Subgroups — #12064955

Order 1280.

836 conjugacy classes of subgroups.

The subgroup lattice has 400 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	C₂×#65214	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#681	C₂	1	1	yes	maximal, characteristic
4	#10601536	C₂	1	4	yes	maximal, complemented
5	#10601534	C₂	1	2	yes	maximal, complemented
6	#10601532	C₂	1	2	yes	maximal, complemented
7	#10600640	C₂	1	2	yes	maximal, complemented
8	M₁₆×#168	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂²×#681	C₄	1	2	yes	—
11	C₅×#432	C₄	1	2	yes	—
12	C₅×#432	C₄	1	2	yes	—
13	C₅×#431	C₂²	1	2	yes	—
14	C₅×#431	C₂²	1	2	yes	—
15	C₅×#423	C₄	1	2	yes	—
16	C₅×#407	C₄	1	2	yes	—
17	C₄×C₅×M₁₆	C₂²	1	2	yes	—
18	C₂×C₂²⋊#168	C₄	1	2	yes	—
19	#65214	C₄	1	2	yes	—
20	#65214	C₄	1	2	yes	—
21	#65214	C₂²	1	2	yes	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65214	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#168	C₄	1	2	yes	—
25	C₄×#681	C₄	1	2	yes	—
26	C₄×#681	C₄	1	2	yes	—
27	C₄×#681	C₂²	1	1	yes	characteristic
28	C₄×#681	C₂²	1	1	yes	characteristic
29	C₄×#681	C₂²	1	2	yes	—
30	C₂×#3935	C₄	1	2	yes	—
31	C₂×C₄×#168	C₂²	1	2	yes	—
32	C₂×C₄×#168	C₂²	1	2	yes	—
33	#64675	C₂²	1	4	yes	complemented
34	#64674	C₂²	1	4	yes	complemented
35	#64674	C₂²	1	4	yes	complemented
36	C₈×#168	C₂²	1	4	yes	complemented
37	#17327	—	5	1	no	maximal, Sylow
38	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×#681	—	2	8	no	—
55	C₂×#681	C₂×C₄	1	2	yes	—
56	C₂×#681	C₂×C₄	1	4	yes	—
57	C₂×#681	C₂×C₄	1	2	yes	—
58	C₂²×#168	C₂×C₄	1	4	yes	—
59	C₂²×#168	C₂×C₄	1	4	yes	—
60	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
63	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
64	C₅×#97	C₂×C₄	1	4	yes	—
65	C₄×C₅×C₈	C₂³	1	4	yes	—
66	C₂²⋊#168	C₂×C₄	1	4	yes	—
67	C₂²⋊#168	C₂×C₄	1	2	yes	—
68	C₂²⋊#168	C₂×C₄	1	2	yes	—
69	C₄⋊#168	C₂×C₄	1	4	yes	—
70	C₄⋊#168	C₂×C₄	1	2	yes	—
71	C₄⋊#168	C₂×C₄	1	2	yes	—
72	#3935	C₂×C₄	1	2	yes	—
73	#3935	C₂×C₄	1	4	yes	—
74	#3935	C₂×C₄	1	2	yes	—
75	C₄×#168	C₂×C₄	1	4	yes	—
76	C₄×#168	C₂×C₄	1	4	yes	—
77	C₄×#168	C₂³	1	2	yes	—
78	C₄×#168	C₂³	1	2	yes	—
79	C₄×#168	C₂³	1	2	yes	—
80	C₄×#168	C₂³	1	2	yes	—
81	#2920	D₅	1	1	yes	characteristic
82	C₂×#431	—	5	1	no	—
83	C₂×C₄×M₁₆	—	5	1	no	—
84	#1453	—	5	4	no	—
85	#1451	—	5	2	no	—
86	#1451	—	5	2	no	—
87	C₈×M₁₆	—	5	2	no	—
88	C₈×M₁₆	—	5	2	no	—
89	C₂⁴×C₅	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₅	—	2	4	no	—
91	C₂²×C₄×C₅	—	2	4	no	—
92	C₂²×C₄×C₅	—	4	2	no	—
93	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	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	C₅×M₁₆	—	2	8	no	—
112	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
113	C₄²×C₅	C₄²	1	1	yes	characteristic
114	C₄²×C₅	C₄²	1	1	yes	characteristic
115	C₄²×C₅	C₄²	1	1	yes	characteristic
116	C₄²×C₅	C₄²	1	1	yes	characteristic
117	C₄²×C₅	C₄²	1	1	yes	characteristic
118	C₄²×C₅	C₄²	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	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	C₂⁴	1	1	yes	characteristic
129	#681	—	2	4	no	—
130	#681	—	2	8	no	—
131	#681	M₁₆	1	8	yes	complemented
132	C₂×#168	—	2	8	no	—
133	C₂×#168	—	4	4	no	—
134	C₂×#168	C₂²×C₄	1	4	yes	—
135	C₂×#168	C₂²×C₄	1	4	yes	—
136	C₂×#168	C₂²×C₄	1	4	yes	—
137	C₂×#168	C₂²×C₄	1	4	yes	—
138	C₂²×M₁₆	—	5	2	no	—
139	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
140	#432	Dic₅	1	2	yes	—
141	#432	Dic₅	1	2	yes	—
142	#431	—	5	2	no	—
143	#431	—	5	2	no	—
144	#431	—	5	1	no	—
145	#431	—	5	1	no	—
146	#431	—	5	2	no	—
147	#431	C₂×D₅	1	2	yes	—
148	#431	C₂×D₅	1	2	yes	—
149	#423	Dic₅	1	2	yes	—
150	C₂×C₄⋊C₈	—	5	2	no	—
151	#407	Dic₅	1	2	yes	—
152	C₂×C₂²⋊C₈	—	5	2	no	—
153	C₄×M₁₆	—	5	2	no	—
154	C₄×M₁₆	—	5	2	no	—
155	C₄×M₁₆	—	5	1	no	—
156	C₄×M₁₆	—	5	1	no	—
157	C₄×M₁₆	—	5	2	no	—
158	C₄×M₁₆	C₂×D₅	1	2	yes	—
159	C₂×#97	—	5	2	no	—
160	C₂×C₄×C₈	—	5	2	no	—
161	C₂×C₄×C₈	—	5	2	no	—
162	#322	—	5	4	no	—
163	#322	—	5	4	no	—
164	#322	—	5	4	no	—
165	C₈²	—	5	4	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	4	1	no	—
169	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
171	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
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	—	4	1	no	—
186	C₂×C₄×C₅	—	4	1	no	—
187	C₂×C₄×C₅	—	4	1	no	—
188	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
198	C₂×C₄×C₅	#131	1	4	yes	—
199	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₅×C₈	—	2	8	no	—
203	#168	—	2	4	no	—
204	#168	—	2	4	no	—
205	#168	—	2	4	no	—
206	#168	C₂×M₁₆	1	8	yes	—
207	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
209	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
210	C₂×M₁₆	—	5	2	no	—
211	C₂×M₁₆	—	5	4	no	—
212	C₂×M₁₆	—	5	2	no	—
213	C₂×M₁₆	—	10	8	no	—
214	C₂×M₁₆	C₂×Dic₅	1	4	yes	—
215	C₂²×C₈	—	5	4	no	—
216	C₂²×C₈	—	5	4	no	—
217	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
219	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
221	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
223	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
224	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
226	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
227	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
228	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
229	C₄⋊C₈	—	5	2	no	—
230	C₄⋊C₈	—	5	2	no	—
231	C₄⋊C₈	—	5	4	no	—
232	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
233	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
234	C₂²⋊C₈	—	5	2	no	—
235	C₂²⋊C₈	—	5	2	no	—
236	C₂²⋊C₈	—	5	4	no	—
237	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
238	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
239	#97	—	5	2	no	—
240	#97	—	5	4	no	—
241	#97	—	5	2	no	—
242	#97	C₂×Dic₅	1	4	yes	—
243	C₄×C₈	—	5	4	no	—
244	C₄×C₈	—	5	4	no	—
245	C₄×C₈	—	5	2	no	—
246	C₄×C₈	—	5	2	no	—
247	C₄×C₈	—	5	2	no	—
248	C₄×C₈	—	5	2	no	—
249	C₄×C₈	C₂²×D₅	1	4	yes	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	C₄×M₁₆	1	2	yes	—
259	C₂²×C₅	#405	1	2	yes	—
260	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	C₄×M₁₆	1	2	yes	—
269	C₄×C₅	#405	1	2	yes	—
270	C₄×C₅	C₂²×M₁₆	1	2	yes	—
271	C₄×C₅	C₂×#131	1	2	yes	—
272	C₄×C₅	#568	1	2	yes	—
273	C₂⁴	C₄×Dic₅	1	1	yes	characteristic
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
278	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
279	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
281	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
282	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
283	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
295	M₁₆	—	2	8	no	—
296	M₁₆	—	5	8	no	—
297	M₁₆	—	10	8	no	—
298	M₁₆	—	10	4	no	—
299	C₂×C₈	—	5	4	no	—
300	C₂×C₈	—	5	4	no	—
301	C₂×C₈	—	5	4	no	—
302	C₂×C₈	—	5	4	no	—
303	C₂×C₈	—	10	8	no	—
304	C₂×C₈	—	20	4	no	—
305	C₂×C₈	C₂²×Dic₅	1	8	yes	—
306	C₄²	C₄×Dic₅	1	1	yes	characteristic
307	C₄²	C₄×Dic₅	1	1	yes	characteristic
308	C₄²	C₄×Dic₅	1	1	yes	characteristic
309	C₄²	C₄×Dic₅	1	1	yes	characteristic
310	C₄²	C₄×Dic₅	1	1	yes	characteristic
311	C₄²	C₄×Dic₅	1	1	yes	characteristic
312	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
313	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
318	C₄²	C₂²×Dic₅	1	1	yes	characteristic
319	C₄²	C₂²×Dic₅	1	1	yes	characteristic
320	C₄²	C₂²×Dic₅	1	1	yes	characteristic
321	C₄²	C₂³×D₅	1	1	yes	characteristic
322	C₂×C₅	—	2	2	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	4	1	no	—
325	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
326	C₂×C₅	C₂×#405	1	1	yes	characteristic
327	C₂×C₅	#2873	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
332	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
333	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	D₅×M₁₆	1	4	yes	—
351	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
360	C₂×C₄	#4094	1	4	yes	—
361	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
363	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
364	C₈	—	2	8	no	—
365	C₈	—	5	8	no	—
366	C₈	—	10	4	no	—
367	C₈	—	10	4	no	—
368	C₈	—	10	4	no	—
369	C₅	#17327	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	4	no	—
378	C₂²	#65286	1	2	yes	—
379	C₂²	M₁₆×Dic₅	1	2	yes	—
380	C₂²	C₂²×C₄×Dic₅	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	#65286	1	2	yes	—
389	C₄	M₁₆×Dic₅	1	2	yes	—
390	C₄	C₂×D₅×M₁₆	1	2	yes	—
391	C₄	#66079	1	2	yes	—
392	C₄	C₂×#4094	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	—	4	1	no	—
396	C₂	C₂×#65286	1	1	yes	characteristic
397	C₂	C₂×M₁₆×Dic₅	1	1	yes	characteristic
398	C₂	#10615478	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	#17327
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. #10601536	C₂	semidirect
5. #10601534	C₂	semidirect
6. #10601532	C₂	semidirect
7. #10600640	C₂	semidirect
8. M₁₆×#168	C₂	semidirect
33. #64675	C₂²	semidirect
34. #64674	C₂²	semidirect
35. #64674	C₂²	semidirect
36. C₈×#168	C₂²	semidirect
131. #681	M₁₆	semidirect
369. C₅	#17327	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
C₂×#65214	2
C₂×C₄×#681	2
#10601536	2
#10601534	2
#10601532	2
#10600640	2
M₁₆×#168	2
#17327	5