Subgroups — #12068743

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614166	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4088	C₂	1	1	yes	maximal, characteristic
3	#10610744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601213	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600527	C₂	1	1	yes	maximal, characteristic
7	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599008	C₂	1	2	yes	maximal, complemented
9	#10599007	C₂	1	2	yes	maximal, complemented
10	#10599006	C₂	1	2	yes	maximal, complemented
11	#10599005	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×#4088	C₄	1	1	yes	characteristic
14	C₄×#709	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	#65514	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₅	—	2	2	no	—
19	#65319	C₄	1	2	yes	—
20	C₄×#689	C₂²	1	2	yes	—
21	#65315	C₄	1	2	yes	—
22	C₄×#688	C₂²	1	2	yes	—
23	Q₈×#168	—	2	1	no	—
24	Q₈×#168	—	2	1	no	—
25	Q₈×#168	C₂²	1	2	yes	—
26	Q₈×#168	C₂²	1	2	yes	—
27	#65255	C₄	1	1	yes	characteristic
28	#65253	C₄	1	1	yes	characteristic
29	#65214	—	2	2	no	—
30	#65214	C₂²	1	1	yes	characteristic
31	#65214	C₂²	1	1	yes	characteristic
32	C₄×#681	C₂²	1	1	yes	characteristic
33	#65123	C₂²	1	2	yes	—
34	#65122	—	2	1	no	—
35	D₅×C₄⋊C₈	—	2	1	no	—
36	#65119	C₂²	1	2	yes	—
37	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
39	#64700	C₂²	1	2	yes	—
40	#64699	C₂²	1	2	yes	—
41	#64679	C₂²	1	1	yes	characteristic
42	#64679	C₂²	1	1	yes	characteristic
43	#64676	C₂²	1	1	yes	characteristic
44	#64676	C₂²	1	1	yes	characteristic
45	#64674	C₂²	1	2	yes	—
46	C₈×#168	C₂²	1	2	yes	—
47	#17853	—	5	1	no	maximal, Sylow
48	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#709	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	—	2	1	no	—
51	C₂²×C₅×C₈	—	2	1	no	—
52	C₄×C₅×Q₈	—	2	1	no	—
53	C₄×C₅×Q₈	—	2	1	no	—
54	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
55	C₄×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	—	2	1	no	—
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₂×#689	C₂×C₄	1	2	yes	—
61	#4088	C₈	1	8	yes	complemented
62	C₂×#688	C₂×C₄	1	2	yes	—
63	C₄×C₂²⋊D₅	—	2	1	no	—
64	C₄×C₂²⋊D₅	—	2	1	no	—
65	#4072	C₂×C₄	1	1	yes	characteristic
66	C₂×#681	C₂×C₄	1	1	yes	characteristic
67	C₂×#681	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₅	—	2	2	no	—
69	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
70	C₄×D₂₀	C₂³	1	1	yes	characteristic
71	#4018	—	2	1	no	—
72	C₄²×D₅	—	2	1	no	—
73	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×C₄⋊C₈	C₂³	1	2	yes	—
77	C₄×C₅×C₈	—	2	1	no	—
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
80	#3967	C₂×C₄	1	2	yes	—
81	#3967	C₂×C₄	1	2	yes	—
82	C₂²⋊#168	—	2	1	no	—
83	C₂²⋊#168	D₄	1	2	yes	—
84	#3952	—	2	2	no	—
85	#3946	—	2	2	no	—
86	C₈×Dic₅	—	2	2	no	—
87	#3942	C₂×C₄	1	2	yes	—
88	#3941	C₂×C₄	1	2	yes	—
89	#3940	C₂×C₄	1	2	yes	—
90	#3939	C₂×C₄	1	2	yes	—
91	C₄⋊#168	—	2	2	no	—
92	C₄⋊#168	—	2	2	no	—
93	C₄⋊#168	D₄	1	1	yes	characteristic
94	C₄⋊#168	D₄	1	1	yes	characteristic
95	C₄⋊#168	C₂³	1	1	yes	characteristic
96	C₄⋊#168	C₂³	1	1	yes	characteristic
97	#3935	C₂×C₄	1	2	yes	—
98	C₄×#168	—	2	1	no	—
99	C₄×#168	—	2	2	no	—
100	C₄×#168	—	2	2	no	—
101	C₄×#168	C₂³	1	2	yes	—
102	C₄×#168	C₂³	1	2	yes	—
103	#2988	—	5	1	no	—
104	#2982	—	5	1	no	—
105	C₄×#137	—	5	1	no	—
106	#1579	—	5	2	no	—
107	SD₁₆⋊C₈	—	5	2	no	—
108	C₈×Q₁₆	—	5	2	no	—
109	C₈×SD₁₆	—	5	2	no	—
110	#1565	—	5	1	no	—
111	#1476	—	5	1	no	—
112	C₂×Q₈⋊C₈	D₅	1	1	yes	characteristic, complemented
113	C₈×M₁₆	—	5	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	C₂×C₈	1	4	yes	complemented
117	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	1	yes	characteristic
123	C₂×C₂²⋊D₅	—	2	1	no	—
124	#709	—	2	2	no	—
125	#709	C₂×C₈	1	4	yes	—
126	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	—	2	1	no	—
128	C₂×C₄×D₅	—	2	1	no	—
129	C₂×C₄×D₅	—	2	1	no	—
130	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	4	2	no	—
135	C₂×C₅×C₈	—	8	1	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₅	#41	1	1	yes	characteristic
145	C₄²×C₅	C₂⁴	1	1	yes	characteristic
146	C₂²⋊Dic₅	—	2	1	no	—
147	#689	C₂×C₈	1	8	yes	complemented
148	#688	C₂×C₈	1	8	yes	complemented
149	#685	—	2	1	no	—
150	#685	—	2	1	no	—
151	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
153	#683	—	2	1	no	—
154	#683	—	2	1	no	—
155	C₄×Dic₅	—	2	1	no	—
156	C₄×Dic₅	—	2	1	no	—
157	C₄×Dic₅	—	2	1	no	—
158	#681	—	2	2	no	—
159	#681	C₂×C₈	1	4	yes	complemented
160	C₂×#168	—	2	1	no	—
161	C₂×#168	—	2	1	no	—
162	C₂×#168	C₂²×C₄	1	2	yes	—
163	C₂×#168	C₂²×C₄	1	2	yes	—
164	C₂×#168	C₂×D₄	1	2	yes	—
165	C₂×#168	C₂×D₄	1	2	yes	—
166	C₈×D₅	—	8	2	no	—
167	C₂×#137	—	5	1	no	—
168	C₄×#41	—	5	1	no	—
169	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
170	C₈×Q₈	—	5	2	no	—
171	C₈×Q₈	—	5	2	no	—
172	C₈×Q₈	—	5	2	no	—
173	C₈×Q₈	—	10	1	no	—
174	C₈×Q₈	—	10	1	no	—
175	#441	—	5	2	no	—
176	#440	—	5	2	no	—
177	C₄×Q₁₆	—	5	2	no	—
178	C₄×SD₁₆	—	5	2	no	—
179	C₈×D₄	—	5	2	no	—
180	C₈×D₄	—	10	2	no	—
181	#431	—	5	1	no	—
182	#431	—	5	1	no	—
183	#431	—	10	2	no	—
184	#431	—	10	1	no	—
185	#428	—	5	1	no	—
186	C₂×C₄⋊C₈	—	10	1	no	—
187	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
188	#419	—	5	1	no	—
189	#417	—	5	1	no	—
190	C₄×M₁₆	—	5	1	no	—
191	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
192	#335	—	5	2	no	—
193	#334	—	5	2	no	—
194	Q₈⋊C₈	—	5	1	no	—
195	Q₈⋊C₈	—	5	1	no	—
196	Q₈⋊C₈	C₂×D₅	1	2	yes	—
197	Q₈⋊C₈	C₂×D₅	1	2	yes	—
198	D₄⋊C₈	—	5	1	no	—
199	D₄⋊C₈	—	5	1	no	—
200	#322	—	5	2	no	—
201	C₈²	—	5	2	no	—
202	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂²×D₅	—	2	1	no	—
204	C₅×Q₈	—	2	2	no	—
205	C₅×Q₈	—	2	4	no	—
206	C₅×Q₈	C₂²×C₈	1	4	yes	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	8	1	no	—
214	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
218	C₂×C₄×C₅	#131	1	2	yes	—
219	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₂²⋊D₅	—	2	4	no	—
223	C₂×Dic₅	—	2	1	no	—
224	C₂×Dic₅	—	2	1	no	—
225	C₂×Dic₅	—	2	1	no	—
226	D₂₀	—	2	1	no	—
227	D₂₀	C₂²×C₈	1	2	yes	—
228	C₄×D₅	—	2	4	no	—
229	C₄×D₅	—	4	1	no	—
230	C₄×D₅	—	4	1	no	—
231	C₄×D₅	—	8	1	no	—
232	Dic₁₀	—	2	1	no	—
233	Dic₁₀	C₂²×C₈	1	2	yes	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	4	1	no	—
236	C₅×C₈	—	4	2	no	—
237	#168	—	2	2	no	—
238	#168	—	2	2	no	—
239	#168	—	2	2	no	—
240	#168	—	4	1	no	—
241	#168	—	4	1	no	—
242	#168	C₂²×C₈	1	4	yes	—
243	C₂×#41	—	5	1	no	—
244	C₂²×Q₈	C₄×D₅	1	1	yes	characteristic
245	#137	—	5	8	no	—
246	C₂×Q₁₆	—	5	2	no	—
247	C₂×SD₁₆	—	5	2	no	—
248	C₂×M₁₆	—	5	1	no	—
249	C₂×M₁₆	—	5	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	10	2	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	—	5	1	no	—
256	C₄×Q₈	—	5	1	no	—
257	C₄×Q₈	C₄×D₅	1	2	yes	—
258	C₄×Q₈	C₂²×D₅	1	2	yes	—
259	C₄×D₄	—	5	1	no	—
260	C₄×D₄	—	5	1	no	—
261	C₄×D₄	—	10	1	no	—
262	C₄×D₄	—	10	1	no	—
263	#117	—	5	1	no	—
264	#117	—	10	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	10	1	no	—
269	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
270	#107	—	5	2	no	—
271	#106	—	5	2	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	5	1	no	—
274	C₄⋊C₈	—	5	1	no	—
275	C₄⋊C₈	—	5	1	no	—
276	C₄⋊C₈	—	5	1	no	—
277	C₄⋊C₈	—	10	2	no	—
278	C₄⋊C₈	—	10	2	no	—
279	C₄⋊C₈	—	10	2	no	—
280	C₄⋊C₈	C₂²×D₅	1	2	yes	—
281	#103	—	5	2	no	—
282	#103	—	5	2	no	—
283	#103	—	5	2	no	—
284	#102	—	5	2	no	—
285	C₂²⋊C₈	—	5	2	no	—
286	C₂²⋊C₈	—	10	2	no	—
287	C₂²⋊C₈	—	10	1	no	—
288	#97	—	5	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	5	2	no	—
291	C₄×C₈	—	5	2	no	—
292	C₄×C₈	—	10	2	no	—
293	C₄×C₈	—	10	2	no	—
294	C₄×C₈	—	10	2	no	—
295	C₄×C₈	—	10	1	no	—
296	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
298	C₂²×C₅	—	2	1	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	C₈×D₄	1	2	yes	—
301	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×D₅	—	2	2	no	—
303	C₂×D₅	—	4	1	no	—
304	C₂×D₅	—	4	1	no	—
305	C₄×C₅	—	2	4	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	C₈×D₄	1	2	yes	—
311	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
312	C₄×C₅	C₂×#131	1	1	yes	characteristic
313	C₄×C₅	#577	1	1	yes	characteristic
314	C₄×C₅	#578	1	1	yes	characteristic
315	Dic₅	—	2	2	no	—
316	Dic₅	—	4	1	no	—
317	Dic₅	—	4	1	no	—
318	#41	—	5	4	no	—
319	#41	—	10	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	5	1	no	—
323	C₂×Q₈	C₈×D₅	1	4	yes	complemented
324	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
325	C₂×D₄	—	5	1	no	—
326	C₂×D₄	—	10	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	10	1	no	—
330	C₂²×C₄	—	10	1	no	—
331	C₂²×C₄	—	10	1	no	—
332	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
334	C₂²×C₄	#711	1	1	yes	characteristic
335	Q₁₆	—	5	8	no	—
336	SD₁₆	—	5	8	no	—
337	M₁₆	—	5	4	no	—
338	M₁₆	—	10	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	5	2	no	—
344	C₂×C₈	—	5	2	no	—
345	C₂×C₈	—	5	2	no	—
346	C₂×C₈	—	5	2	no	—
347	C₂×C₈	—	8	1	no	—
348	C₂×C₈	—	10	1	no	—
349	C₂×C₈	—	10	1	no	—
350	C₂×C₈	—	40	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	5	1	no	—
355	C₄⋊C₄	—	5	1	no	—
356	C₄⋊C₄	—	10	1	no	—
357	C₄⋊C₄	—	10	1	no	—
358	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
359	C₂²⋊C₄	—	10	1	no	—
360	C₂²⋊C₄	—	10	1	no	—
361	C₂²⋊C₄	—	10	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	10	1	no	—
365	C₄²	—	10	1	no	—
366	C₄²	—	10	1	no	—
367	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
368	C₄²	D₄×D₅	1	1	yes	characteristic
369	C₄²	#711	1	1	yes	characteristic
370	C₄²	C₂³×D₅	1	1	yes	characteristic
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
373	C₂×C₅	#2947	1	1	yes	characteristic
374	C₂×C₅	#2956	1	1	yes	characteristic
375	D₅	—	4	2	no	—
376	C₂³	—	10	1	no	—
377	C₂³	#4027	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	5	2	no	—
381	Q₈	—	10	1	no	—
382	Q₈	C₂×C₈×D₅	1	4	yes	—
383	D₄	—	5	2	no	—
384	D₄	—	10	4	no	—
385	D₄	—	10	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	10	1	no	—
394	C₂×C₄	—	10	4	no	—
395	C₂×C₄	—	10	1	no	—
396	C₂×C₄	—	10	1	no	—
397	C₂×C₄	—	20	1	no	—
398	C₂×C₄	—	20	1	no	—
399	C₂×C₄	—	40	1	no	—
400	C₂×C₄	#4027	1	1	yes	characteristic
401	C₂×C₄	#4027	1	1	yes	characteristic
402	C₂×C₄	#4027	1	1	yes	characteristic
403	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
404	C₂×C₄	#4053	1	2	yes	—
405	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
406	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
407	C₂×C₄	C₂×#711	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	—	5	4	no	—
412	C₈	—	10	2	no	—
413	C₈	—	10	2	no	—
414	C₈	—	10	2	no	—
415	C₈	—	20	1	no	—
416	C₈	—	20	1	no	—
417	C₅	#17853	1	1	yes	characteristic, complemented, Sylow
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	10	2	no	—
421	C₂²	—	20	1	no	—
422	C₂²	—	20	1	no	—
423	C₂²	#65014	1	2	yes	—
424	C₂²	C₂×#4027	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	10	2	no	—
431	C₄	—	20	1	no	—
432	C₄	—	20	1	no	—
433	C₄	#65014	1	2	yes	—
434	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
435	C₄	C₂×#4053	1	1	yes	characteristic
436	C₄	#66096	1	1	yes	characteristic
437	C₄	#66100	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	20	2	no	—
440	C₂	C₂×#65014	1	1	yes	characteristic
441	C₂	#10610505	1	1	yes	characteristic
442	C₂	#10610711	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₄²	C₂³×D₅
Fitting	C₂×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₅
hypocenter	C₅	#17853
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. #10614166	C₂	semidirect
4. C₂×C₅×Q₈⋊C₈	C₂	semidirect
5. #10601213	C₂	semidirect
7. C₈×#681	C₂	semidirect
8. #10599008	C₂	semidirect
9. #10599007	C₂	semidirect
10. #10599006	C₂	semidirect
11. #10599005	C₂	semidirect
61. #4088	C₈	semidirect
112. C₂×Q₈⋊C₈	D₅	semidirect
116. C₂×C₅×Q₈	C₂×C₈	semidirect
147. #689	C₂×C₈	semidirect
148. #688	C₂×C₈	semidirect
159. #681	C₂×C₈	semidirect
323. C₂×Q₈	C₈×D₅	semidirect
417. C₅	#17853	semidirect

Maximal subgroups

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

subgroup	index
#10614166	2
C₄×#4088	2
#10610744	2
C₂×C₅×Q₈⋊C₈	2
#10601213	2
#10600527	2
C₈×#681	2
#10599008	2
#10599007	2
#10599006	2
#10599005	2
#17853	5