Subgroups — #14313001

Order 1920.

440 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	D₁₅×#131	C₂	1	1	yes	maximal, characteristic
2	D₁₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#350	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746382	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746336	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746329	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599918	—	3	1	no	maximal, Hall
9	#41×D₁₅	C₄	1	1	yes	characteristic
10	C₃×C₅×#131	C₂²	1	1	yes	characteristic
11	#91837	C₄	1	1	yes	characteristic
12	#91796	—	2	1	no	—
13	#91796	C₄	1	1	yes	characteristic
14	M₁₆×D₁₅	—	2	1	no	—
15	M₁₆×D₁₅	C₄	1	1	yes	characteristic
16	#91790	—	2	1	no	—
17	#91790	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₅	—	2	1	no	—
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
22	#91096	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
24	#91082	—	2	1	no	—
25	#91082	—	2	1	no	—
26	#91082	—	2	1	no	—
27	C₁₆×D₁₅	—	2	1	no	—
28	#69125	—	5	1	no	maximal, Hall
29	D₅×#131	—	3	1	no	—
30	D₅×M₃₂	—	3	1	no	—
31	C₂×#3930	—	3	1	no	—
32	C₅×#350	D₃	1	1	yes	characteristic, complemented
33	#64781	—	3	1	no	—
34	#64735	—	3	1	no	—
35	#64728	—	3	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic
37	#6821	C₈	1	1	yes	characteristic
38	Q₈×D₁₅	C₈	1	1	yes	characteristic
39	#6819	—	2	1	no	—
40	#6819	C₈	1	1	yes	characteristic
41	D₄×D₁₅	—	2	1	no	—
42	D₄×D₁₅	C₈	1	1	yes	characteristic
43	#6817	—	2	1	no	—
44	#6817	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₅	—	2	1	no	—
46	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	#6710	—	2	1	no	—
52	#6710	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
55	#6705	—	2	1	no	—
56	#6705	—	2	1	no	—
57	#6705	—	2	1	no	—
58	C₈×D₁₅	—	2	1	no	—
59	C₈×D₁₅	—	2	1	no	—
60	C₈×D₁₅	—	2	1	no	—
61	C₈×D₁₅	D₄	1	1	yes	characteristic
62	C₈×D₁₅	D₄	1	1	yes	characteristic
63	C₈×D₁₅	D₄	1	1	yes	characteristic
64	C₈×D₁₅	D₄	1	1	yes	characteristic
65	C₃×C₅×C₁₆	—	2	1	no	—
66	C₃×C₅×C₁₆	—	2	1	no	—
67	C₃⋊#672	—	2	1	no	—
68	C₃⋊#672	—	2	1	no	—
69	D₃×#131	—	5	1	no	—
70	D₃×M₃₂	—	5	1	no	—
71	C₂×#798	—	5	1	no	—
72	C₃×#350	D₅	1	1	yes	characteristic, complemented
73	#4561	—	5	1	no	—
74	#4515	—	5	1	no	—
75	#4508	—	5	1	no	—
76	D₅×#41	—	3	1	no	—
77	C₅×#131	C₂×D₃	1	1	yes	characteristic
78	#4094	—	3	1	no	—
79	#4053	—	3	1	no	—
80	#4053	—	6	1	no	—
81	D₅×M₁₆	—	3	1	no	—
82	D₅×M₁₆	—	6	1	no	—
83	#4047	—	3	1	no	—
84	#4047	—	6	1	no	—
85	C₂×C₈×D₅	—	3	1	no	—
86	C₂×C₈×D₅	—	6	1	no	—
87	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
89	#3944	—	3	1	no	—
90	C₂×#672	—	3	1	no	—
91	#3930	—	6	1	no	—
92	#3930	—	6	1	no	—
93	#3930	—	6	1	no	—
94	D₅×C₁₆	—	6	1	no	—
95	#2117	—	15	1	no	Sylow
96	C₂²×D₁₅	—	2	1	no	—
97	C₂²×D₁₅	M₁₆	1	1	yes	characteristic
98	C₃×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
99	C₃×C₅×D₄	—	2	1	no	—
100	C₃×C₅×D₄	C₂×C₈	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	#1220	—	2	1	no	—
104	#1220	—	2	1	no	—
105	#1220	—	2	1	no	—
106	C₂×Dic₁₅	—	2	1	no	—
107	C₂×Dic₁₅	M₁₆	1	1	yes	characteristic
108	D₆₀	—	2	1	no	—
109	D₆₀	C₂×C₈	1	1	yes	characteristic
110	C₄×D₁₅	—	2	1	no	—
111	C₄×D₁₅	—	2	1	no	—
112	C₄×D₁₅	—	2	1	no	—
113	C₄×D₁₅	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×D₁₅	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
116	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
117	Dic₃₀	—	2	1	no	—
118	Dic₃₀	C₂×C₈	1	1	yes	characteristic
119	C₃×C₅×C₈	—	2	1	no	—
120	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
121	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
122	C₃⋊#168	—	2	1	no	—
123	C₃⋊#168	C₂²⋊C₄	1	1	yes	characteristic
124	C₃⋊#168	C₂²⋊C₄	1	1	yes	characteristic
125	D₃×#41	—	5	1	no	—
126	C₃×#131	C₂×D₅	1	1	yes	characteristic
127	#948	—	5	1	no	—
128	#907	—	5	1	no	—
129	#907	—	10	1	no	—
130	D₃×M₁₆	—	5	1	no	—
131	D₃×M₁₆	—	10	1	no	—
132	#901	—	5	1	no	—
133	#901	—	10	1	no	—
134	C₂×D₃×C₈	—	5	1	no	—
135	C₂×D₃×C₈	—	10	1	no	—
136	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
137	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
138	#812	—	5	1	no	—
139	C₂×C₃⋊C₁₆	—	5	1	no	—
140	#798	—	10	1	no	—
141	#798	—	10	1	no	—
142	#798	—	10	1	no	—
143	D₃×C₁₆	—	10	1	no	—
144	C₅×#41	C₄×D₃	1	1	yes	characteristic
145	#713	—	3	1	no	—
146	Q₈×D₅	—	3	1	no	—
147	#711	—	3	1	no	—
148	#711	—	6	1	no	—
149	D₄×D₅	—	3	1	no	—
150	D₄×D₅	—	6	1	no	—
151	#709	—	3	1	no	—
152	#709	—	6	1	no	—
153	C₂×C₄×D₅	—	3	1	no	—
154	C₂×C₄×D₅	—	6	1	no	—
155	C₅×M₁₆	—	2	1	no	—
156	C₅×M₁₆	C₄×D₃	1	1	yes	characteristic
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
159	#681	—	3	1	no	—
160	#681	—	6	1	no	—
161	C₂×#168	—	3	1	no	—
162	C₂×#168	—	6	1	no	—
163	#676	—	6	1	no	—
164	#676	—	6	1	no	—
165	#676	—	6	1	no	—
166	C₈×D₅	—	3	1	no	—
167	C₈×D₅	—	3	1	no	—
168	C₈×D₅	—	3	1	no	—
169	C₈×D₅	—	3	1	no	—
170	C₈×D₅	—	6	1	no	—
171	C₈×D₅	—	6	1	no	—
172	C₈×D₅	—	6	1	no	—
173	C₅×C₁₆	—	2	1	no	—
174	C₅×C₁₆	—	2	1	no	—
175	#672	—	6	1	no	—
176	#672	—	6	1	no	—
177	C₂×#131	—	15	1	no	—
178	C₂×M₃₂	—	15	1	no	—
179	C₂×M₃₂	—	15	1	no	—
180	#350	—	15	1	no	—
181	#350	—	15	1	no	—
182	#350	—	15	1	no	—
183	#350	D₁₅	1	1	yes	characteristic, complemented
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
186	C₂×D₁₅	—	2	1	no	—
187	C₂×D₁₅	—	4	1	no	—
188	C₂×D₁₅	—	4	2	no	—
189	C₂×D₁₅	C₂²⋊C₈	1	1	yes	characteristic
190	C₂×D₁₅	C₂²⋊C₈	1	1	yes	characteristic
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
194	Dic₁₅	—	2	1	no	—
195	Dic₁₅	C₂²⋊C₈	1	1	yes	characteristic
196	Dic₁₅	C₂²⋊C₈	1	1	yes	characteristic
197	C₃×#41	C₄×D₅	1	1	yes	characteristic
198	#239	—	5	1	no	—
199	D₃×Q₈	—	5	1	no	—
200	#237	—	5	1	no	—
201	#237	—	10	1	no	—
202	D₃×D₄	—	5	1	no	—
203	D₃×D₄	—	10	1	no	—
204	#235	—	5	1	no	—
205	#235	—	10	1	no	—
206	C₂×C₄×D₃	—	5	1	no	—
207	C₂×C₄×D₃	—	10	1	no	—
208	C₃×M₁₆	—	2	1	no	—
209	C₃×M₁₆	C₄×D₅	1	1	yes	characteristic
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
212	#208	—	5	1	no	—
213	#208	—	10	1	no	—
214	C₂×C₃⋊C₈	—	5	1	no	—
215	C₂×C₃⋊C₈	—	10	1	no	—
216	ΓL(1,𝔽₂₅)	—	10	1	no	—
217	ΓL(1,𝔽₂₅)	—	10	1	no	—
218	ΓL(1,𝔽₂₅)	—	10	1	no	—
219	D₃×C₈	—	5	1	no	—
220	D₃×C₈	—	5	1	no	—
221	D₃×C₈	—	5	1	no	—
222	D₃×C₈	—	5	1	no	—
223	D₃×C₈	—	10	1	no	—
224	D₃×C₈	—	10	1	no	—
225	D₃×C₈	—	10	1	no	—
226	C₃×C₁₆	—	2	1	no	—
227	C₃×C₁₆	—	2	1	no	—
228	C₃⋊C₁₆	—	10	1	no	—
229	C₃⋊C₁₆	—	10	1	no	—
230	C₂²×D₅	—	3	1	no	—
231	C₂²×D₅	—	6	1	no	—
232	C₅×Q₈	D₃×C₈	1	1	yes	characteristic
233	C₅×D₄	—	2	1	no	—
234	C₅×D₄	D₃×C₈	1	1	yes	characteristic
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂²⋊D₅	—	6	1	no	—
238	C₂²⋊D₅	—	6	1	no	—
239	C₂²⋊D₅	—	6	1	no	—
240	C₂×Dic₅	—	3	1	no	—
241	C₂×Dic₅	—	6	1	no	—
242	D₂₀	—	3	1	no	—
243	D₂₀	—	6	1	no	—
244	C₄×D₅	—	3	1	no	—
245	C₄×D₅	—	3	1	no	—
246	C₄×D₅	—	3	1	no	—
247	C₄×D₅	—	3	1	no	—
248	C₄×D₅	—	6	1	no	—
249	C₄×D₅	—	6	1	no	—
250	C₄×D₅	—	6	1	no	—
251	Dic₁₀	—	3	1	no	—
252	Dic₁₀	—	6	1	no	—
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	D₃×D₄	1	1	yes	characteristic
255	C₅×C₈	D₃×D₄	1	1	yes	characteristic
256	#168	—	3	1	no	—
257	#168	—	3	1	no	—
258	#168	—	6	1	no	—
259	C₂×#41	—	15	1	no	—
260	#131	—	15	1	no	—
261	#131	—	15	1	no	—
262	#131	—	15	1	no	—
263	#131	—	30	1	no	—
264	#131	—	30	1	no	—
265	#131	C₂×D₁₅	1	1	yes	characteristic
266	C₂×M₁₆	—	15	1	no	—
267	C₂×M₁₆	—	30	1	no	—
268	C₂²×C₈	—	15	1	no	—
269	C₂²×C₈	—	30	1	no	—
270	M₃₂	—	15	1	no	—
271	M₃₂	—	30	1	no	—
272	M₃₂	—	30	1	no	—
273	M₃₂	—	30	1	no	—
274	M₃₂	C₂×D₁₅	1	1	yes	characteristic, complemented
275	C₂×C₁₆	—	15	1	no	—
276	C₂×C₁₆	—	30	1	no	—
277	C₂×C₁₆	C₂×D₁₅	1	1	yes	characteristic, complemented
278	C₂×C₃×C₅	—	2	1	no	—
279	C₂×C₃×C₅	—	4	1	no	—
280	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
281	D₁₅	—	2	1	no	—
282	D₁₅	—	2	1	no	—
283	D₁₅	—	4	1	no	—
284	C₂²×D₃	—	5	1	no	—
285	C₂²×D₃	—	10	1	no	—
286	C₃×Q₈	C₈×D₅	1	1	yes	characteristic
287	C₃×D₄	—	2	1	no	—
288	C₃×D₄	C₈×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	#67	—	10	1	no	—
292	#67	—	10	1	no	—
293	#67	—	10	1	no	—
294	C₂×Dic₃	—	5	1	no	—
295	C₂×Dic₃	—	10	1	no	—
296	D₁₂	—	5	1	no	—
297	D₁₂	—	10	1	no	—
298	C₄×D₃	—	5	1	no	—
299	C₄×D₃	—	5	1	no	—
300	C₄×D₃	—	5	1	no	—
301	C₄×D₃	—	5	1	no	—
302	C₄×D₃	—	10	1	no	—
303	C₄×D₃	—	10	1	no	—
304	C₄×D₃	—	10	1	no	—
305	Dic₆	—	5	1	no	—
306	Dic₆	—	10	1	no	—
307	C₃×C₈	—	2	1	no	—
308	C₃×C₈	D₄×D₅	1	1	yes	characteristic
309	C₃×C₈	D₄×D₅	1	1	yes	characteristic
310	C₃⋊C₈	—	5	1	no	—
311	C₃⋊C₈	—	5	1	no	—
312	C₃⋊C₈	—	10	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
315	C₂×D₅	—	3	1	no	—
316	C₂×D₅	—	3	1	no	—
317	C₂×D₅	—	6	1	no	—
318	C₂×D₅	—	12	1	no	—
319	C₂×D₅	—	12	2	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
322	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
323	Dic₅	—	3	1	no	—
324	Dic₅	—	3	1	no	—
325	Dic₅	—	6	1	no	—
326	#41	—	15	1	no	—
327	#41	—	15	1	no	—
328	#41	—	15	1	no	—
329	#41	—	30	1	no	—
330	#41	—	30	1	no	—
331	#41	C₄×D₁₅	1	1	yes	characteristic
332	C₂×Q₈	—	15	1	no	—
333	C₂×D₄	—	15	1	no	—
334	C₂×D₄	—	30	1	no	—
335	C₂²×C₄	—	15	1	no	—
336	C₂²×C₄	—	30	1	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	15	1	no	—
339	M₁₆	—	30	1	no	—
340	M₁₆	—	30	1	no	—
341	M₁₆	—	30	1	no	—
342	M₁₆	—	30	1	no	—
343	M₁₆	C₄×D₁₅	1	1	yes	characteristic
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	15	1	no	—
346	C₂×C₈	—	15	1	no	—
347	C₂×C₈	—	15	1	no	—
348	C₂×C₈	—	15	1	no	—
349	C₂×C₈	—	15	1	no	—
350	C₂×C₈	—	30	1	no	—
351	C₂×C₈	—	30	1	no	—
352	C₂×C₈	—	30	1	no	—
353	C₂×C₈	—	30	1	no	—
354	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
355	C₁₆	—	2	1	no	—
356	C₁₆	—	2	1	no	—
357	C₁₆	—	30	1	no	—
358	C₁₆	—	30	1	no	—
359	C₃×C₅	#2117	1	1	yes	characteristic, complemented, Hall
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
362	C₂×D₃	—	5	1	no	—
363	C₂×D₃	—	5	1	no	—
364	C₂×D₃	—	10	1	no	—
365	C₂×D₃	—	20	1	no	—
366	C₂×D₃	—	20	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
369	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
370	Dic₃	—	5	1	no	—
371	Dic₃	—	5	1	no	—
372	Dic₃	—	10	1	no	—
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	—	4	1	no	—
375	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
376	D₅	—	6	1	no	—
377	D₅	—	6	1	no	—
378	D₅	—	12	1	no	—
379	C₂³	—	15	1	no	—
380	C₂³	—	30	1	no	—
381	Q₈	—	15	1	no	—
382	Q₈	—	30	1	no	—
383	Q₈	C₈×D₁₅	1	1	yes	characteristic
384	D₄	—	2	1	no	—
385	D₄	—	15	1	no	—
386	D₄	—	30	1	no	—
387	D₄	—	30	1	no	—
388	D₄	—	30	1	no	—
389	D₄	—	30	1	no	—
390	D₄	C₈×D₁₅	1	1	yes	characteristic
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	15	1	no	—
393	C₂×C₄	—	15	1	no	—
394	C₂×C₄	—	15	1	no	—
395	C₂×C₄	—	15	1	no	—
396	C₂×C₄	—	15	1	no	—
397	C₂×C₄	—	30	1	no	—
398	C₂×C₄	—	30	1	no	—
399	C₂×C₄	—	30	1	no	—
400	C₂×C₄	—	30	1	no	—
401	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	15	1	no	—
404	C₈	—	15	1	no	—
405	C₈	—	30	1	no	—
406	C₈	D₄×D₁₅	1	1	yes	characteristic
407	C₈	D₄×D₁₅	1	1	yes	characteristic
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	4	1	no	—
410	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
411	D₃	—	10	1	no	—
412	D₃	—	10	1	no	—
413	D₃	—	20	1	no	—
414	C₅	#69125	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	2	1	no	—
416	C₂²	—	15	1	no	—
417	C₂²	—	15	1	no	—
418	C₂²	—	30	1	no	—
419	C₂²	—	60	1	no	—
420	C₂²	—	60	2	no	—
421	C₂²	M₁₆×D₁₅	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	15	1	no	—
424	C₄	—	15	1	no	—
425	C₄	—	30	1	no	—
426	C₄	C₂²⋊C₄×D₁₅	1	1	yes	characteristic
427	C₄	C₂×C₈×D₁₅	1	1	yes	characteristic
428	C₃	#10599918	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	2	1	no	—
430	C₂	—	4	1	no	—
431	C₂	—	30	1	no	—
432	C₂	—	30	1	no	—
433	C₂	—	60	1	no	—
434	C₂	D₁₅×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄×D₁₅
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₁₅
Fitting	C₃×C₅×#350	C₂
socle	C₂×C₃×C₅	C₂×C₂²⋊C₈
prime radical	#41×D₁₅	C₄
cosocle	C₂×C₃×C₅×C₈	C₂³
hypercenter	#350	D₁₅
hypocenter	C₃×C₅	#2117
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #350

Complements

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

N	H ≅ G/N	type
2. D₁₅×M₃₂	C₂	semidirect
3. C₂×#91082	C₂	semidirect
4. C₃×C₅×#350	C₂	semidirect
5. #11746382	C₂	semidirect
6. #11746336	C₂	semidirect
7. #11746329	C₂	semidirect
20. C₃×C₅×M₃₂	C₂²	semidirect
21. C₂×C₃×C₅×C₁₆	C₂²	semidirect
22. #91096	C₂²	semidirect
23. C₂×C₃⋊#672	C₂²	semidirect
32. C₅×#350	D₃	semidirect
72. C₃×#350	D₅	semidirect
87. C₅×M₃₂	C₂×D₃	semidirect
88. C₂×C₅×C₁₆	C₂×D₃	semidirect
136. C₃×M₃₂	C₂×D₅	semidirect
137. C₂×C₃×C₁₆	C₂×D₅	semidirect
183. #350	D₁₅	semidirect
274. M₃₂	C₂×D₁₅	semidirect
277. C₂×C₁₆	C₂×D₁₅	semidirect
359. C₃×C₅	#2117	semidirect
414. C₅	#69125	semidirect
428. C₃	#10599918	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×#131	2
D₁₅×M₃₂	2
C₂×#91082	2
C₃×C₅×#350	2
#11746382	2
#11746336	2
#11746329	2
#10599918	3
#69125	5