Subgroups — #12070304

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614173	C₂	1	1	yes	maximal, characteristic
2	Q₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
3	#10610735	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601215	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600528	C₂	1	1	yes	maximal, characteristic
7	#10600518	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599019	C₂	1	2	yes	maximal, complemented
9	#10599016	C₂	1	2	yes	maximal, complemented
10	#10599013	C₂	1	2	yes	maximal, complemented
11	#10599007	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×#4047	—	2	1	no	—
14	#65811	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	#65516	C₄	1	2	yes	—
18	#65399	—	2	1	no	—
19	#65316	C₄	1	1	yes	characteristic
20	#65316	C₄	1	1	yes	characteristic
21	C₄×#688	C₂²	1	2	yes	—
22	C₄×#688	C₂²	1	2	yes	—
23	#65313	—	2	2	no	—
24	#65313	C₂²	1	2	yes	—
25	Q₈×#168	C₂²	1	2	yes	—
26	#65309	C₄	1	1	yes	characteristic
27	#65309	C₄	1	1	yes	characteristic
28	#65257	C₄	1	2	yes	—
29	#65214	C₂²	1	1	yes	characteristic
30	#65213	—	2	1	no	—
31	#65213	C₂²	1	1	yes	characteristic
32	C₄×#681	—	2	1	no	—
33	C₄×#681	C₂²	1	1	yes	characteristic
34	#65127	C₂²	1	2	yes	—
35	#65125	—	2	2	no	—
36	#65123	C₂²	1	2	yes	—
37	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	#64699	C₂²	1	2	yes	—
42	#64699	C₂²	1	2	yes	—
43	#64679	C₂²	1	2	yes	—
44	#64679	C₂²	1	2	yes	—
45	#64675	C₂²	1	2	yes	—
46	#64674	C₂²	1	2	yes	—
47	#18004	—	5	1	no	maximal, Sylow
48	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#709	—	2	1	no	—
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	1	yes	characteristic
55	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
56	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	—	2	1	no	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×#688	C₂×C₄	1	2	yes	—
63	C₂×#688	C₂×C₄	1	2	yes	—
64	#4076	—	2	1	no	—
65	#4076	C₂×C₄	1	2	yes	—
66	C₂×#681	—	2	1	no	—
67	C₂×#681	D₄	1	1	yes	characteristic
68	C₂×#681	D₄	1	1	yes	characteristic
69	#4047	—	4	4	no	—
70	C₂×#676	—	2	2	no	—
71	C₂×C₈×D₅	—	2	2	no	—
72	#4021	—	2	1	no	—
73	#4020	C₂×C₄	1	1	yes	characteristic
74	C₄×D₂₀	—	2	1	no	—
75	C₄×D₂₀	C₂³	1	2	yes	—
76	#4015	C₂×C₄	1	1	yes	characteristic
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₅×C₈	—	2	1	no	—
81	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
83	#3967	C₂×C₄	1	2	yes	—
84	#3967	C₂×C₄	1	2	yes	—
85	C₂²⋊#168	C₂×C₄	1	2	yes	—
86	#3952	—	2	2	no	—
87	#3952	—	2	2	no	—
88	#3941	C₂×C₄	1	2	yes	—
89	#3941	C₂×C₄	1	2	yes	—
90	#3940	C₂×C₄	1	2	yes	—
91	#3940	C₂×C₄	1	2	yes	—
92	C₄⋊#168	—	2	1	no	—
93	C₄⋊#168	—	2	2	no	—
94	C₄⋊#168	—	2	2	no	—
95	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
97	C₄⋊#168	C₂³	1	2	yes	—
98	#3935	—	2	2	no	—
99	#3935	D₄	1	2	yes	—
100	C₄×#168	—	2	2	no	—
101	C₄×#168	C₂³	1	2	yes	—
102	C₄×#168	C₂³	1	2	yes	—
103	#3103	—	5	1	no	—
104	Q₈×M₁₆	—	5	1	no	—
105	#2935	—	5	1	no	—
106	#1592	—	5	2	no	—
107	#1588	—	5	2	no	—
108	#1585	—	5	2	no	—
109	SD₁₆⋊C₈	—	5	2	no	—
110	#1571	—	5	1	no	—
111	#1492	—	5	1	no	—
112	C₂×Q₈⋊C₈	D₅	1	1	yes	characteristic, complemented
113	#1451	—	5	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	4	1	no	—
117	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₂×C₂²⋊D₅	—	2	2	no	—
125	#709	—	4	2	no	—
126	#709	—	4	2	no	—
127	C₂×D₂₀	—	2	1	no	—
128	C₂×D₂₀	—	2	1	no	—
129	C₂×D₂₀	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₅	—	2	2	no	—
131	C₂×Dic₁₀	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	4	2	no	—
137	C₂×C₅×C₈	—	4	2	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₅	#41	1	1	yes	characteristic
152	C₄²×C₅	C₂⁴	1	1	yes	characteristic
153	#688	—	2	4	no	—
154	#688	—	4	2	no	—
155	#685	—	2	2	no	—
156	#685	—	2	2	no	—
157	C₄⋊Dic₅	—	2	1	no	—
158	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
159	#681	—	2	2	no	—
160	#681	—	2	2	no	—
161	#681	—	4	2	no	—
162	C₂×#168	—	2	2	no	—
163	C₂×#168	C₂²×C₄	1	2	yes	—
164	C₂×#168	C₂²×C₄	1	2	yes	—
165	C₂×#168	C₂×D₄	1	2	yes	—
166	C₂×#168	C₂×D₄	1	2	yes	—
167	#676	—	4	4	no	—
168	C₈×D₅	—	4	4	no	—
169	C₂×#131	—	10	1	no	—
170	#532	—	5	1	no	—
171	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
172	#481	—	5	2	no	—
173	#475	—	5	1	no	—
174	#475	—	5	1	no	—
175	#460	—	5	1	no	—
176	#460	—	5	1	no	—
177	#448	—	5	2	no	—
178	#446	—	5	2	no	—
179	#446	—	10	2	no	—
180	C₈×Q₈	—	5	2	no	—
181	C₄×SD₁₆	—	5	2	no	—
182	C₄×SD₁₆	—	5	2	no	—
183	#436	—	5	2	no	—
184	#435	—	10	2	no	—
185	C₈×D₄	—	5	2	no	—
186	#431	—	5	1	no	—
187	#423	—	5	1	no	—
188	#423	—	10	1	no	—
189	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
190	#408	—	10	1	no	—
191	C₄×M₁₆	—	5	1	no	—
192	C₄×M₁₆	—	10	1	no	—
193	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
194	#335	—	5	2	no	—
195	#335	—	5	2	no	—
196	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
197	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
198	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
199	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
200	D₄⋊C₈	—	5	2	no	—
201	D₄⋊C₈	—	5	2	no	—
202	#322	—	5	2	no	—
203	#322	—	5	2	no	—
204	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
205	C₂²×D₅	—	2	2	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	2	1	no	—
208	C₅×Q₈	—	2	1	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×Q₈	#131	1	2	yes	complemented
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	8	1	no	—
220	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₅	#137	1	2	yes	—
225	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₅	—	4	4	no	—
229	C₂×Dic₅	—	2	2	no	—
230	D₂₀	—	2	2	no	—
231	D₂₀	—	2	2	no	—
232	D₂₀	—	4	2	no	—
233	D₂₀	—	8	1	no	—
234	C₄×D₅	—	4	2	no	—
235	C₄×D₅	—	4	2	no	—
236	Dic₁₀	—	4	2	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	4	1	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	4	1	no	—
241	#168	—	2	2	no	—
242	#168	—	2	2	no	—
243	#168	—	2	2	no	—
244	#168	—	2	2	no	—
245	#168	—	4	2	no	—
246	C₂×#41	—	10	1	no	—
247	C₂²×Q₈	C₄×D₅	1	1	yes	characteristic
248	C₂×SD₁₆	—	5	2	no	—
249	C₂×SD₁₆	—	5	2	no	—
250	#131	—	20	4	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂×M₁₆	—	5	1	no	—
253	C₂×M₁₆	—	10	2	no	—
254	C₂×M₁₆	—	10	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	10	2	no	—
258	C₄⋊Q₈	—	5	1	no	—
259	#127	—	5	1	no	—
260	#124	—	10	1	no	—
261	#121	—	5	2	no	—
262	#121	—	10	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
266	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
267	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
268	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
269	C₄×D₄	—	5	2	no	—
270	C₄×D₄	—	10	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
275	#106	—	5	2	no	—
276	#106	—	5	2	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	5	1	no	—
279	C₄⋊C₈	—	5	1	no	—
280	C₄⋊C₈	—	5	2	no	—
281	C₄⋊C₈	—	10	2	no	—
282	C₄⋊C₈	—	10	2	no	—
283	C₄⋊C₈	—	10	1	no	—
284	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
285	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
286	#103	—	5	2	no	—
287	#103	—	5	2	no	—
288	#102	—	5	2	no	—
289	#102	—	5	2	no	—
290	C₂²⋊C₈	—	5	2	no	—
291	C₂²⋊C₈	—	10	2	no	—
292	C₂²⋊C₈	—	10	2	no	—
293	#97	—	5	2	no	—
294	#97	—	10	2	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	5	2	no	—
297	C₄×C₈	—	5	2	no	—
298	C₄×C₈	—	10	2	no	—
299	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
300	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	#440	1	2	yes	—
304	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂×D₅	—	4	2	no	—
306	C₂×D₅	—	4	2	no	—
307	C₂×D₅	—	4	2	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	#440	1	2	yes	—
316	C₄×C₅	C₂×#131	1	1	yes	characteristic
317	C₄×C₅	#568	1	1	yes	characteristic
318	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₄×C₅	C₂×#137	1	1	yes	characteristic
320	Dic₅	—	4	2	no	—
321	#41	—	20	2	no	—
322	#41	—	20	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	10	1	no	—
327	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
328	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
329	C₂×D₄	—	5	2	no	—
330	C₂×D₄	—	10	2	no	—
331	C₂×D₄	—	10	1	no	—
332	C₂×D₄	—	10	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	10	2	no	—
336	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
338	C₂²×C₄	#711	1	1	yes	characteristic
339	SD₁₆	—	10	4	no	—
340	SD₁₆	—	20	2	no	—
341	M₁₆	—	10	2	no	—
342	M₁₆	—	10	2	no	—
343	M₁₆	—	20	4	no	—
344	M₁₆	—	20	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	10	2	no	—
356	C₂×C₈	—	20	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	5	2	no	—
363	C₄⋊C₄	—	10	1	no	—
364	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
365	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
366	C₂²⋊C₄	—	10	2	no	—
367	C₂²⋊C₄	—	10	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
373	C₄²	D₄×D₅	1	1	yes	characteristic
374	C₄²	#711	1	1	yes	characteristic
375	C₄²	C₂³×D₅	1	1	yes	characteristic
376	C₂×C₅	—	2	2	no	—
377	C₂×C₅	#2933	1	1	yes	characteristic
378	C₂×C₅	C₂×#440	1	1	yes	characteristic
379	C₂×C₅	#2956	1	1	yes	characteristic
380	D₅	—	8	2	no	—
381	C₂³	—	10	2	no	—
382	C₂³	#4027	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	20	2	no	—
388	Q₈	#4047	1	2	yes	complemented
389	D₄	—	10	2	no	—
390	D₄	—	10	2	no	—
391	D₄	—	20	4	no	—
392	D₄	—	20	2	no	—
393	D₄	—	40	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	20	2	no	—
405	C₂×C₄	—	20	2	no	—
406	C₂×C₄	#4027	1	1	yes	characteristic
407	C₂×C₄	#4027	1	1	yes	characteristic
408	C₂×C₄	#4027	1	1	yes	characteristic
409	C₂×C₄	#4060	1	2	yes	—
410	C₂×C₄	#4064	1	2	yes	—
411	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
413	C₂×C₄	C₂×#711	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	10	2	no	—
419	C₈	—	10	2	no	—
420	C₈	—	10	2	no	—
421	C₈	—	10	2	no	—
422	C₈	—	20	2	no	—
423	C₅	#18004	1	1	yes	characteristic, complemented, Sylow
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	20	2	no	—
427	C₂²	—	20	2	no	—
428	C₂²	—	20	2	no	—
429	C₂²	#65106	1	2	yes	—
430	C₂²	C₂×#4027	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	20	2	no	—
439	C₄	#65106	1	2	yes	—
440	C₄	C₂×#4047	1	1	yes	characteristic
441	C₄	#66079	1	1	yes	characteristic
442	C₄	C₂×#4060	1	1	yes	characteristic
443	C₄	C₂×#4064	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	40	2	no	—
446	C₂	#10610327	1	1	yes	characteristic
447	C₂	C₂×#65106	1	1	yes	characteristic
448	C₂	#10610711	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₂×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65811	C₂²
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₅
hypocenter	C₅	#18004
LCS	G ▷ C₂×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
2. Q₈×#681	C₂	semidirect
4. C₂×C₅×Q₈⋊C₈	C₂	semidirect
5. #10601215	C₂	semidirect
7. #10600518	C₂	semidirect
8. #10599019	C₂	semidirect
9. #10599016	C₂	semidirect
10. #10599013	C₂	semidirect
11. #10599007	C₂	semidirect
112. C₂×Q₈⋊C₈	D₅	semidirect
210. C₅×Q₈	#131	semidirect
388. Q₈	#4047	semidirect
423. C₅	#18004	semidirect

Maximal subgroups

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

subgroup	index
#10614173	2
Q₈×#681	2
#10610735	2
C₂×C₅×Q₈⋊C₈	2
#10601215	2
#10600528	2
#10600518	2
#10599019	2
#10599016	2
#10599013	2
#10599007	2
#18004	5