Subgroups — C₅×D₄×SD₃₂ #11956567

Order 1280.

738 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×SD₃₂	C₂	1	2	yes	maximal, complemented
2	C₅×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×D₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2217	C₂	1	2	yes	maximal, complemented
6	C₅×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2187	C₂	1	2	yes	maximal, complemented
9	C₅×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	complemented
13	C₂²×C₅×D₈	C₂²	1	2	yes	—
14	C₅×D₄×Q₈	—	2	1	no	—
15	C₅×D₄²	—	2	1	no	—
16	C₂×C₅×SD₃₂	—	2	8	no	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
22	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
23	C₅×#494	C₂²	1	1	yes	characteristic, complemented
24	C₅×#493	C₂²	1	1	yes	characteristic
25	C₅×#467	C₂²	1	2	yes	complemented
26	C₅×#466	C₂²	1	2	yes	—
27	C₅×#462	—	2	1	no	—
28	C₅×#459	—	2	1	no	—
29	C₅×#451	—	2	2	no	—
30	C₅×#447	—	2	2	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₅×#367	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₅×#358	C₂²	1	1	yes	characteristic, complemented
37	C₅×#358	C₂²	1	2	yes	complemented
38	C₅×#357	C₂²	1	1	yes	characteristic
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
42	D₄×SD₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	—	2	2	no	—
44	C₂²×C₅×D₄	—	2	2	no	—
45	C₂²×C₅×D₄	—	4	1	no	—
46	C₂×C₅×Q₁₆	—	2	4	no	—
47	C₂×C₅×Q₁₆	—	2	2	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	—	4	2	no	—
50	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×D₈	—	2	4	no	—
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	4	2	no	—
56	C₂×C₅×D₈	C₂³	1	2	yes	—
57	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	4	1	no	—
61	C₅×#127	—	2	1	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×C₂²⋊Q₈	—	4	2	no	—
64	C₅×#121	—	2	2	no	—
65	C₅×#121	—	4	1	no	—
66	C₅×#120	—	4	2	no	—
67	C₄×C₅×Q₈	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	4	1	no	—
70	C₄×C₅×D₄	D₄	1	1	yes	characteristic
71	C₅×SD₃₂	—	2	4	no	—
72	C₅×SD₃₂	—	2	4	no	—
73	C₅×SD₃₂	—	2	4	no	—
74	C₅×SD₃₂	—	4	2	no	—
75	C₅×SD₃₂	D₄	1	4	yes	direct product factor
76	C₂×C₅×C₁₆	—	2	4	no	—
77	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₁₆	C₂³	1	2	yes	—
79	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂³	1	1	yes	characteristic
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×#103	—	2	1	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	1	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×C₂²⋊C₈	D₄	1	2	yes	—
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂²×SD₃₂	C₂×C₅	1	2	yes	complemented
90	D₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
91	D₄×D₈	C₂×C₅	1	1	yes	characteristic
92	#2248	C₂×C₅	1	1	yes	characteristic, complemented
93	#2217	C₂×C₅	1	2	yes	complemented
94	#2208	C₂×C₅	1	1	yes	characteristic, complemented
95	#2207	C₂×C₅	1	1	yes	characteristic, complemented
96	#2187	C₂×C₅	1	2	yes	complemented
97	#2185	C₂×C₅	1	2	yes	complemented
98	C₄×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
99	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	4	2	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	2	no	—
103	C₂×C₅×Q₈	—	4	4	no	—
104	C₂×C₅×Q₈	—	4	2	no	—
105	C₂×C₅×Q₈	—	8	2	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	4	4	no	—
109	C₂×C₅×D₄	—	4	2	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	—	8	2	no	—
114	C₂×C₅×D₄	—	8	4	no	—
115	C₂×C₅×D₄	D₈	1	1	yes	characteristic
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×Q₁₆	—	2	1	no	—
121	C₅×Q₁₆	—	2	2	no	—
122	C₅×Q₁₆	—	4	4	no	—
123	C₅×Q₁₆	—	8	1	no	—
124	C₅×Q₁₆	C₂×D₄	1	2	yes	complemented
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	2	1	no	—
127	C₅×D₈	—	2	2	no	—
128	C₅×D₈	—	4	4	no	—
129	C₅×D₈	—	8	1	no	—
130	C₅×D₈	C₂×D₄	1	2	yes	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	4	1	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	—	4	2	no	—
146	C₅×C₂²⋊C₄	D₈	1	2	yes	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₅×C₁₆	—	2	2	no	—
150	C₅×C₁₆	—	2	1	no	—
151	C₅×C₁₆	C₂×D₄	1	2	yes	complemented
152	C₂²×Q₁₆	C₂²×C₅	1	2	yes	complemented
153	C₂²×D₈	C₂²×C₅	1	2	yes	—
154	D₄×Q₈	—	2	1	no	—
155	D₄²	—	2	1	no	—
156	C₂×SD₃₂	—	2	8	no	—
157	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
158	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
159	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
160	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
161	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
162	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
163	#494	C₂²×C₅	1	1	yes	characteristic, complemented
164	#493	C₂²×C₅	1	1	yes	characteristic
165	#467	C₂²×C₅	1	2	yes	complemented
166	#466	C₂²×C₅	1	2	yes	—
167	#462	—	2	1	no	—
168	#459	—	2	1	no	—
169	#451	—	2	2	no	—
170	#447	—	2	2	no	—
171	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
173	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
174	#367	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	#358	C₂²×C₅	1	1	yes	characteristic, complemented
177	#358	C₂²×C₅	1	2	yes	complemented
178	#357	C₂²×C₅	1	1	yes	characteristic
179	#357	C₂²×C₅	1	2	yes	complemented
180	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
181	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	8	4	no	—
185	C₂³×C₅	—	8	4	no	—
186	C₂³×C₅	—	16	2	no	—
187	C₂³×C₅	C₂×D₈	1	2	yes	—
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	4	1	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	8	4	no	—
193	C₅×D₄	—	2	2	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	8	4	no	—
198	C₅×D₄	—	8	4	no	—
199	C₅×D₄	—	8	2	no	—
200	C₅×D₄	—	16	1	no	—
201	C₅×D₄	SD₃₂	1	4	yes	direct product factor
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	8	4	no	—
209	C₂×C₄×C₅	—	8	2	no	—
210	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
217	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	4	1	no	—
221	C₂×Q₁₆	—	2	4	no	—
222	C₂×Q₁₆	—	2	2	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	4	2	no	—
225	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
226	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
227	C₂×D₈	—	2	4	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	4	2	no	—
231	C₂×D₈	C₂³×C₅	1	2	yes	—
232	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	4	1	no	—
236	#127	—	2	1	no	—
237	C₂²⋊Q₈	—	2	2	no	—
238	C₂²⋊Q₈	—	4	2	no	—
239	#121	—	2	2	no	—
240	#121	—	4	1	no	—
241	#120	—	4	2	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	4	1	no	—
245	C₄×D₄	C₅×D₄	1	1	yes	characteristic
246	SD₃₂	—	2	4	no	—
247	SD₃₂	—	2	4	no	—
248	SD₃₂	—	2	4	no	—
249	SD₃₂	—	4	2	no	—
250	SD₃₂	C₅×D₄	1	4	yes	direct product factor
251	C₂×C₁₆	—	2	4	no	—
252	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₅	1	2	yes	—
254	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
255	#107	C₂³×C₅	1	1	yes	characteristic
256	#107	C₂³×C₅	1	1	yes	characteristic
257	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
258	#103	—	2	1	no	—
259	#103	—	2	2	no	—
260	#102	—	2	1	no	—
261	#102	—	2	2	no	—
262	C₂²⋊C₈	C₅×D₄	1	2	yes	—
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	4	2	no	—
267	C₂²×C₅	—	8	1	no	—
268	C₂²×C₅	—	8	1	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	16	8	no	—
273	C₂²×C₅	C₂×SD₃₂	1	4	yes	complemented
274	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	2	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	8	1	no	—
279	C₄×C₅	—	8	1	no	—
280	C₄×C₅	—	8	2	no	—
281	C₄×C₅	C₂×SD₃₂	1	2	yes	complemented
282	C₄×C₅	D₄²	1	1	yes	characteristic
283	C₄×C₅	#576	1	1	yes	characteristic
284	C₂⁴	—	4	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	—	8	4	no	—
299	C₂×D₄	C₅×D₈	1	1	yes	characteristic
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	1	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	4	4	no	—
307	Q₁₆	—	8	1	no	—
308	Q₁₆	C₂×C₅×D₄	1	2	yes	complemented
309	D₈	—	2	2	no	—
310	D₈	—	2	1	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	4	no	—
313	D₈	—	8	1	no	—
314	D₈	C₂×C₅×D₄	1	2	yes	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
319	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	C₅×D₈	1	2	yes	—
331	C₄²	—	4	1	no	—
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	1	no	—
335	C₁₆	C₂×C₅×D₄	1	2	yes	complemented
336	C₂×C₅	—	2	4	no	—
337	C₂×C₅	—	8	2	no	—
338	C₂×C₅	—	16	2	no	—
339	C₂×C₅	D₄×D₈	1	1	yes	characteristic
340	C₂×C₅	C₂²×SD₃₂	1	1	yes	characteristic
341	C₂×C₅	#3416	1	1	yes	characteristic
342	C₂³	—	4	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	4	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	16	2	no	—
347	C₂³	C₂×C₅×D₈	1	2	yes	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	4	no	—
353	D₄	—	2	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	4	no	—
358	D₄	—	8	4	no	—
359	D₄	—	8	2	no	—
360	D₄	—	16	1	no	—
361	D₄	C₅×SD₃₂	1	4	yes	direct product factor
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
372	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	2	1	no	—
376	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
378	C₅	D₄×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×C₅×SD₃₂	1	4	yes	complemented
389	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×C₅×SD₃₂	1	2	yes	complemented
397	C₄	C₅×D₄²	1	1	yes	characteristic
398	C₄	C₅×#576	1	1	yes	characteristic
399	C₂	—	2	4	no	—
400	C₂	—	8	2	no	—
401	C₂	—	16	2	no	—
402	C₂	C₅×D₄×D₈	1	1	yes	characteristic
403	C₂	C₂²×C₅×SD₃₂	1	1	yes	characteristic
404	C₂	C₅×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×D₄×D₈	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×SD₃₂	C₂	semidirect
2. C₅×D₄×Q₁₆	C₂	semidirect
4. C₅×#2248	C₂	semidirect
5. C₅×#2217	C₂	semidirect
6. C₅×#2208	C₂	semidirect
7. C₅×#2207	C₂	semidirect
8. C₅×#2187	C₂	semidirect
9. C₅×#2185	C₂	semidirect
10. C₄×C₅×SD₃₂	C₂	semidirect
11. C₅×D₄×C₁₆	C₂	semidirect
12. C₂²×C₅×Q₁₆	C₂²	semidirect
19. C₂×C₅×SD₃₂	C₂²	semidirect
20. C₂×C₅×SD₃₂	C₂²	semidirect
21. C₂×C₅×SD₃₂	C₂²	semidirect
22. C₂²×C₅×C₁₆	C₂²	semidirect
23. C₅×#494	C₂²	semidirect
25. C₅×#467	C₂²	semidirect
31. C₄×C₅×Q₁₆	C₂²	semidirect
34. C₅×#367	C₂²	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
37. C₅×#358	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
40. C₅×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₅×C₁₆	C₂²	semidirect
42. D₄×SD₃₂	C₅	direct (N × H)
75. C₅×SD₃₂	D₄	direct (N × H)
89. C₂²×SD₃₂	C₂×C₅	semidirect
90. D₄×Q₁₆	C₂×C₅	semidirect
92. #2248	C₂×C₅	semidirect
93. #2217	C₂×C₅	semidirect
94. #2208	C₂×C₅	semidirect
95. #2207	C₂×C₅	semidirect
96. #2187	C₂×C₅	semidirect
97. #2185	C₂×C₅	semidirect
98. C₄×SD₃₂	C₂×C₅	semidirect
99. D₄×C₁₆	C₂×C₅	semidirect
124. C₅×Q₁₆	C₂×D₄	semidirect
151. C₅×C₁₆	C₂×D₄	semidirect
152. C₂²×Q₁₆	C₂²×C₅	semidirect
159. C₂×SD₃₂	C₂²×C₅	semidirect
160. C₂×SD₃₂	C₂²×C₅	semidirect
161. C₂×SD₃₂	C₂²×C₅	semidirect
162. C₂²×C₁₆	C₂²×C₅	semidirect
163. #494	C₂²×C₅	semidirect
165. #467	C₂²×C₅	semidirect
171. C₄×Q₁₆	C₂²×C₅	semidirect
174. #367	C₂²×C₅	semidirect
175. C₄⋊C₁₆	C₂²×C₅	semidirect
176. #358	C₂²×C₅	semidirect
177. #358	C₂²×C₅	semidirect
179. #357	C₂²×C₅	semidirect
180. C₂²⋊C₁₆	C₂²×C₅	semidirect
181. C₄×C₁₆	C₂²×C₅	semidirect
201. C₅×D₄	SD₃₂	direct (N × H)
250. SD₃₂	C₅×D₄	direct (N × H)
273. C₂²×C₅	C₂×SD₃₂	semidirect
281. C₄×C₅	C₂×SD₃₂	semidirect
308. Q₁₆	C₂×C₅×D₄	semidirect
335. C₁₆	C₂×C₅×D₄	semidirect
361. D₄	C₅×SD₃₂	direct (N × H)
378. C₅	D₄×SD₃₂	direct (N × H)
388. C₂²	C₂×C₅×SD₃₂	semidirect
396. C₄	C₂×C₅×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×SD₃₂	2
C₅×D₄×Q₁₆	2
C₅×D₄×D₈	2
C₅×#2248	2
C₅×#2217	2
C₅×#2208	2
C₅×#2207	2
C₅×#2187	2
C₅×#2185	2
C₄×C₅×SD₃₂	2
C₅×D₄×C₁₆	2
D₄×SD₃₂	5

Subgroups — C5×D4×SD32 #11956567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×SD₃₂ #11956567