	#67	—	5	1	no	—
257	#67	—	5	1	no	—
258	#67	—	5	1	no	—
259	#67	—	5	1	no	—
260	#67	—	5	1	no	—
261	#67	—	5	1	no	—
262	C₂×Dic₃	—	5	1	no	—
263	C₂×Dic₃	C₄×D₅	1	1	yes	characteristic
264	D₁₂	—	5	1	no	—
265	D₁₂	—	5	1	no	—
266	D₁₂	—	5	1	no	—
267	D₁₂	—	5	1	no	—
268	C₄×D₃	—	5	1	no	—
269	C₄×D₃	—	5	1	no	—
270	C₄×D₃	—	5	1	no	—
271	C₄×D₃	—	5	1	no	—
272	C₄×D₃	C₄×D₅	1	1	yes	characteristic
273	C₄×D₃	C₄×D₅	1	1	yes	characteristic
274	C₄×D₃	C₂²×D₅	1	1	yes	characteristic
275	C₄×D₃	C₂²×D₅	1	1	yes	characteristic
276	Dic₆	—	5	1	no	—
277	Dic₆	—	5	1	no	—
278	Dic₆	—	5	1	no	—
279	Dic₆	—	5	1	no	—
280	C₃×C₈	—	5	2	no	—
281	C₃×C₈	C₂²×D₅	1	2	yes	—
282	C₃⋊C₈	—	5	2	no	—
283	C₃⋊C₈	C₂²×D₅	1	2	yes	—
284	C₂²×C₅	—	3	1	no	—
285	C₂²×C₅	—	3	1	no	—
286	C₂²×C₅	—	12	1	no	—
287	C₂²×C₅	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×D₅	—	3	1	no	—
289	C₂×D₅	—	3	1	no	—
290	C₂×D₅	—	4	1	no	—
291	C₂×D₅	—	12	1	no	—
292	C₂×D₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×D₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₄×C₅	—	3	1	no	—
295	C₄×C₅	—	3	1	no	—
296	C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
297	C₄×C₅	C₂³×D₃	1	1	yes	characteristic
298	Dic₅	—	3	1	no	—
299	Dic₅	—	3	1	no	—
300	Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
301	Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
302	#41	—	15	1	no	—
303	#41	—	15	1	no	—
304	#41	—	15	1	no	—
305	#41	—	15	1	no	—
306	#41	—	15	1	no	—
307	#41	—	15	1	no	—
308	#41	—	15	1	no	—
309	#41	—	15	1	no	—
310	C₂×Q₈	—	15	1	no	—
311	C₂×D₄	—	15	1	no	—
312	C₂×D₄	—	15	1	no	—
313	C₂×D₄	—	15	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	15	1	no	—
317	M₁₆	—	3	1	no	—
318	M₁₆	—	3	2	no	—
319	M₁₆	—	5	1	no	—
320	M₁₆	—	5	2	no	—
321	M₁₆	—	15	2	no	—
322	M₁₆	—	15	2	no	—
323	M₁₆	—	15	2	no	—
324	M₁₆	—	15	1	no	—
325	M₁₆	—	15	2	no	—
326	M₁₆	D₃×D₅	1	1	yes	characteristic
327	C₂×C₈	—	3	2	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	15	2	no	—
330	C₂×C₈	—	15	2	no	—
331	C₂×C₈	—	15	2	no	—
332	C₂×C₈	—	15	2	no	—
333	C₃×C₅	#568	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	5	1	no	—
335	C₂²×C₃	—	5	1	no	—
336	C₂²×C₃	—	20	1	no	—
337	C₂²×C₃	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂×D₃	—	4	1	no	—
339	C₂×D₃	—	5	1	no	—
340	C₂×D₃	—	5	1	no	—
341	C₂×D₃	—	20	1	no	—
342	C₂×D₃	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×D₃	C₂×C₄×D₅	1	1	yes	characteristic
344	C₃×C₄	—	5	1	no	—
345	C₃×C₄	—	5	1	no	—
346	C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₃×C₄	C₂³×D₅	1	1	yes	characteristic
348	Dic₃	—	5	1	no	—
349	Dic₃	—	5	1	no	—
350	Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
351	Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	6	1	no	—
354	C₂×C₅	—	6	1	no	—
355	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
356	D₅	—	2	1	no	—
357	D₅	—	2	1	no	—
358	D₅	—	6	1	no	—
359	D₅	—	6	1	no	—
360	C₂³	—	3	1	no	—
361	C₂³	—	5	1	no	—
362	C₂³	—	15	1	no	—
363	Q₈	—	15	1	no	—
364	Q₈	—	15	1	no	—
365	Q₈	—	15	1	no	—
366	Q₈	—	15	1	no	—
367	D₄	—	15	1	no	—
368	D₄	—	15	1	no	—
369	D₄	—	15	1	no	—
370	D₄	—	15	1	no	—
371	D₄	—	15	1	no	—
372	D₄	—	15	1	no	—
373	D₄	—	15	1	no	—
374	D₄	—	15	1	no	—
375	D₄	—	15	1	no	—
376	D₄	—	15	1	no	—
377	D₄	—	15	1	no	—
378	D₄	—	15	1	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	15	1	no	—
390	C₂×C₄	—	15	1	no	—
391	C₂×C₄	—	15	1	no	—
392	C₂×C₄	—	15	1	no	—
393	C₂×C₄	—	15	1	no	—
394	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
395	C₈	—	3	2	no	—
396	C₈	—	5	2	no	—
397	C₈	—	15	2	no	—
398	C₈	C₂×D₃×D₅	1	2	yes	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	10	1	no	—
401	C₂×C₃	—	10	1	no	—
402	C₂×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
403	D₃	—	2	1	no	—
404	D₃	—	2	1	no	—
405	D₃	—	10	1	no	—
406	D₃	—	10	1	no	—
407	C₅	#5745	1	1	yes	characteristic, complemented, Sylow
408	C₂²	—	3	1	no	—
409	C₂²	—	3	1	no	—
410	C₂²	—	5	1	no	—
411	C₂²	—	5	1	no	—
412	C₂²	—	12	1	no	—
413	C₂²	—	15	1	no	—
414	C₂²	—	15	1	no	—
415	C₂²	—	20	1	no	—
416	C₂²	—	60	1	no	—
417	C₂²	C₄×D₃×D₅	1	1	yes	characteristic
418	C₄	—	3	1	no	—
419	C₄	—	3	1	no	—
420	C₄	—	5	1	no	—
421	C₄	—	5	1	no	—
422	C₄	—	15	1	no	—
423	C₄	—	15	1	no	—
424	C₄	C₄×D₃×D₅	1	1	yes	characteristic
425	C₄	C₂²×D₃×D₅	1	1	yes	characteristic
426	C₃	#66079	1	1	yes	characteristic, complemented, Sylow
427	C₂	—	2	1	no	—
428	C₂	—	6	1	no	—
429	C₂	—	6	1	no	—
430	C₂	—	10	1	no	—
431	C₂	—	10	1	no	—
432	C₂	—	30	1	no	—
433	C₂	—	30	1	no	—
434	C₂	C₂×C₄×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×M₁₆	C₂²
prime radical	C₂×#6771	C₂
cosocle	C₃×C₄×C₅	C₂⁴
hypercenter	M₁₆	D₃×D₅
hypocenter	C₃×C₅	#568
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₁₅	C₂	semidirect
3. C₅×D₃×M₁₆	C₂	semidirect
4. C₃×D₅×M₁₆	C₂	semidirect
5. #91292	C₂	semidirect
6. D₃×#681	C₂	semidirect
7. D₅×#208	C₂	semidirect
8. #91268	C₂	semidirect
9. #91267	C₂	semidirect
10. #91266	C₂	semidirect
11. #91265	C₂	semidirect
30. #6705	C₂²	semidirect
31. C₈×D₁₅	C₂²	semidirect
33. C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
34. C₅×D₃×C₈	C₂²	semidirect
36. C₃×#676	C₂²	semidirect
37. C₃×C₈×D₅	C₂²	semidirect
38. #6651	C₂²	semidirect
39. #6650	C₂²	semidirect
40. #6649	C₂²	semidirect
41. #6648	C₂²	semidirect
42. D₃×#168	C₂²	semidirect
43. D₅×C₃⋊C₈	C₂²	semidirect
53. D₅×M₁₆	D₃	semidirect
103. D₃×M₁₆	D₅	semidirect
132. #676	C₂×D₃	semidirect
136. C₈×D₅	C₂×D₃	semidirect
182. ΓL(1,𝔽₂₅)	C₂×D₅	semidirect
186. D₃×C₈	C₂×D₅	semidirect
333. C₃×C₅	#568	semidirect
407. C₅	#5745	semidirect
426. C₃	#66079	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6771	2
M₁₆×D₁₅	2
C₅×D₃×M₁₆	2
C₃×D₅×M₁₆	2
#91292	2
D₃×#681	2
D₅×#208	2
#91268	2
#91267	2
#91266	2
#91265	2
#66079	3
#5745	5