Subgroups — #12064928

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	#10613780	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#168	C₂	1	1	yes	maximal, characteristic
4	#10601535	C₂	1	2	yes	maximal, complemented
5	#10601534	C₂	1	2	yes	maximal, complemented
6	#10601533	C₂	1	2	yes	maximal, complemented
7	#10601532	C₂	1	2	yes	maximal, complemented
8	#10600640	C₂	1	2	yes	maximal, complemented
9	M₁₆×#168	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂³×#168	C₄	1	2	yes	—
12	C₅×#432	C₄	1	2	yes	—
13	C₅×#432	C₄	1	2	yes	—
14	C₅×#431	C₂²	1	2	yes	—
15	C₅×#431	C₂²	1	2	yes	—
16	C₅×#423	C₄	1	2	yes	—
17	C₅×#407	C₄	1	2	yes	—
18	C₄×C₅×M₁₆	C₂²	1	2	yes	—
19	#65496	C₄	1	2	yes	—
20	#65215	C₄	1	2	yes	—
21	#65215	C₄	1	2	yes	—
22	#65214	C₂²	1	2	yes	—
23	#65214	C₂²	1	2	yes	—
24	#65213	C₄	1	2	yes	—
25	C₄×#681	C₂²	1	2	yes	—
26	C₂×C₄×#168	C₄	1	2	yes	—
27	C₂×C₄×#168	C₄	1	2	yes	—
28	C₂×C₄×#168	C₄	1	2	yes	—
29	C₂×C₄×#168	C₂²	1	1	yes	characteristic
30	C₂×C₄×#168	C₂²	1	1	yes	characteristic
31	C₂×C₄×#168	C₂²	1	1	yes	characteristic
32	C₂×C₄×#168	C₂²	1	1	yes	characteristic
33	C₂×C₄×#168	C₂²	1	1	yes	characteristic
34	C₂×C₄×#168	C₂²	1	1	yes	characteristic
35	#64675	C₂²	1	4	yes	complemented
36	#64674	C₂²	1	4	yes	complemented
37	#64674	C₂²	1	4	yes	complemented
38	C₈×#168	C₂²	1	4	yes	complemented
39	#17323	—	5	1	no	maximal, Sylow
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₂×#681	C₂×C₄	1	4	yes	—
57	C₂²×#168	—	2	8	no	—
58	C₂²×#168	C₂×C₄	1	2	yes	—
59	C₂²×#168	C₂×C₄	1	2	yes	—
60	C₂²×#168	C₂×C₄	1	2	yes	—
61	C₂²×#168	C₂×C₄	1	2	yes	—
62	C₂²×#168	C₂×C₄	1	2	yes	—
63	C₂²×#168	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
66	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
67	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
68	C₅×#97	C₂×C₄	1	4	yes	—
69	C₄×C₅×C₈	C₂³	1	4	yes	—
70	C₂²⋊#168	C₂×C₄	1	4	yes	—
71	C₂²⋊#168	C₂×C₄	1	4	yes	—
72	C₄⋊#168	C₂×C₄	1	4	yes	—
73	C₄⋊#168	C₂×C₄	1	4	yes	—
74	#3935	C₂×C₄	1	4	yes	—
75	C₄×#168	C₂×C₄	1	2	yes	—
76	C₄×#168	C₂×C₄	1	2	yes	—
77	C₄×#168	C₂×C₄	1	2	yes	—
78	C₄×#168	C₂×C₄	1	2	yes	—
79	C₄×#168	C₂×C₄	1	2	yes	—
80	C₄×#168	C₂×C₄	1	2	yes	—
81	C₄×#168	C₂³	1	1	yes	characteristic
82	C₄×#168	C₂³	1	4	yes	—
83	C₄×#168	C₂³	1	1	yes	characteristic
84	C₄×#168	C₂³	1	1	yes	characteristic
85	C₄×#168	C₂³	1	1	yes	characteristic
86	#2920	—	5	1	no	—
87	#2920	D₅	1	1	yes	characteristic
88	C₂²×C₄×C₈	—	5	1	no	—
89	#1452	—	5	2	no	—
90	#1451	—	5	2	no	—
91	#1451	—	5	2	no	—
92	#1450	—	5	2	no	—
93	C₈×M₁₆	—	5	2	no	—
94	C₈×M₁₆	—	5	2	no	—
95	C₂⁴×C₅	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₅	—	2	4	no	—
97	C₂²×C₄×C₅	—	2	4	no	—
98	C₂²×C₄×C₅	—	2	4	no	—
99	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₅×M₁₆	—	2	8	no	—
118	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
119	C₄²×C₅	C₄²	1	1	yes	characteristic
120	C₄²×C₅	C₄²	1	1	yes	characteristic
121	C₄²×C₅	C₄²	1	1	yes	characteristic
122	C₄²×C₅	C₄²	1	1	yes	characteristic
123	C₄²×C₅	C₄²	1	1	yes	characteristic
124	C₄²×C₅	C₄²	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₅	C₂⁴	1	1	yes	characteristic
135	#681	—	2	8	no	—
136	C₂×#168	—	2	4	no	—
137	C₂×#168	—	2	4	no	—
138	C₂×#168	—	2	4	no	—
139	C₂×#168	—	2	4	no	—
140	C₂×#168	—	2	4	no	—
141	C₂×#168	M₁₆	1	8	yes	complemented
142	C₂×#168	C₂²×C₄	1	2	yes	—
143	C₂×#168	C₂²×C₄	1	2	yes	—
144	C₂×#168	C₂²×C₄	1	8	yes	—
145	C₂×#168	C₂²×C₄	1	2	yes	—
146	C₂×#168	C₂²×C₄	1	2	yes	—
147	C₂³×C₈	—	5	2	no	—
148	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
149	#432	—	5	2	no	—
150	#432	—	5	2	no	—
151	#432	Dic₅	1	2	yes	—
152	#432	Dic₅	1	2	yes	—
153	#431	—	5	2	no	—
154	#431	—	5	2	no	—
155	#431	C₂×D₅	1	2	yes	—
156	#431	C₂×D₅	1	2	yes	—
157	#423	—	5	2	no	—
158	#423	Dic₅	1	2	yes	—
159	#407	—	5	2	no	—
160	#407	Dic₅	1	2	yes	—
161	C₄×M₁₆	—	5	2	no	—
162	C₄×M₁₆	C₂×D₅	1	2	yes	—
163	C₂×C₄×C₈	—	5	2	no	—
164	C₂×C₄×C₈	—	5	2	no	—
165	C₂×C₄×C₈	—	5	2	no	—
166	C₂×C₄×C₈	—	5	1	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	C₂×C₄×C₈	—	5	1	no	—
169	C₂×C₄×C₈	—	5	1	no	—
170	C₂×C₄×C₈	—	5	1	no	—
171	C₂×C₄×C₈	—	5	1	no	—
172	#322	—	5	4	no	—
173	#322	—	5	4	no	—
174	#322	—	5	4	no	—
175	C₈²	—	5	4	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	—	2	2	no	—
178	C₂³×C₅	—	2	2	no	—
179	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
180	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
181	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
207	C₂×C₄×C₅	#131	1	4	yes	—
208	C₂×C₄×C₅	#131	1	4	yes	—
209	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₅×C₈	—	2	8	no	—
213	#168	—	2	2	no	—
214	#168	—	2	2	no	—
215	#168	—	2	8	no	—
216	#168	C₂×M₁₆	1	4	yes	—
217	#168	C₂×M₁₆	1	4	yes	—
218	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
219	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
221	C₂×M₁₆	—	5	4	no	—
222	C₂×M₁₆	C₂×Dic₅	1	4	yes	—
223	C₂²×C₈	—	5	2	no	—
224	C₂²×C₈	—	5	2	no	—
225	C₂²×C₈	—	5	2	no	—
226	C₂²×C₈	—	5	2	no	—
227	C₂²×C₈	—	5	2	no	—
228	C₂²×C₈	—	5	2	no	—
229	C₂²×C₈	—	10	8	no	—
230	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
242	C₄⋊C₈	—	5	4	no	—
243	C₄⋊C₈	—	5	4	no	—
244	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
245	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
246	C₂²⋊C₈	—	5	4	no	—
247	C₂²⋊C₈	—	5	4	no	—
248	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
249	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
250	#97	—	5	4	no	—
251	#97	C₂×Dic₅	1	4	yes	—
252	C₄×C₈	—	5	2	no	—
253	C₄×C₈	—	5	2	no	—
254	C₄×C₈	—	5	2	no	—
255	C₄×C₈	—	5	2	no	—
256	C₄×C₈	—	5	2	no	—
257	C₄×C₈	—	5	2	no	—
258	C₄×C₈	—	5	1	no	—
259	C₄×C₈	—	5	4	no	—
260	C₄×C₈	—	5	1	no	—
261	C₄×C₈	—	5	1	no	—
262	C₄×C₈	—	5	1	no	—
263	C₄×C₈	C₂²×D₅	1	4	yes	—
264	C₂²×C₅	—	2	8	no	—
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	C₄×M₁₆	1	2	yes	—
272	C₂²×C₅	#405	1	2	yes	—
273	C₂²×C₅	#405	1	2	yes	—
274	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	C₄×M₁₆	1	2	yes	—
282	C₄×C₅	#405	1	2	yes	—
283	C₄×C₅	#405	1	2	yes	—
284	C₄×C₅	C₂²×M₁₆	1	2	yes	—
285	C₄×C₅	C₂×#131	1	2	yes	—
286	C₄×C₅	C₂×#131	1	2	yes	—
287	C₂⁴	C₄×Dic₅	1	1	yes	characteristic
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
292	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
293	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
294	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
295	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
296	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
297	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
298	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
299	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
306	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
308	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
309	M₁₆	—	2	8	no	—
310	M₁₆	—	10	8	no	—
311	C₂×C₈	—	5	2	no	—
312	C₂×C₈	—	5	2	no	—
313	C₂×C₈	—	5	8	no	—
314	C₂×C₈	—	5	2	no	—
315	C₂×C₈	—	5	2	no	—
316	C₂×C₈	—	5	8	no	—
317	C₂×C₈	—	10	4	no	—
318	C₂×C₈	—	10	4	no	—
319	C₂×C₈	—	10	4	no	—
320	C₂×C₈	—	10	4	no	—
321	C₂×C₈	—	10	4	no	—
322	C₂×C₈	C₂²×Dic₅	1	8	yes	—
323	C₄²	C₄×Dic₅	1	1	yes	characteristic
324	C₄²	C₄×Dic₅	1	1	yes	characteristic
325	C₄²	C₄×Dic₅	1	1	yes	characteristic
326	C₄²	C₄×Dic₅	1	1	yes	characteristic
327	C₄²	C₄×Dic₅	1	1	yes	characteristic
328	C₄²	C₄×Dic₅	1	1	yes	characteristic
329	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
333	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
334	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
335	C₄²	C₂²×Dic₅	1	1	yes	characteristic
336	C₄²	C₂²×Dic₅	1	1	yes	characteristic
337	C₄²	C₂²×Dic₅	1	1	yes	characteristic
338	C₄²	C₂³×D₅	1	1	yes	characteristic
339	C₂×C₅	—	2	2	no	—
340	C₂×C₅	—	2	2	no	—
341	C₂×C₅	—	2	2	no	—
342	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
343	C₂×C₅	C₂×#405	1	1	yes	characteristic
344	C₂×C₅	C₂×#405	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
349	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
350	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	D₅×M₁₆	1	4	yes	—
367	C₂×C₄	#4053	1	4	yes	—
368	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
377	C₂×C₄	#4094	1	4	yes	—
378	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
380	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
381	C₈	—	2	8	no	—
382	C₈	—	5	4	no	—
383	C₈	—	5	4	no	—
384	C₈	—	10	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	8	no	—
387	C₅	#17323	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	2	8	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	#65286	1	2	yes	—
396	C₂²	M₁₆×Dic₅	1	2	yes	—
397	C₂²	#65411	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₅	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	#65286	1	2	yes	—
406	C₄	M₁₆×Dic₅	1	2	yes	—
407	C₄	#65411	1	2	yes	—
408	C₄	C₂×D₅×M₁₆	1	2	yes	—
409	C₄	C₂×#4053	1	2	yes	—
410	C₄	C₂×#4094	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	C₂×#65286	1	1	yes	characteristic
415	C₂	C₂×M₁₆×Dic₅	1	1	yes	characteristic
416	C₂	C₂×#65411	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#2920	C₂
prime radical	C₂⁴×C₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2920	D₅
hypocenter	C₅	#17323
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
4. #10601535	C₂	semidirect
5. #10601534	C₂	semidirect
6. #10601533	C₂	semidirect
7. #10601532	C₂	semidirect
8. #10600640	C₂	semidirect
9. M₁₆×#168	C₂	semidirect
35. #64675	C₂²	semidirect
36. #64674	C₂²	semidirect
37. #64674	C₂²	semidirect
38. C₈×#168	C₂²	semidirect
141. C₂×#168	M₁₆	semidirect
387. C₅	#17323	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2920	2
#10613780	2
C₂²×C₄×#168	2
#10601535	2
#10601534	2
#10601533	2
#10601532	2
#10600640	2
M₁₆×#168	2
#17323	5