Subgroups — #12016157

Order 1280.

554 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#64727	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598295	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598295	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊#168	C₄	1	1	yes	characteristic
14	C₈×C₂²⋊D₅	—	2	2	no	—
15	C₈×C₂²⋊D₅	—	2	2	no	—
16	C₂×#3952	C₄	1	1	yes	characteristic
17	C₂×#3946	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×#672	C₂²	1	1	yes	characteristic
20	C₂²×#672	C₂²	1	1	yes	characteristic
21	C₂×#3930	—	2	2	no	—
22	C₂×#3930	—	2	2	no	—
23	C₂×#3930	—	2	2	no	—
24	C₅×C₂²⋊C₁₆	—	2	2	no	—
25	C₂²⋊#672	—	2	2	no	—
26	#64727	—	2	2	no	—
27	#12977	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₂²⋊D₅	C₈	1	1	yes	characteristic
30	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	—	2	1	no	—
32	C₂²×C₅×C₈	—	2	1	no	—
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₂²×C₅×C₈	—	2	1	no	—
37	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
39	C₂×C₂²⋊Dic₅	C₈	1	1	yes	characteristic
40	C₄×C₂²⋊D₅	—	2	2	no	—
41	C₄×C₂²⋊D₅	—	2	2	no	—
42	C₂×#685	C₈	1	1	yes	characteristic
43	C₂×#683	C₈	1	1	yes	characteristic
44	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×#168	C₂×C₄	1	1	yes	characteristic
46	C₂²×#168	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₅	—	2	1	no	—
48	C₂×C₈×D₅	—	2	1	no	—
49	C₂×C₈×D₅	—	2	1	no	—
50	C₂×C₈×D₅	—	2	1	no	—
51	C₂×C₈×D₅	D₄	1	2	yes	—
52	C₂×C₈×D₅	D₄	1	2	yes	—
53	C₂×C₅×C₁₆	—	2	1	no	—
54	C₂×C₅×C₁₆	—	2	1	no	—
55	C₂×C₅×C₁₆	—	2	1	no	—
56	C₂×C₅×C₁₆	—	2	1	no	—
57	C₂×C₅×C₁₆	—	2	1	no	—
58	C₂×C₅×C₁₆	D₄	1	2	yes	complemented
59	C₂²⋊#168	—	2	2	no	—
60	#3952	—	2	2	no	—
61	#3946	—	2	2	no	—
62	C₈×Dic₅	—	2	1	no	—
63	C₈×Dic₅	—	2	1	no	—
64	C₂×#672	—	2	1	no	—
65	C₂×#672	—	2	1	no	—
66	C₂×#672	—	2	1	no	—
67	C₂×#672	—	2	1	no	—
68	C₂×#672	—	2	1	no	—
69	C₂×#672	D₄	1	2	yes	complemented
70	#3930	—	2	8	no	—
71	C₂²×M₃₂	—	5	1	no	—
72	C₂×C₈×D₄	—	5	1	no	—
73	C₂×C₂²⋊C₁₆	—	5	1	no	—
74	C₂×C₂²⋊C₁₆	—	5	1	no	—
75	C₂×C₂²⋊C₁₆	D₅	1	1	yes	characteristic, complemented
76	#1374	—	5	1	no	—
77	#1374	—	5	1	no	—
78	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
79	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₅	—	2	1	no	—
81	C₂²×C₄×C₅	—	2	1	no	—
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	1	no	—
84	C₂²×C₄×C₅	—	2	1	no	—
85	C₂²×C₄×C₅	—	2	1	no	—
86	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊D₅	—	2	2	no	—
89	C₂×C₂²⋊D₅	—	2	2	no	—
90	C₂×C₂²⋊D₅	—	2	2	no	—
91	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
92	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
93	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₅	—	2	1	no	—
95	C₂×C₄×D₅	—	2	1	no	—
96	C₂×C₄×D₅	—	2	1	no	—
97	C₂×C₄×D₅	—	2	1	no	—
98	C₂×C₄×D₅	C₂²⋊C₄	1	2	yes	—
99	C₂×C₄×D₅	M₁₆	1	2	yes	—
100	C₂×C₅×C₈	—	2	1	no	—
101	C₂×C₅×C₈	—	2	1	no	—
102	C₂×C₅×C₈	—	2	1	no	—
103	C₂×C₅×C₈	—	4	1	no	—
104	C₂×C₅×C₈	—	4	1	no	—
105	C₂×C₅×C₈	—	4	1	no	—
106	C₂×C₅×C₈	—	4	1	no	—
107	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
109	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₅×C₈	#41	1	1	yes	characteristic
112	C₂×C₅×C₈	#41	1	1	yes	characteristic
113	C₂²⋊Dic₅	—	2	2	no	—
114	#685	—	2	2	no	—
115	#683	—	2	2	no	—
116	C₄×Dic₅	—	2	1	no	—
117	C₄×Dic₅	—	2	1	no	—
118	C₂×#168	—	2	1	no	—
119	C₂×#168	—	2	1	no	—
120	C₂×#168	—	2	1	no	—
121	C₂×#168	—	2	1	no	—
122	C₂×#168	—	2	1	no	—
123	C₂×#168	C₂²⋊C₄	1	2	yes	—
124	C₈×D₅	—	2	2	no	—
125	C₈×D₅	—	2	2	no	—
126	C₈×D₅	—	2	2	no	—
127	C₈×D₅	—	2	2	no	—
128	C₅×C₁₆	—	2	2	no	—
129	C₅×C₁₆	—	4	1	no	—
130	#672	—	2	2	no	—
131	#672	—	4	1	no	—
132	C₂³×C₈	—	5	1	no	—
133	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
134	C₂×C₄×D₄	—	5	1	no	—
135	C₂×M₃₂	—	10	2	no	—
136	C₂×M₃₂	—	10	2	no	—
137	C₂×M₃₂	—	10	2	no	—
138	C₂²×C₁₆	—	5	1	no	—
139	C₂²×C₁₆	—	5	1	no	—
140	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
141	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
142	C₈×D₄	—	10	2	no	—
143	C₈×D₄	—	10	2	no	—
144	C₂×C₄⋊C₈	—	5	1	no	—
145	C₂×C₂²⋊C₈	—	5	1	no	—
146	C₂×C₂²⋊C₈	—	5	1	no	—
147	C₂×C₄×C₈	—	5	1	no	—
148	C₂²⋊C₁₆	—	2	2	no	—
149	C₂²⋊C₁₆	—	10	2	no	—
150	C₂²⋊C₁₆	—	10	2	no	—
151	C₂³×C₅	—	2	1	no	—
152	C₂³×C₅	—	2	1	no	—
153	C₂³×C₅	—	2	1	no	—
154	C₂³×C₅	—	2	1	no	—
155	C₂³×C₅	—	2	1	no	—
156	C₂³×C₅	—	2	1	no	—
157	C₂³×C₅	M₃₂	1	2	yes	complemented
158	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
159	C₂²×D₅	—	2	1	no	—
160	C₂²×D₅	—	2	1	no	—
161	C₂²×D₅	—	2	1	no	—
162	C₂²×D₅	—	2	1	no	—
163	C₂²×D₅	—	2	1	no	—
164	C₂²×D₅	—	2	1	no	—
165	C₂²×D₅	C₂²⋊C₈	1	2	yes	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	4	1	no	—
170	C₂×C₄×C₅	—	4	1	no	—
171	C₂×C₄×C₅	—	4	1	no	—
172	C₂×C₄×C₅	—	4	1	no	—
173	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₅	#131	1	1	yes	characteristic
178	C₂×C₄×C₅	#131	1	1	yes	characteristic
179	C₂²⋊D₅	—	2	8	no	—
180	C₂×Dic₅	—	2	1	no	—
181	C₂×Dic₅	—	2	1	no	—
182	C₂×Dic₅	—	2	1	no	—
183	C₂×Dic₅	—	2	1	no	—
184	C₂×Dic₅	—	2	1	no	—
185	C₂×Dic₅	—	2	1	no	—
186	C₂×Dic₅	—	2	1	no	—
187	C₂×Dic₅	C₂²⋊C₈	1	2	yes	—
188	C₂×Dic₅	M₃₂	1	2	yes	complemented
189	C₄×D₅	—	2	2	no	—
190	C₄×D₅	—	2	2	no	—
191	C₄×D₅	—	2	2	no	—
192	C₄×D₅	—	2	2	no	—
193	C₅×C₈	—	4	1	no	—
194	C₅×C₈	#120	1	1	yes	characteristic
195	C₅×C₈	#121	1	1	yes	characteristic
196	C₅×C₈	#121	1	1	yes	characteristic
197	C₅×C₈	#123	1	1	yes	characteristic
198	#168	—	2	2	no	—
199	#168	—	4	1	no	—
200	C₂²×D₄	—	5	1	no	—
201	C₂³×C₄	—	5	1	no	—
202	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
203	C₂²×C₈	—	2	1	no	—
204	C₂²×C₈	—	2	1	no	—
205	C₂²×C₈	—	2	1	no	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	2	1	no	—
208	C₂²×C₈	—	2	1	no	—
209	C₂²×C₈	—	5	1	no	—
210	C₂²×C₈	—	5	2	no	—
211	C₂²×C₈	—	5	2	no	—
212	C₂²×C₈	—	5	1	no	—
213	C₂²×C₈	—	10	1	no	—
214	C₂²×C₈	—	10	1	no	—
215	C₂²×C₈	—	10	1	no	—
216	C₂²×C₈	—	10	1	no	—
217	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
218	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
219	C₄×D₄	—	10	2	no	—
220	C₄×D₄	—	10	2	no	—
221	C₂×C₄⋊C₄	—	5	1	no	—
222	C₂×C₂²⋊C₄	—	5	1	no	—
223	C₂×C₂²⋊C₄	—	5	1	no	—
224	C₂×C₄²	—	5	1	no	—
225	M₃₂	—	10	8	no	—
226	C₂×C₁₆	—	2	1	no	—
227	C₂×C₁₆	—	2	1	no	—
228	C₂×C₁₆	—	2	1	no	—
229	C₂×C₁₆	—	2	1	no	—
230	C₂×C₁₆	—	2	1	no	—
231	C₂×C₁₆	—	5	2	no	—
232	C₂×C₁₆	—	10	1	no	—
233	C₂×C₁₆	—	10	1	no	—
234	C₂×C₁₆	—	10	1	no	—
235	C₂×C₁₆	—	10	1	no	—
236	C₂×C₁₆	—	10	1	no	—
237	C₂×C₁₆	C₂²⋊D₅	1	2	yes	complemented
238	C₄⋊C₈	—	10	2	no	—
239	C₂²⋊C₈	—	10	2	no	—
240	C₂²⋊C₈	—	10	2	no	—
241	C₄×C₈	—	10	1	no	—
242	C₄×C₈	—	10	1	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	4	1	no	—
247	C₂²×C₅	—	4	1	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	—	4	1	no	—
250	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
251	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
252	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
253	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
254	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
255	C₂²×C₅	#504	1	1	yes	characteristic
256	C₂²×C₅	#504	1	1	yes	characteristic
257	C₂×D₅	—	2	2	no	—
258	C₂×D₅	—	2	2	no	—
259	C₂×D₅	—	2	2	no	—
260	C₂×D₅	—	4	1	no	—
261	C₂×D₅	—	4	1	no	—
262	C₂×D₅	—	4	1	no	—
263	C₂×D₅	—	4	1	no	—
264	C₄×C₅	—	4	1	no	—
265	C₄×C₅	#386	1	1	yes	characteristic
266	C₄×C₅	#408	1	1	yes	characteristic
267	C₄×C₅	#435	1	1	yes	characteristic
268	C₄×C₅	#435	1	1	yes	characteristic
269	Dic₅	—	2	2	no	—
270	Dic₅	—	2	2	no	—
271	Dic₅	—	4	1	no	—
272	C₂⁴	—	5	1	no	—
273	C₂⁴	C₈×D₅	1	1	yes	characteristic
274	C₂×D₄	—	10	2	no	—
275	C₂×D₄	—	10	2	no	—
276	C₂×D₄	—	10	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	5	1	no	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	5	2	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	10	1	no	—
289	C₂²×C₄	—	10	1	no	—
290	C₂²×C₄	—	10	1	no	—
291	C₂²×C₄	—	10	1	no	—
292	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	5	2	no	—
302	C₂×C₈	—	10	1	no	—
303	C₂×C₈	—	10	1	no	—
304	C₂×C₈	—	10	2	no	—
305	C₂×C₈	—	10	2	no	—
306	C₂×C₈	—	10	2	no	—
307	C₂×C₈	—	10	2	no	—
308	C₂×C₈	—	10	1	no	—
309	C₂×C₈	—	10	1	no	—
310	C₂×C₈	—	10	1	no	—
311	C₂×C₈	#709	1	1	yes	characteristic
312	C₂×C₈	D₄×D₅	1	1	yes	characteristic
313	C₂×C₈	D₄×D₅	1	1	yes	characteristic
314	C₂×C₈	D₄×D₅	1	1	yes	characteristic
315	C₂×C₈	#711	1	1	yes	characteristic
316	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
317	C₄⋊C₄	—	10	2	no	—
318	C₂²⋊C₄	—	10	2	no	—
319	C₂²⋊C₄	—	10	2	no	—
320	C₄²	—	10	1	no	—
321	C₄²	—	10	1	no	—
322	C₁₆	—	2	2	no	—
323	C₁₆	—	4	1	no	—
324	C₁₆	—	10	2	no	—
325	C₁₆	—	20	1	no	—
326	C₂×C₅	—	4	2	no	—
327	C₂×C₅	#1869	1	1	yes	characteristic
328	C₂×C₅	#2112	1	1	yes	characteristic
329	C₂×C₅	#2113	1	1	yes	characteristic
330	C₂×C₅	#2168	1	1	yes	characteristic
331	C₂×C₅	#2168	1	1	yes	characteristic
332	C₂×C₅	#2169	1	1	yes	characteristic
333	C₂×C₅	#2169	1	1	yes	characteristic
334	D₅	—	4	2	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	5	2	no	—
342	C₂³	—	10	1	no	—
343	C₂³	—	10	1	no	—
344	C₂³	—	10	1	no	—
345	C₂³	—	10	1	no	—
346	C₂³	—	10	1	no	—
347	C₂³	—	10	1	no	—
348	C₂³	#3930	1	2	yes	complemented
349	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
350	D₄	—	10	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	5	2	no	—
359	C₂×C₄	—	5	2	no	—
360	C₂×C₄	—	10	1	no	—
361	C₂×C₄	—	10	1	no	—
362	C₂×C₄	—	10	1	no	—
363	C₂×C₄	—	10	1	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	10	2	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	—	10	1	no	—
369	C₂×C₄	—	10	1	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂×C₄	#4027	1	1	yes	characteristic
373	C₂×C₄	#4047	1	1	yes	characteristic
374	C₂×C₄	D₅×M₁₆	1	1	yes	characteristic
375	C₂×C₄	#4053	1	1	yes	characteristic
376	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
377	C₈	—	4	1	no	—
378	C₈	—	10	2	no	—
379	C₈	—	20	1	no	—
380	C₈	#4029	1	1	yes	characteristic
381	C₈	#4030	1	1	yes	characteristic
382	C₈	#4083	1	1	yes	characteristic
383	C₈	#4084	1	1	yes	characteristic
384	C₅	#12977	1	1	yes	characteristic, complemented, Sylow
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	10	2	no	—
393	C₂²	—	10	2	no	—
394	C₂²	—	10	2	no	—
395	C₂²	—	20	1	no	—
396	C₂²	—	20	1	no	—
397	C₂²	—	20	1	no	—
398	C₂²	—	20	1	no	—
399	C₂²	D₅×C₂²⋊C₈	1	1	yes	characteristic
400	C₂²	#65014	1	1	yes	characteristic
401	C₂²	C₂×#3930	1	1	yes	characteristic
402	C₂²	#65190	1	1	yes	characteristic
403	C₂²	D₅×M₃₂	1	1	yes	characteristic
404	C₂²	#65196	1	1	yes	characteristic
405	C₂²	C₈×C₂²⋊D₅	1	1	yes	characteristic
406	C₄	—	4	1	no	—
407	C₄	—	10	2	no	—
408	C₄	—	10	2	no	—
409	C₄	—	20	1	no	—
410	C₄	#65016	1	1	yes	characteristic
411	C₄	#65017	1	1	yes	characteristic
412	C₄	#65245	1	1	yes	characteristic
413	C₄	#65416	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	20	2	no	—
416	C₂	#10599895	1	1	yes	characteristic
417	C₂	#10599897	1	1	yes	characteristic
418	C₂	#10599899	1	1	yes	characteristic
419	C₂	#10599900	1	1	yes	characteristic
420	C₂	#10600750	1	1	yes	characteristic
421	C₂	#10602200	1	1	yes	characteristic
422	C₂	#10602223	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₅
commutator, socle	C₂³×C₅	C₂²×C₈
Fitting	C₂×C₅×C₂²⋊C₁₆	C₂
prime radical	C₂²×C₂²⋊D₅	C₈
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₅
hypocenter	C₅	#12977
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×#3930	C₂	semidirect
3. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
4. C₂×C₂²⋊#672	C₂	semidirect
5. C₂×#64727	C₂	semidirect
6. #10598295	C₂	semidirect
7. #10598295	C₂	semidirect
58. C₂×C₅×C₁₆	D₄	semidirect
69. C₂×#672	D₄	semidirect
75. C₂×C₂²⋊C₁₆	D₅	semidirect
157. C₂³×C₅	M₃₂	semidirect
188. C₂×Dic₅	M₃₂	semidirect
237. C₂×C₁₆	C₂²⋊D₅	semidirect
348. C₂³	#3930	semidirect
384. C₅	#12977	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂²⋊D₅	2
C₂²×#3930	2
C₂×C₅×C₂²⋊C₁₆	2
C₂×C₂²⋊#672	2
C₂×#64727	2
#10598295	2
#12977	5