Subgroups — C₂×D₁₅×SD₃₂ #14478215

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91111	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₅×SD₃₂	C₂	1	8	yes	maximal, direct product factor
7	C₂×#91084	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₆×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₅×SD₃₂	—	3	1	no	maximal, Hall
10	C₂×Q₈×D₁₅	—	2	1	no	—
11	C₂×D₄×D₁₅	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×#6718	—	2	1	no	—
15	C₂×#6715	—	2	1	no	—
16	Q₁₆×D₁₅	—	2	2	no	—
17	Q₁₆×D₁₅	C₂²	1	4	yes	complemented
18	D₈×D₁₅	—	2	2	no	—
19	D₈×D₁₅	C₂²	1	4	yes	—
20	C₂×Dic₆₀	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	#91112	C₂²	1	4	yes	complemented
26	#91111	C₂²	1	4	yes	complemented
27	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
28	#91084	C₂²	1	4	yes	complemented
29	C₁₆×D₁₅	C₂²	1	4	yes	complemented
30	C₂×D₃×SD₃₂	—	5	1	no	maximal, Hall
31	C₂×D₅×Q₁₆	—	3	1	no	—
32	C₂×D₅×D₈	—	3	1	no	—
33	C₂×C₅×SD₃₂	D₃	1	1	yes	characteristic, complemented
34	C₂×#3960	—	3	1	no	—
35	C₂×#3959	—	3	1	no	—
36	D₅×SD₃₂	—	3	8	no	—
37	C₂×#3932	—	3	1	no	—
38	C₂×D₅×C₁₆	—	3	1	no	—
39	C₂³×D₁₅	—	4	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×#1220	—	4	1	no	—
43	Q₈×D₁₅	—	2	4	no	—
44	Q₈×D₁₅	—	4	2	no	—
45	D₄×D₁₅	—	2	4	no	—
46	D₄×D₁₅	—	4	2	no	—
47	C₂×D₆₀	—	2	1	no	—
48	C₂×C₄×D₁₅	—	4	1	no	—
49	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
50	C₂×Dic₃₀	—	2	1	no	—
51	C₂×Dic₃₀	—	4	1	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	complemented
54	C₃×C₅×D₈	—	2	1	no	—
55	C₃×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	#6718	—	2	4	no	—
58	#6715	—	2	4	no	—
59	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
60	Dic₆₀	—	2	1	no	—
61	Dic₆₀	C₂³	1	2	yes	complemented
62	D₁₂₀	—	2	1	no	—
63	D₁₂₀	C₂³	1	2	yes	—
64	C₈×D₁₅	D₄	1	2	yes	—
65	C₈×D₁₅	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₃⋊#672	C₂³	1	2	yes	complemented
68	C₂×D₃×Q₁₆	—	5	1	no	—
69	C₂×D₃×D₈	—	5	1	no	—
70	C₂×C₃×SD₃₂	D₅	1	1	yes	characteristic, complemented
71	C₂×#828	—	5	1	no	—
72	C₂×#827	—	5	1	no	—
73	D₃×SD₃₂	—	5	8	no	—
74	C₂×#800	—	5	1	no	—
75	C₂×D₃×C₁₆	—	5	1	no	—
76	C₂×Q₈×D₅	—	6	1	no	—
77	C₂×D₄×D₅	—	6	1	no	—
78	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
80	C₂×#689	—	6	1	no	—
81	C₂×#686	—	6	1	no	—
82	D₅×Q₁₆	—	3	4	no	—
83	D₅×Q₁₆	—	6	2	no	—
84	D₅×D₈	—	3	4	no	—
85	D₅×D₈	—	6	2	no	—
86	C₂×Dic₂₀	—	3	1	no	—
87	C₂×D₄₀	—	3	1	no	—
88	C₂×C₈×D₅	—	3	1	no	—
89	C₅×SD₃₂	C₂×D₃	1	4	yes	complemented
90	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
91	#3960	—	3	4	no	—
92	#3959	—	3	4	no	—
93	C₂×#672	—	3	1	no	—
94	#3932	—	3	4	no	—
95	D₅×C₁₆	—	3	4	no	—
96	C₂²×SD₃₂	—	15	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×D₁₅	—	4	1	no	—
99	C₂²×D₁₅	—	4	4	no	—
100	C₂²×D₁₅	—	8	4	no	—
101	C₂²×D₁₅	D₈	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	4	1	no	—
104	C₃×C₅×D₄	—	2	2	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	#1220	—	4	4	no	—
109	C₂×Dic₁₅	—	4	1	no	—
110	C₂×Dic₁₅	D₈	1	1	yes	characteristic
111	D₆₀	—	2	2	no	—
112	D₆₀	—	4	1	no	—
113	C₄×D₁₅	—	4	4	no	—
114	C₄×D₁₅	D₈	1	2	yes	—
115	C₄×D₁₅	C₂×D₄	1	2	yes	—
116	Dic₃₀	—	2	2	no	—
117	Dic₃₀	—	4	1	no	—
118	Dic₃₀	—	4	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₃⋊#168	C₂×D₄	1	2	yes	—
122	C₂×D₃×Q₈	—	10	1	no	—
123	C₂×D₃×D₄	—	10	1	no	—
124	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
125	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
126	C₂×#216	—	10	1	no	—
127	C₂×#213	—	10	1	no	—
128	D₃×Q₁₆	—	5	4	no	—
129	D₃×Q₁₆	—	10	2	no	—
130	D₃×D₈	—	5	4	no	—
131	D₃×D₈	—	10	2	no	—
132	C₂×Dic₁₂	—	5	1	no	—
133	C₂×D₂₄	—	5	1	no	—
134	C₂×D₃×C₈	—	5	1	no	—
135	C₃×SD₃₂	C₂×D₅	1	4	yes	complemented
136	C₂×C₃×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
137	#828	—	5	4	no	—
138	#827	—	5	4	no	—
139	C₂×C₃⋊C₁₆	—	5	1	no	—
140	#800	—	5	4	no	—
141	D₃×C₁₆	—	5	4	no	—
142	C₂³×D₅	—	12	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₂²⋊D₅	—	12	1	no	—
146	Q₈×D₅	—	6	4	no	—
147	Q₈×D₅	—	12	2	no	—
148	D₄×D₅	—	6	4	no	—
149	D₄×D₅	—	12	2	no	—
150	C₂×D₂₀	—	6	1	no	—
151	C₂×C₄×D₅	—	3	1	no	—
152	C₂×C₄×D₅	—	12	1	no	—
153	C₂×Dic₁₀	—	6	1	no	—
154	C₂×Dic₁₀	—	12	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	C₂²×D₃	1	2	yes	complemented
157	C₅×D₈	—	2	1	no	—
158	C₅×D₈	C₂²×D₃	1	2	yes	—
159	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
160	#689	—	6	4	no	—
161	#686	—	6	4	no	—
162	C₂×#168	—	3	1	no	—
163	Dic₂₀	—	3	2	no	—
164	Dic₂₀	—	6	1	no	—
165	D₄₀	—	3	2	no	—
166	D₄₀	—	6	1	no	—
167	C₈×D₅	—	3	2	no	—
168	C₈×D₅	—	3	2	no	—
169	C₅×C₁₆	C₂²×D₃	1	2	yes	complemented
170	#672	—	3	2	no	—
171	C₂²×Q₁₆	—	15	1	no	—
172	C₂²×D₈	—	15	1	no	—
173	C₂×SD₃₂	—	15	1	no	—
174	C₂×SD₃₂	—	15	1	no	—
175	C₂×SD₃₂	—	15	8	no	—
176	C₂×SD₃₂	—	15	1	no	—
177	C₂×SD₃₂	D₁₅	1	1	yes	characteristic, direct product factor
178	C₂²×C₁₆	—	15	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	8	2	no	—
181	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
182	C₂×D₁₅	—	4	2	no	—
183	C₂×D₁₅	—	8	2	no	—
184	C₂×D₁₅	—	8	8	no	—
185	C₂×D₁₅	SD₃₂	1	4	yes	direct product factor
186	C₂×D₁₅	C₂×D₈	1	2	yes	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
190	Dic₁₅	—	4	2	no	—
191	Dic₁₅	C₂×D₈	1	2	yes	—
192	C₂³×D₃	—	20	1	no	—
193	C₂×C₃×Q₈	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×#67	—	20	1	no	—
196	D₃×Q₈	—	10	4	no	—
197	D₃×Q₈	—	20	2	no	—
198	D₃×D₄	—	10	4	no	—
199	D₃×D₄	—	20	2	no	—
200	C₂×D₁₂	—	10	1	no	—
201	C₂×C₄×D₃	—	5	1	no	—
202	C₂×C₄×D₃	—	20	1	no	—
203	C₂×Dic₆	—	10	1	no	—
204	C₂×Dic₆	—	20	1	no	—
205	C₃×Q₁₆	—	2	1	no	—
206	C₃×Q₁₆	C₂²×D₅	1	2	yes	complemented
207	C₃×D₈	—	2	1	no	—
208	C₃×D₈	C₂²×D₅	1	2	yes	—
209	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
210	#216	—	10	4	no	—
211	#213	—	10	4	no	—
212	C₂×C₃⋊C₈	—	5	1	no	—
213	Dic₁₂	—	5	2	no	—
214	Dic₁₂	—	10	1	no	—
215	D₂₄	—	5	2	no	—
216	D₂₄	—	10	1	no	—
217	D₃×C₈	—	5	2	no	—
218	D₃×C₈	—	5	2	no	—
219	C₃×C₁₆	C₂²×D₅	1	2	yes	complemented
220	C₃⋊C₁₆	—	5	2	no	—
221	C₂³×C₅	—	4	1	no	—
222	C₂²×D₅	—	3	1	no	—
223	C₂²×D₅	—	12	4	no	—
224	C₂²×D₅	—	12	1	no	—
225	C₂²×D₅	—	24	4	no	—
226	C₅×Q₈	—	2	2	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂²⋊D₅	—	12	4	no	—
233	C₂×Dic₅	—	3	1	no	—
234	C₂×Dic₅	—	12	1	no	—
235	D₂₀	—	6	2	no	—
236	D₂₀	—	12	1	no	—
237	C₄×D₅	—	3	2	no	—
238	C₄×D₅	—	3	2	no	—
239	C₄×D₅	—	12	4	no	—
240	Dic₁₀	—	6	2	no	—
241	Dic₁₀	—	12	4	no	—
242	Dic₁₀	—	12	1	no	—
243	C₅×C₈	D₃×D₄	1	1	yes	characteristic
244	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
245	#168	—	3	2	no	—
246	C₂²×Q₈	—	30	1	no	—
247	C₂²×D₄	—	30	1	no	—
248	C₂×Q₁₆	—	15	4	no	—
249	C₂×Q₁₆	—	15	1	no	—
250	C₂×Q₁₆	—	30	2	no	—
251	C₂×Q₁₆	—	30	1	no	—
252	C₂×Q₁₆	C₂×D₁₅	1	1	yes	characteristic, complemented
253	C₂×D₈	—	15	4	no	—
254	C₂×D₈	—	15	1	no	—
255	C₂×D₈	—	30	2	no	—
256	C₂×D₈	—	30	1	no	—
257	C₂×D₈	C₂×D₁₅	1	1	yes	characteristic
258	C₂²×C₈	—	15	1	no	—
259	SD₃₂	—	15	4	no	—
260	SD₃₂	—	15	4	no	—
261	SD₃₂	—	15	4	no	—
262	SD₃₂	C₂×D₁₅	1	4	yes	direct product factor
263	C₂×C₁₆	—	15	1	no	—
264	C₂×C₁₆	—	15	4	no	—
265	C₂×C₁₆	C₂×D₁₅	1	1	yes	characteristic, complemented
266	C₂×C₃×C₅	—	8	2	no	—
267	C₂×C₃×C₅	C₂×SD₃₂	1	2	yes	complemented
268	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
269	D₁₅	—	8	2	no	—
270	D₁₅	C₂×SD₃₂	1	4	yes	direct product factor
271	C₂³×C₃	—	4	1	no	—
272	C₂²×D₃	—	5	1	no	—
273	C₂²×D₃	—	20	4	no	—
274	C₂²×D₃	—	20	1	no	—
275	C₂²×D₃	—	40	4	no	—
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	4	1	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
282	#67	—	20	4	no	—
283	C₂×Dic₃	—	5	1	no	—
284	C₂×Dic₃	—	20	1	no	—
285	D₁₂	—	10	2	no	—
286	D₁₂	—	20	1	no	—
287	C₄×D₃	—	5	2	no	—
288	C₄×D₃	—	5	2	no	—
289	C₄×D₃	—	20	4	no	—
290	Dic₆	—	10	2	no	—
291	Dic₆	—	20	4	no	—
292	Dic₆	—	20	1	no	—
293	C₃×C₈	D₄×D₅	1	1	yes	characteristic
294	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
295	C₃⋊C₈	—	5	2	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
299	C₂×D₅	—	3	4	no	—
300	C₂×D₅	—	3	2	no	—
301	C₂×D₅	—	12	2	no	—
302	C₂×D₅	—	24	8	no	—
303	C₂×D₅	—	24	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	D₃×D₈	1	1	yes	characteristic
306	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
307	Dic₅	—	3	2	no	—
308	Dic₅	—	12	2	no	—
309	C₂⁴	—	60	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	30	4	no	—
312	C₂×Q₈	—	30	1	no	—
313	C₂×Q₈	—	60	1	no	—
314	C₂×Q₈	—	60	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	30	4	no	—
317	C₂×D₄	—	30	1	no	—
318	C₂×D₄	—	60	2	no	—
319	C₂×D₄	—	60	1	no	—
320	C₂²×C₄	—	15	1	no	—
321	C₂²×C₄	—	60	1	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	15	2	no	—
324	Q₁₆	—	30	4	no	—
325	Q₁₆	—	30	1	no	—
326	Q₁₆	C₂²×D₁₅	1	2	yes	complemented
327	D₈	—	2	1	no	—
328	D₈	—	15	2	no	—
329	D₈	—	30	4	no	—
330	D₈	—	30	1	no	—
331	D₈	C₂²×D₁₅	1	2	yes	—
332	C₂×C₈	—	15	1	no	—
333	C₂×C₈	—	15	2	no	—
334	C₂×C₈	—	15	2	no	—
335	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
336	C₁₆	—	15	2	no	—
337	C₁₆	C₂²×D₁₅	1	2	yes	complemented
338	C₃×C₅	C₂²×SD₃₂	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	8	2	no	—
341	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
342	C₂×D₃	—	5	2	no	—
343	C₂×D₃	—	5	4	no	—
344	C₂×D₃	—	20	2	no	—
345	C₂×D₃	—	40	8	no	—
346	C₂×D₃	—	40	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	D₅×D₈	1	1	yes	characteristic
349	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
350	Dic₃	—	5	2	no	—
351	Dic₃	—	20	2	no	—
352	C₂×C₅	—	8	2	no	—
353	C₂×C₅	D₃×SD₃₂	1	2	yes	complemented
354	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
355	D₅	—	3	4	no	—
356	D₅	—	24	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	15	1	no	—
359	C₂³	—	60	4	no	—
360	C₂³	—	60	1	no	—
361	C₂³	—	120	4	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	1	no	—
364	Q₈	—	30	2	no	—
365	Q₈	—	60	4	no	—
366	Q₈	—	60	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	1	no	—
369	D₄	—	30	2	no	—
370	D₄	—	60	4	no	—
371	D₄	—	60	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	15	1	no	—
374	C₂×C₄	—	15	2	no	—
375	C₂×C₄	—	15	2	no	—
376	C₂×C₄	—	60	4	no	—
377	C₂×C₄	—	60	1	no	—
378	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
379	C₈	—	15	2	no	—
380	C₈	D₄×D₁₅	1	1	yes	characteristic
381	C₈	C₂³×D₁₅	1	1	yes	characteristic
382	C₂×C₃	—	8	2	no	—
383	C₂×C₃	D₅×SD₃₂	1	2	yes	complemented
384	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
385	D₃	—	5	4	no	—
386	D₃	—	40	2	no	—
387	C₅	C₂×D₃×SD₃₂	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	4	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	15	4	no	—
391	C₂²	—	15	2	no	—
392	C₂²	—	60	2	no	—
393	C₂²	—	120	8	no	—
394	C₂²	—	120	2	no	—
395	C₂²	D₈×D₁₅	1	1	yes	characteristic
396	C₄	—	4	2	no	—
397	C₄	—	15	2	no	—
398	C₄	—	60	2	no	—
399	C₄	D₈×D₁₅	1	1	yes	characteristic
400	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
401	C₃	C₂×D₅×SD₃₂	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	8	2	no	—
403	C₂	—	15	4	no	—
404	C₂	—	120	2	no	—
405	C₂	D₁₅×SD₃₂	1	2	yes	direct product factor
406	C₂	C₂×D₈×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₅
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂³×D₁₅
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂×D₈×D₁₅	C₂
hypercenter	C₂×SD₃₂	D₁₅
hypocenter	C₃×C₅	C₂²×SD₃₂
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×D₁₅	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×#91112	C₂	semidirect
5. C₂×#91111	C₂	semidirect
6. D₁₅×SD₃₂	C₂	direct (N × H)
7. C₂×#91084	C₂	semidirect
8. C₂×C₁₆×D₁₅	C₂	semidirect
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. Q₁₆×D₁₅	C₂²	semidirect
20. C₂×Dic₆₀	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₃×C₅×C₁₆	C₂²	semidirect
25. #91112	C₂²	semidirect
26. #91111	C₂²	semidirect
27. C₂×C₃⋊#672	C₂²	semidirect
28. #91084	C₂²	semidirect
29. C₁₆×D₁₅	C₂²	semidirect
33. C₂×C₅×SD₃₂	D₃	semidirect
53. C₃×C₅×Q₁₆	C₂³	semidirect
61. Dic₆₀	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₃⋊#672	C₂³	semidirect
70. C₂×C₃×SD₃₂	D₅	semidirect
78. C₂×C₅×Q₁₆	C₂×D₃	semidirect
89. C₅×SD₃₂	C₂×D₃	semidirect
90. C₂×C₅×C₁₆	C₂×D₃	semidirect
124. C₂×C₃×Q₁₆	C₂×D₅	semidirect
135. C₃×SD₃₂	C₂×D₅	semidirect
136. C₂×C₃×C₁₆	C₂×D₅	semidirect
156. C₅×Q₁₆	C₂²×D₃	semidirect
169. C₅×C₁₆	C₂²×D₃	semidirect
177. C₂×SD₃₂	D₁₅	direct (N × H)
185. C₂×D₁₅	SD₃₂	direct (N × H)
206. C₃×Q₁₆	C₂²×D₅	semidirect
219. C₃×C₁₆	C₂²×D₅	semidirect
252. C₂×Q₁₆	C₂×D₁₅	semidirect
262. SD₃₂	C₂×D₁₅	direct (N × H)
265. C₂×C₁₆	C₂×D₁₅	semidirect
267. C₂×C₃×C₅	C₂×SD₃₂	semidirect
270. D₁₅	C₂×SD₃₂	direct (N × H)
326. Q₁₆	C₂²×D₁₅	semidirect
337. C₁₆	C₂²×D₁₅	semidirect
338. C₃×C₅	C₂²×SD₃₂	semidirect
353. C₂×C₅	D₃×SD₃₂	semidirect
383. C₂×C₃	D₅×SD₃₂	semidirect
387. C₅	C₂×D₃×SD₃₂	semidirect
401. C₃	C₂×D₅×SD₃₂	semidirect
405. C₂	D₁₅×SD₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×D₁₅	2
C₂×D₈×D₁₅	2
C₂×C₃×C₅×SD₃₂	2
C₂×#91112	2
C₂×#91111	2
D₁₅×SD₃₂	2
C₂×#91084	2
C₂×C₁₆×D₁₅	2
C₂×D₅×SD₃₂	3
C₂×D₃×SD₃₂	5

Subgroups — C2×D15×SD32 #14478215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₅×SD₃₂ #14478215