Subgroups — #12252513

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#2169	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602226	C₂	1	2	yes	maximal, complemented
5	#10601651	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600077	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600070	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599899	C₂	1	2	yes	maximal, complemented
9	#10599896	C₂	1	2	yes	maximal, complemented
10	C₁₆×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#3930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₅	C₂²	1	2	yes	—
13	C₄×D₄×D₅	C₄	1	1	yes	characteristic
14	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
15	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
16	C₈×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂×#3944	C₂²	1	2	yes	complemented
18	D₄×#168	C₄	1	1	yes	characteristic
19	D₅×M₃₂	—	2	8	no	—
20	C₂×#3930	C₂²	1	2	yes	—
21	C₂×#3930	C₂²	1	1	yes	characteristic
22	C₂×#3930	C₂²	1	1	yes	characteristic
23	C₂×D₅×C₁₆	C₂²	1	2	yes	complemented
24	C₂×D₅×C₁₆	C₂²	1	2	yes	complemented
25	#65123	C₄	1	1	yes	characteristic
26	D₅×C₄⋊C₈	C₄	1	1	yes	characteristic
27	#65014	C₄	1	2	yes	—
28	D₅×C₂²⋊C₈	C₄	1	2	yes	—
29	C₈×D₂₀	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
31	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²⋊#672	C₂²	1	2	yes	complemented
35	#64727	C₂²	1	2	yes	complemented
36	#64727	C₂²	1	2	yes	complemented
37	#64722	C₂²	1	1	yes	characteristic, complemented
38	#64722	C₂²	1	1	yes	characteristic, complemented
39	#64721	C₂²	1	2	yes	complemented
40	C₄⋊#672	C₂²	1	1	yes	characteristic, complemented
41	C₄×#672	C₂²	1	1	yes	characteristic, complemented
42	D₄×M₃₂	—	5	1	no	maximal, Sylow
43	C₂×D₄×D₅	C₈	1	1	yes	characteristic
44	C₂²×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	D₄×Dic₅	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
49	C₂²×#168	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₅	—	2	4	no	—
51	C₂×C₈×D₅	—	2	4	no	—
52	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂³	1	2	yes	—
56	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
57	#4039	C₈	1	1	yes	characteristic
58	D₅×C₄⋊C₄	C₈	1	1	yes	characteristic
59	#4027	C₈	1	2	yes	—
60	D₅×C₂²⋊C₄	C₈	1	2	yes	—
61	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
63	C₅×M₃₂	—	2	4	no	—
64	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₁₆	C₂³	1	2	yes	—
66	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
67	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
69	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²⋊#168	C₂×C₄	1	2	yes	—
71	#3952	C₂×C₄	1	2	yes	—
72	#3952	C₂×C₄	1	2	yes	—
73	#3946	C₂×C₄	1	2	yes	—
74	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₅	C₂³	1	1	yes	characteristic
76	#3944	—	2	4	no	—
77	C₂×#672	C₂³	1	1	yes	characteristic
78	C₂×#672	C₂³	1	2	yes	—
79	C₂×#672	C₂³	1	1	yes	characteristic
80	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
81	C₄×#168	C₂×C₄	1	1	yes	characteristic
82	#3930	—	2	4	no	—
83	#3930	—	2	2	no	—
84	#3930	D₄	1	4	yes	complemented
85	D₅×C₁₆	—	2	4	no	—
86	D₅×C₁₆	—	2	4	no	—
87	C₂²×M₃₂	—	5	2	no	—
88	C₂×C₈×D₄	—	5	1	no	—
89	#2169	—	5	1	no	—
90	#2169	D₅	1	1	yes	characteristic, complemented
91	#2168	—	5	2	no	—
92	#2168	—	5	2	no	—
93	D₄×C₁₆	—	5	1	no	—
94	D₄×C₁₆	—	5	1	no	—
95	#2150	—	5	1	no	—
96	#2112	—	5	2	no	—
97	C₄×M₃₂	—	5	1	no	—
98	C₂³×D₅	C₂×C₈	1	2	yes	—
99	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
102	C₂²×Dic₅	C₂×C₈	1	2	yes	—
103	D₄×D₅	—	2	4	no	—
104	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₅	—	2	4	no	—
106	C₂×C₄×D₅	—	2	4	no	—
107	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
108	C₂×C₄×D₅	C₂×C₈	1	2	yes	—
109	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
110	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
118	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
119	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
122	#685	C₂×C₈	1	2	yes	—
123	#685	C₂×C₈	1	2	yes	—
124	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
125	#683	C₂×C₈	1	2	yes	—
126	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×#168	—	2	4	no	—
130	C₂×#168	C₂²×C₄	1	1	yes	characteristic
131	C₂×#168	C₂²×C₄	1	2	yes	—
132	C₂×#168	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₅	—	2	4	no	—
134	C₈×D₅	—	2	2	no	—
135	C₈×D₅	—	2	2	no	—
136	C₈×D₅	—	2	2	no	—
137	C₈×D₅	—	2	4	no	—
138	C₈×D₅	C₂×D₄	1	2	yes	—
139	C₈×D₅	#41	1	2	yes	—
140	C₅×C₁₆	—	2	2	no	—
141	C₅×C₁₆	—	2	1	no	—
142	C₅×C₁₆	C₂×D₄	1	2	yes	complemented
143	#672	—	2	2	no	—
144	#672	—	2	1	no	—
145	#672	C₂×D₄	1	2	yes	complemented
146	C₂³×C₈	—	5	2	no	—
147	C₂×C₄×D₄	—	5	1	no	—
148	C₂×M₃₂	—	5	2	no	—
149	C₂×M₃₂	—	5	1	no	—
150	C₂×M₃₂	—	5	1	no	—
151	C₂×M₃₂	—	5	2	no	—
152	C₂×M₃₂	—	10	8	no	—
153	C₂×M₃₂	C₂×D₅	1	2	yes	complemented
154	C₂²×C₁₆	—	5	2	no	—
155	C₂²×C₁₆	—	5	2	no	—
156	C₈×D₄	—	5	2	no	—
157	C₈×D₄	—	5	1	no	—
158	C₈×D₄	—	5	1	no	—
159	C₈×D₄	—	5	2	no	—
160	C₈×D₄	—	5	1	no	—
161	C₈×D₄	C₂×D₅	1	1	yes	characteristic
162	C₂×C₄⋊C₈	—	5	1	no	—
163	C₂×C₂²⋊C₈	—	5	2	no	—
164	C₂×C₄×C₈	—	5	1	no	—
165	C₄⋊C₁₆	—	5	2	no	—
166	C₄⋊C₁₆	—	5	1	no	—
167	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
168	C₂²⋊C₁₆	—	5	2	no	—
169	C₂²⋊C₁₆	—	5	2	no	—
170	C₂²⋊C₁₆	—	5	2	no	—
171	C₂²⋊C₁₆	C₂×D₅	1	2	yes	complemented
172	#346	—	5	1	no	—
173	#346	—	5	1	no	—
174	C₄×C₁₆	—	5	1	no	—
175	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
176	C₂³×C₅	C₂²×C₈	1	2	yes	—
177	C₂²×D₅	—	2	4	no	—
178	C₂²×D₅	—	2	4	no	—
179	C₂²×D₅	—	4	2	no	—
180	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
181	C₂²×D₅	C₂²×C₈	1	2	yes	—
182	C₅×D₄	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
187	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₅	—	2	4	no	—
190	C₂×Dic₅	—	2	4	no	—
191	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
192	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
193	C₂×Dic₅	C₂²×C₈	1	2	yes	—
194	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
195	D₂₀	M₃₂	1	4	yes	complemented
196	C₄×D₅	—	2	4	no	—
197	C₄×D₅	—	2	2	no	—
198	C₄×D₅	—	2	2	no	—
199	C₄×D₅	—	2	2	no	—
200	C₄×D₅	—	2	4	no	—
201	C₄×D₅	—	4	1	no	—
202	C₄×D₅	C₄×D₄	1	2	yes	—
203	C₄×D₅	#131	1	2	yes	—
204	C₅×C₈	—	2	2	no	—
205	C₅×C₈	—	2	1	no	—
206	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
207	C₅×C₈	C₂×#41	1	1	yes	characteristic
208	#168	—	2	2	no	—
209	#168	—	2	1	no	—
210	#168	C₄×D₄	1	2	yes	—
211	C₂²×D₄	—	5	1	no	—
212	C₂³×C₄	—	5	2	no	—
213	C₂²×C₈	—	5	1	no	—
214	C₂²×C₈	—	5	2	no	—
215	C₂²×C₈	—	5	2	no	—
216	C₂²×C₈	—	5	2	no	—
217	C₂²×C₈	—	5	1	no	—
218	C₂²×C₈	—	5	2	no	—
219	C₂²×C₈	—	10	4	no	—
220	C₂²×C₈	—	10	4	no	—
221	C₂²×C₈	C₂²×D₅	1	2	yes	—
222	C₄×D₄	—	5	1	no	—
223	C₄×D₄	—	5	2	no	—
224	C₄×D₄	—	5	1	no	—
225	C₄×D₄	—	5	2	no	—
226	C₄×D₄	—	5	1	no	—
227	C₄×D₄	C₄×D₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	—	5	1	no	—
229	C₂×C₂²⋊C₄	—	5	2	no	—
230	C₂×C₄²	—	5	1	no	—
231	M₃₂	—	2	4	no	—
232	M₃₂	—	5	4	no	—
233	M₃₂	—	10	2	no	—
234	M₃₂	—	10	4	no	—
235	M₃₂	—	10	4	no	—
236	C₂×C₁₆	—	5	1	no	—
237	C₂×C₁₆	—	5	1	no	—
238	C₂×C₁₆	—	5	2	no	—
239	C₂×C₁₆	—	10	4	no	—
240	C₂×C₁₆	—	10	4	no	—
241	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
242	C₂×C₁₆	C₂²×D₅	1	2	yes	—
243	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
244	C₄⋊C₈	—	5	2	no	—
245	C₄⋊C₈	—	5	1	no	—
246	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
247	C₂²⋊C₈	—	5	2	no	—
248	C₂²⋊C₈	—	5	2	no	—
249	C₂²⋊C₈	—	5	2	no	—
250	C₂²⋊C₈	C₄×D₅	1	2	yes	—
251	C₄×C₈	—	5	1	no	—
252	C₄×C₈	—	5	1	no	—
253	C₄×C₈	—	5	1	no	—
254	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
259	C₂×D₅	—	2	1	no	—
260	C₂×D₅	—	2	1	no	—
261	C₂×D₅	—	2	2	no	—
262	C₂×D₅	—	2	2	no	—
263	C₂×D₅	—	4	8	no	—
264	C₂×D₅	C₈×D₄	1	2	yes	—
265	C₂×D₅	C₂×M₃₂	1	4	yes	complemented
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	C₂×M₃₂	1	2	yes	complemented
269	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₅	C₂×#131	1	1	yes	characteristic
271	Dic₅	—	2	1	no	—
272	Dic₅	—	2	1	no	—
273	Dic₅	—	2	2	no	—
274	Dic₅	C₈×D₄	1	2	yes	—
275	C₂⁴	—	5	2	no	—
276	C₂×D₄	—	5	2	no	—
277	C₂×D₄	—	5	1	no	—
278	C₂×D₄	—	10	4	no	—
279	C₂×D₄	C₈×D₅	1	1	yes	characteristic
280	C₂²×C₄	—	5	1	no	—
281	C₂²×C₄	—	5	2	no	—
282	C₂²×C₄	—	5	2	no	—
283	C₂²×C₄	—	5	1	no	—
284	C₂²×C₄	—	5	2	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	10	4	no	—
288	C₂²×C₄	—	10	4	no	—
289	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	5	1	no	—
293	C₂×C₈	—	5	2	no	—
294	C₂×C₈	—	5	2	no	—
295	C₂×C₈	—	5	1	no	—
296	C₂×C₈	—	5	2	no	—
297	C₂×C₈	—	10	4	no	—
298	C₂×C₈	—	10	4	no	—
299	C₂×C₈	—	10	2	no	—
300	C₂×C₈	—	10	4	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	—	10	2	no	—
303	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
305	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
306	C₄⋊C₄	—	5	2	no	—
307	C₄⋊C₄	—	5	1	no	—
308	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
309	C₂²⋊C₄	—	5	2	no	—
310	C₂²⋊C₄	—	5	2	no	—
311	C₂²⋊C₄	—	5	2	no	—
312	C₂²⋊C₄	C₈×D₅	1	2	yes	—
313	C₄²	—	5	1	no	—
314	C₄²	—	5	1	no	—
315	C₄²	—	5	1	no	—
316	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	5	2	no	—
320	C₁₆	—	10	2	no	—
321	C₁₆	—	10	1	no	—
322	C₁₆	D₄×D₅	1	2	yes	complemented
323	C₂×C₅	—	4	2	no	—
324	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
325	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
326	C₂×C₅	#3407	1	1	yes	characteristic
327	D₅	—	2	2	no	—
328	D₅	—	2	4	no	—
329	C₂³	—	5	2	no	—
330	C₂³	—	5	1	no	—
331	C₂³	—	10	4	no	—
332	C₂³	—	10	4	no	—
333	C₂³	—	20	2	no	—
334	C₂³	C₂×C₈×D₅	1	2	yes	—
335	D₄	—	2	2	no	—
336	D₄	—	5	4	no	—
337	D₄	—	10	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	5	2	no	—
342	C₂×C₄	—	5	2	no	—
343	C₂×C₄	—	5	1	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	10	4	no	—
347	C₂×C₄	—	10	4	no	—
348	C₂×C₄	—	10	4	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	—	10	2	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	20	1	no	—
353	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
354	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
355	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	2	no	—
359	C₈	—	5	2	no	—
360	C₈	—	10	1	no	—
361	C₈	—	10	2	no	—
362	C₈	C₂×D₄×D₅	1	1	yes	characteristic
363	C₈	D₅×#41	1	1	yes	characteristic
364	C₅	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	5	2	no	—
369	C₂²	—	5	4	no	—
370	C₂²	—	10	2	no	—
371	C₂²	—	10	1	no	—
372	C₂²	—	10	1	no	—
373	C₂²	—	10	2	no	—
374	C₂²	—	20	8	no	—
375	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	1	no	—
378	C₄	—	5	2	no	—
379	C₄	—	10	2	no	—
380	C₄	—	10	1	no	—
381	C₄	—	10	1	no	—
382	C₄	D₅×M₃₂	1	2	yes	complemented
383	C₄	C₄×D₄×D₅	1	1	yes	characteristic
384	C₄	D₅×#131	1	1	yes	characteristic
385	C₂	—	4	2	no	—
386	C₂	—	10	2	no	—
387	C₂	—	10	4	no	—
388	C₂	C₈×D₄×D₅	1	1	yes	characteristic
389	C₂	C₂×D₅×M₃₂	1	1	yes	characteristic
390	C₂	#10613743	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2169	C₂
prime radical	C₂×D₄×D₅	C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2169	D₅
hypocenter	C₅	D₄×M₃₂
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2169

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×M₃₂	C₂	semidirect
3. C₅×#2169	C₂	semidirect
4. #10602226	C₂	semidirect
5. #10601651	C₂	semidirect
6. #10600077	C₂	semidirect
7. #10600070	C₂	semidirect
8. #10599899	C₂	semidirect
9. #10599896	C₂	semidirect
10. C₁₆×D₂₀	C₂	semidirect
11. C₄×#3930	C₂	semidirect
14. C₂×C₅×M₃₂	C₂²	semidirect
17. C₂×#3944	C₂²	semidirect
23. C₂×D₅×C₁₆	C₂²	semidirect
24. C₂×D₅×C₁₆	C₂²	semidirect
31. C₅×C₄⋊C₁₆	C₂²	semidirect
32. C₅×C₂²⋊C₁₆	C₂²	semidirect
33. C₄×C₅×C₁₆	C₂²	semidirect
34. C₂²⋊#672	C₂²	semidirect
35. #64727	C₂²	semidirect
36. #64727	C₂²	semidirect
37. #64722	C₂²	semidirect
38. #64722	C₂²	semidirect
39. #64721	C₂²	semidirect
40. C₄⋊#672	C₂²	semidirect
41. C₄×#672	C₂²	semidirect
84. #3930	D₄	semidirect
90. #2169	D₅	semidirect
142. C₅×C₁₆	C₂×D₄	semidirect
145. #672	C₂×D₄	semidirect
153. C₂×M₃₂	C₂×D₅	semidirect
167. C₄⋊C₁₆	C₂×D₅	semidirect
171. C₂²⋊C₁₆	C₂×D₅	semidirect
175. C₄×C₁₆	C₂×D₅	semidirect
195. D₂₀	M₃₂	semidirect
265. C₂×D₅	C₂×M₃₂	semidirect
268. C₄×C₅	C₂×M₃₂	semidirect
322. C₁₆	D₄×D₅	semidirect
364. C₅	D₄×M₃₂	semidirect
382. C₄	D₅×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×M₃₂	2
C₈×D₄×D₅	2
C₅×#2169	2
#10602226	2
#10601651	2
#10600077	2
#10600070	2
#10599899	2
#10599896	2
C₁₆×D₂₀	2
C₄×#3930	2
D₄×M₃₂	5