Subgroups — M₃₂×C₂²⋊D₅ #12252511

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602756	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602226	C₂	1	2	yes	maximal, complemented
6	#10602224	C₂	1	1	yes	maximal, characteristic, complemented
7	#10602223	C₂	1	2	yes	maximal, complemented
8	#10602213	C₂	1	1	yes	maximal, characteristic, complemented
9	Dic₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#10602200	C₂	1	2	yes	maximal, complemented
11	C₁₆×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×M₃₂	—	2	4	no	—
16	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
19	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊#168	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
29	C₂×#3952	C₄	1	1	yes	characteristic
30	C₂×#3946	C₄	1	1	yes	characteristic
31	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
32	C₂×#3944	C₂²	1	1	yes	characteristic
33	C₂×#3944	C₂²	1	1	yes	characteristic
34	D₅×M₃₂	—	2	4	no	—
35	C₂×#3930	C₂²	1	2	yes	complemented
36	C₂×D₅×C₁₆	C₂²	1	2	yes	complemented
37	C₂²⋊#672	C₂²	1	2	yes	complemented
38	C₂²⋊#672	C₂²	1	2	yes	complemented
39	#64727	C₂²	1	2	yes	complemented
40	#64727	C₂²	1	2	yes	complemented
41	#64722	C₂²	1	2	yes	complemented
42	#64721	C₂²	1	2	yes	complemented
43	#64721	C₂²	1	2	yes	complemented
44	C₁₆×Dic₅	C₂²	1	2	yes	complemented
45	D₄×M₃₂	—	5	1	no	maximal, Sylow
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₅	C₈	1	1	yes	characteristic
48	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₅	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
60	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
62	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×#685	C₈	1	1	yes	characteristic
67	C₂×#683	C₈	1	1	yes	characteristic
68	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₂²×#168	C₂×C₄	1	1	yes	characteristic
70	C₂²×#168	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₅	—	2	2	no	—
72	C₂×C₈×D₅	—	2	2	no	—
73	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
77	C₅×M₃₂	—	2	2	no	—
78	C₅×M₃₂	—	2	4	no	—
79	C₅×M₃₂	D₄	1	4	yes	complemented
80	C₂×C₅×C₁₆	—	2	4	no	—
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
87	#3952	C₂×C₄	1	1	yes	characteristic
88	#3952	C₂×C₄	1	1	yes	characteristic
89	#3952	C₂×C₄	1	1	yes	characteristic
90	#3952	C₂×C₄	1	1	yes	characteristic
91	#3946	C₂×C₄	1	1	yes	characteristic
92	#3946	C₂×C₄	1	1	yes	characteristic
93	#3946	C₂×C₄	1	1	yes	characteristic
94	#3946	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂³	1	1	yes	characteristic
98	C₈×Dic₅	C₂³	1	1	yes	characteristic
99	#3944	—	2	2	no	—
100	#3944	—	2	2	no	—
101	C₂×#672	C₂³	1	2	yes	—
102	C₂×#672	C₂³	1	2	yes	—
103	#3930	—	2	4	no	—
104	D₅×C₁₆	—	2	4	no	—
105	C₂²×M₃₂	—	5	1	no	—
106	C₂²×M₃₂	D₅	1	1	yes	characteristic, complemented
107	C₂×C₈×D₄	—	5	1	no	—
108	#2169	—	5	2	no	—
109	#2168	—	5	2	no	—
110	#2168	—	5	2	no	—
111	D₄×C₁₆	—	5	2	no	—
112	#2150	—	5	1	no	—
113	#2112	—	5	1	no	—
114	#2112	—	5	1	no	—
115	C₄×M₃₂	—	5	1	no	—
116	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
117	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₅	—	2	4	no	—
127	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
130	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
131	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
132	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
133	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
134	C₂×C₄×D₅	—	2	2	no	—
135	C₂×C₄×D₅	—	2	2	no	—
136	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅×C₈	#41	1	2	yes	—
152	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
154	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
155	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
157	#685	C₂×C₈	1	1	yes	characteristic
158	#685	C₂×C₈	1	1	yes	characteristic
159	#685	C₂×C₈	1	1	yes	characteristic
160	#685	C₂×C₈	1	1	yes	characteristic
161	#683	C₂×C₈	1	1	yes	characteristic
162	#683	C₂×C₈	1	1	yes	characteristic
163	#683	C₂×C₈	1	1	yes	characteristic
164	#683	C₂×C₈	1	1	yes	characteristic
165	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
166	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
167	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×#168	—	2	2	no	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	C₂²×C₄	1	1	yes	characteristic
172	C₂×#168	C₂²×C₄	1	1	yes	characteristic
173	C₂×#168	C₂²×C₄	1	1	yes	characteristic
174	C₂×#168	C₂²×C₄	1	1	yes	characteristic
175	C₈×D₅	—	2	2	no	—
176	C₈×D₅	—	2	2	no	—
177	C₈×D₅	—	2	1	no	—
178	C₈×D₅	—	2	1	no	—
179	C₈×D₅	—	2	1	no	—
180	C₈×D₅	—	2	1	no	—
181	C₅×C₁₆	—	2	2	no	—
182	C₅×C₁₆	C₂×D₄	1	4	yes	complemented
183	#672	—	2	2	no	—
184	#672	—	2	2	no	—
185	C₂³×C₈	—	5	1	no	—
186	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
187	C₂×C₄×D₄	—	5	1	no	—
188	C₂×M₃₂	—	2	4	no	—
189	C₂×M₃₂	—	5	1	no	—
190	C₂×M₃₂	—	5	1	no	—
191	C₂×M₃₂	—	5	2	no	—
192	C₂×M₃₂	—	10	4	no	—
193	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
194	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
195	C₂×M₃₂	C₂×D₅	1	2	yes	complemented
196	C₂²×C₁₆	—	5	2	no	—
197	C₂²×C₁₆	C₂×D₅	1	2	yes	complemented
198	C₈×D₄	—	5	1	no	—
199	C₈×D₄	—	5	1	no	—
200	C₈×D₄	—	5	1	no	—
201	C₈×D₄	—	5	1	no	—
202	C₈×D₄	—	5	1	no	—
203	C₈×D₄	—	5	1	no	—
204	C₈×D₄	—	5	1	no	—
205	C₈×D₄	—	5	1	no	—
206	C₂×C₄⋊C₈	—	5	1	no	—
207	C₂×C₂²⋊C₈	—	5	1	no	—
208	C₂×C₂²⋊C₈	—	5	1	no	—
209	C₂×C₄×C₈	—	5	1	no	—
210	C₄⋊C₁₆	—	5	2	no	—
211	C₄⋊C₁₆	—	5	2	no	—
212	C₂²⋊C₁₆	—	5	2	no	—
213	C₂²⋊C₁₆	—	5	2	no	—
214	C₂²⋊C₁₆	—	5	2	no	—
215	C₂²⋊C₁₆	—	5	2	no	—
216	#346	—	5	2	no	—
217	C₄×C₁₆	—	5	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	4	1	no	—
221	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
222	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
223	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
224	C₂²×D₅	—	2	2	no	—
225	C₂²×D₅	—	2	2	no	—
226	C₂²×D₅	—	4	1	no	—
227	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
228	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
240	C₂×C₄×C₅	#131	1	2	yes	—
241	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₂²⋊D₅	—	2	2	no	—
243	C₂²⋊D₅	—	2	2	no	—
244	C₂²⋊D₅	—	2	2	no	—
245	C₂²⋊D₅	M₃₂	1	4	yes	direct product factor
246	C₂×Dic₅	—	2	2	no	—
247	C₂×Dic₅	—	2	2	no	—
248	C₂×Dic₅	—	4	1	no	—
249	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
250	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
251	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
252	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
253	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
254	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
255	C₄×D₅	—	2	1	no	—
256	C₄×D₅	—	2	1	no	—
257	C₄×D₅	—	2	1	no	—
258	C₄×D₅	—	2	1	no	—
259	C₄×D₅	—	2	2	no	—
260	C₄×D₅	—	2	2	no	—
261	C₅×C₈	—	2	1	no	—
262	C₅×C₈	—	2	1	no	—
263	C₅×C₈	C₄×D₄	1	2	yes	—
264	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
265	C₅×C₈	C₂×#41	1	1	yes	characteristic
266	#168	—	2	1	no	—
267	#168	—	2	1	no	—
268	#168	—	2	1	no	—
269	#168	—	2	1	no	—
270	C₂²×D₄	—	5	1	no	—
271	C₂³×C₄	—	5	1	no	—
272	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	5	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	5	1	no	—
280	C₂²×C₈	—	5	1	no	—
281	C₂²×C₈	—	10	2	no	—
282	C₂²×C₈	—	10	2	no	—
283	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
284	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
285	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
288	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
289	C₄×D₄	—	5	1	no	—
290	C₄×D₄	—	5	1	no	—
291	C₄×D₄	—	5	1	no	—
292	C₄×D₄	—	5	1	no	—
293	C₄×D₄	—	5	1	no	—
294	C₄×D₄	—	5	1	no	—
295	C₄×D₄	—	5	1	no	—
296	C₄×D₄	—	5	1	no	—
297	C₂×C₄⋊C₄	—	5	1	no	—
298	C₂×C₂²⋊C₄	—	5	1	no	—
299	C₂×C₂²⋊C₄	—	5	1	no	—
300	C₂×C₄²	—	5	1	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	—	2	4	no	—
303	M₃₂	—	10	2	no	—
304	M₃₂	—	10	2	no	—
305	M₃₂	—	10	4	no	—
306	M₃₂	C₂²⋊D₅	1	4	yes	direct product factor
307	C₂×C₁₆	—	2	4	no	—
308	C₂×C₁₆	—	5	2	no	—
309	C₂×C₁₆	—	5	2	no	—
310	C₂×C₁₆	—	10	4	no	—
311	C₂×C₁₆	C₂²×D₅	1	2	yes	—
312	C₂×C₁₆	C₂²×D₅	1	2	yes	—
313	C₄⋊C₈	—	5	1	no	—
314	C₄⋊C₈	—	5	1	no	—
315	C₄⋊C₈	—	5	1	no	—
316	C₄⋊C₈	—	5	1	no	—
317	C₂²⋊C₈	—	5	1	no	—
318	C₂²⋊C₈	—	5	1	no	—
319	C₂²⋊C₈	—	5	1	no	—
320	C₂²⋊C₈	—	5	1	no	—
321	C₂²⋊C₈	—	5	1	no	—
322	C₂²⋊C₈	—	5	1	no	—
323	C₂²⋊C₈	—	5	1	no	—
324	C₂²⋊C₈	—	5	1	no	—
325	C₄×C₈	—	5	1	no	—
326	C₄×C₈	—	5	1	no	—
327	C₄×C₈	—	5	1	no	—
328	C₄×C₈	—	5	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	1	no	—
334	C₂²×C₅	—	2	1	no	—
335	C₂²×C₅	—	2	1	no	—
336	C₂²×C₅	—	4	4	no	—
337	C₂²×C₅	C₈×D₄	1	2	yes	—
338	C₂²×C₅	C₂×M₃₂	1	2	yes	complemented
339	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
340	C₂×D₅	—	2	1	no	—
341	C₂×D₅	—	2	1	no	—
342	C₂×D₅	—	2	1	no	—
343	C₂×D₅	—	2	1	no	—
344	C₂×D₅	—	2	1	no	—
345	C₂×D₅	—	4	4	no	—
346	C₂×D₅	C₂×M₃₂	1	2	yes	complemented
347	C₄×C₅	—	2	1	no	—
348	C₄×C₅	—	2	1	no	—
349	C₄×C₅	C₈×D₄	1	2	yes	—
350	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
351	C₄×C₅	C₂×#131	1	1	yes	characteristic
352	Dic₅	—	2	1	no	—
353	Dic₅	—	2	1	no	—
354	Dic₅	—	2	1	no	—
355	Dic₅	—	2	1	no	—
356	Dic₅	—	2	1	no	—
357	Dic₅	C₂×M₃₂	1	2	yes	complemented
358	C₂⁴	—	5	1	no	—
359	C₂⁴	C₈×D₅	1	1	yes	characteristic
360	C₂×D₄	—	5	1	no	—
361	C₂×D₄	—	5	1	no	—
362	C₂×D₄	—	5	1	no	—
363	C₂×D₄	—	5	1	no	—
364	C₂×D₄	—	10	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	5	1	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	5	1	no	—
373	C₂²×C₄	—	5	1	no	—
374	C₂²×C₄	—	10	2	no	—
375	C₂²×C₄	—	10	2	no	—
376	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
377	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
378	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	5	1	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	1	no	—
396	C₂×C₈	—	10	1	no	—
397	C₂×C₈	—	10	1	no	—
398	C₂×C₈	—	10	1	no	—
399	C₂×C₈	—	10	2	no	—
400	C₂×C₈	—	10	2	no	—
401	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
402	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₈	#709	1	2	yes	—
405	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
406	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
407	C₄⋊C₄	—	5	1	no	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	5	1	no	—
411	C₂²⋊C₄	—	5	1	no	—
412	C₂²⋊C₄	—	5	1	no	—
413	C₂²⋊C₄	—	5	1	no	—
414	C₂²⋊C₄	—	5	1	no	—
415	C₂²⋊C₄	—	5	1	no	—
416	C₂²⋊C₄	—	5	1	no	—
417	C₂²⋊C₄	—	5	1	no	—
418	C₂²⋊C₄	—	5	1	no	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	—	5	1	no	—
423	C₁₆	—	2	2	no	—
424	C₁₆	—	10	2	no	—
425	C₁₆	—	10	2	no	—
426	C₁₆	C₂×C₂²⋊D₅	1	4	yes	complemented
427	C₂×C₅	—	2	2	no	—
428	C₂×C₅	—	2	2	no	—
429	C₂×C₅	—	4	1	no	—
430	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
431	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
432	C₂×C₅	#3407	1	1	yes	characteristic
433	D₅	—	2	2	no	—
434	D₅	—	4	1	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	5	1	no	—
439	C₂³	—	5	1	no	—
440	C₂³	—	10	2	no	—
441	C₂³	—	10	2	no	—
442	C₂³	—	20	1	no	—
443	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
444	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
445	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
446	D₄	—	5	4	no	—
447	D₄	—	10	2	no	—
448	D₄	—	10	2	no	—
449	D₄	—	10	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	1	no	—
462	C₂×C₄	—	5	1	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	1	no	—
466	C₂×C₄	—	10	1	no	—
467	C₂×C₄	—	10	1	no	—
468	C₂×C₄	—	10	1	no	—
469	C₂×C₄	—	10	2	no	—
470	C₂×C₄	—	10	2	no	—
471	C₂×C₄	—	20	1	no	—
472	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
473	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
474	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
475	C₂×C₄	#4047	1	2	yes	—
476	C₂×C₄	C₄×C₂²⋊D₅	1	2	yes	—
477	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	10	1	no	—
481	C₈	—	10	1	no	—
482	C₈	—	10	1	no	—
483	C₈	—	10	1	no	—
484	C₈	C₄×C₂²⋊D₅	1	2	yes	—
485	C₈	C₂×#709	1	1	yes	characteristic
486	C₈	C₂²×C₂²⋊D₅	1	1	yes	characteristic
487	C₅	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	5	2	no	—
497	C₂²	—	10	1	no	—
498	C₂²	—	10	1	no	—
499	C₂²	—	10	1	no	—
500	C₂²	—	10	1	no	—
501	C₂²	—	10	1	no	—
502	C₂²	—	20	4	no	—
503	C₂²	D₅×M₃₂	1	2	yes	complemented
504	C₂²	C₈×C₂²⋊D₅	1	2	yes	—
505	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	5	2	no	—
509	C₄	—	10	1	no	—
510	C₄	—	10	1	no	—
511	C₄	—	10	1	no	—
512	C₄	—	10	1	no	—
513	C₄	—	10	1	no	—
514	C₄	C₈×C₂²⋊D₅	1	2	yes	—
515	C₄	C₂×#4047	1	1	yes	characteristic
516	C₄	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	10	2	no	—
521	C₂	—	20	1	no	—
522	C₂	C₂×D₅×M₃₂	1	1	yes	characteristic
523	C₂	#10613738	1	1	yes	characteristic
524	C₂	C₂×C₈×C₂²⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×M₃₂	C₂	semidirect
3. C₂×D₅×M₃₂	C₂	semidirect
4. #10602756	C₂	semidirect
5. #10602226	C₂	semidirect
6. #10602224	C₂	semidirect
7. #10602223	C₂	semidirect
8. #10602213	C₂	semidirect
9. Dic₅×M₃₂	C₂	semidirect
10. #10602200	C₂	semidirect
11. C₁₆×C₂²⋊D₅	C₂	semidirect
18. C₂×C₅×M₃₂	C₂²	semidirect
19. C₂²×C₅×C₁₆	C₂²	semidirect
35. C₂×#3930	C₂²	semidirect
36. C₂×D₅×C₁₆	C₂²	semidirect
37. C₂²⋊#672	C₂²	semidirect
38. C₂²⋊#672	C₂²	semidirect
39. #64727	C₂²	semidirect
40. #64727	C₂²	semidirect
41. #64722	C₂²	semidirect
42. #64721	C₂²	semidirect
43. #64721	C₂²	semidirect
44. C₁₆×Dic₅	C₂²	semidirect
79. C₅×M₃₂	D₄	semidirect
106. C₂²×M₃₂	D₅	semidirect
182. C₅×C₁₆	C₂×D₄	semidirect
195. C₂×M₃₂	C₂×D₅	semidirect
197. C₂²×C₁₆	C₂×D₅	semidirect
245. C₂²⋊D₅	M₃₂	direct (N × H)
306. M₃₂	C₂²⋊D₅	direct (N × H)
338. C₂²×C₅	C₂×M₃₂	semidirect
346. C₂×D₅	C₂×M₃₂	semidirect
357. Dic₅	C₂×M₃₂	semidirect
426. C₁₆	C₂×C₂²⋊D₅	semidirect
487. C₅	D₄×M₃₂	semidirect
503. C₂²	D₅×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×M₃₂	2
C₂×C₈×C₂²⋊D₅	2
C₂×D₅×M₃₂	2
#10602756	2
#10602226	2
#10602224	2
#10602223	2
#10602213	2
Dic₅×M₃₂	2
#10602200	2
C₁₆×C₂²⋊D₅	2
D₄×M₃₂	5

Subgroups — M32×C22⋊D5 #12252511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×C₂²⋊D₅ #12252511