Subgroups — C₈×#6763 #14295155

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄×#6763	C₂	1	1	yes	maximal, characteristic
3	D₅⋊#830	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
5	#11746763	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×#6763	C₄	1	2	yes	—
9	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
10	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
12	C₂²×C₃×#168	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₈×D₅	—	2	4	no	—
14	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	#91241	C₄	1	2	yes	complemented
19	#91235	C₄	1	2	yes	—
20	#91232	C₄	1	2	yes	complemented
21	C₈×ΓL(1,𝔽₁₆)	—	2	4	no	—
22	C₈×#217	—	5	1	no	maximal, Hall
23	C₂²×C₈×D₅	D₃	1	1	yes	characteristic
24	C₄×C₂²⋊AGL(1,𝔽₅)	—	3	1	no	—
25	D₅⋊(C₂²⋊C₈)	—	3	1	no	—
26	C₂×C₈×AGL(1,𝔽₅)	—	3	2	no	—
27	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	2	no	—
28	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	4	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	—	2	2	no	—
33	C₂×C₃×C₄×D₅	—	2	2	no	—
34	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
38	#6763	C₈	1	8	yes	direct product factor
39	C₂×C₃⋊#170	C₂×C₄	1	4	yes	—
40	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
41	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
42	D₅⋊(C₃⋊C₈)	—	2	2	no	—
43	D₅⋊(C₃⋊C₈)	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×#168	—	2	2	no	—
48	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
50	C₃×C₈×D₅	—	2	2	no	—
51	C₃×C₈×D₅	—	2	2	no	—
52	C₃×C₈×D₅	—	2	2	no	—
53	C₃×C₈×D₅	D₄	1	4	yes	—
54	C₂³×C₃×C₈	—	5	1	no	—
55	C₄×#217	—	5	1	no	—
56	C₂×#830	—	5	1	no	—
57	C₂×C₈×Dic₃	—	5	2	no	—
58	#4550	—	5	2	no	—
59	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
60	C₂×C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
61	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
62	C₂×D₅⋊C₈	—	3	2	no	—
63	C₂²×C₅×C₈	Dic₃	1	1	yes	characteristic, complemented
64	C₂²×#168	Dic₃	1	1	yes	characteristic, complemented
65	C₂×C₈×D₅	—	2	4	no	—
66	C₂×C₈×D₅	Dic₃	1	1	yes	characteristic, complemented
67	C₂×C₈×D₅	Dic₃	1	1	yes	characteristic, complemented
68	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
69	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
70	C₂²⋊#170	—	3	2	no	—
71	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	2	no	—
72	#4003	—	3	2	no	—
73	C₈×AGL(1,𝔽₅)	—	6	4	no	—
74	C₈×C₂²⋊C₄	—	15	1	no	Sylow
75	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₃×D₅	—	2	2	no	—
77	C₂²×C₃×D₅	—	2	2	no	—
78	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
79	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
80	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
82	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
83	C₂×ΓL(1,𝔽₁₆)	C₂×C₈	1	8	yes	complemented
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×Dic₅	—	2	2	no	—
89	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
91	C₃×C₄×D₅	—	2	2	no	—
92	C₃×C₄×D₅	—	2	1	no	—
93	C₃×C₄×D₅	—	2	1	no	—
94	C₃×C₄×D₅	—	2	2	no	—
95	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
96	C₃×C₄×D₅	#41	1	2	yes	—
97	C₃⋊#170	—	2	4	no	—
98	C₃×C₅×C₈	—	2	1	no	—
99	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	complemented
100	C₃×#168	—	2	1	no	—
101	C₃×#168	C₂²⋊C₄	1	2	yes	complemented
102	C₂³×C₃×C₄	—	5	1	no	—
103	C₂²×C₃×C₈	—	5	1	no	—
104	C₂²×C₃×C₈	—	5	1	no	—
105	C₂²×C₃×C₈	—	5	1	no	—
106	C₂²×C₃×C₈	—	5	1	no	—
107	C₂²×C₃×C₈	—	5	1	no	—
108	C₂²×C₃×C₈	—	10	4	no	—
109	C₂²×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
110	C₂×#217	—	5	2	no	—
111	C₂×C₄×Dic₃	—	5	2	no	—
112	C₂²×C₃⋊C₈	—	5	2	no	—
113	C₃⋊#95	—	5	2	no	—
114	#830	—	5	2	no	—
115	#830	—	5	2	no	—
116	C₈×Dic₃	—	10	4	no	—
117	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
118	C₂²×AGL(1,𝔽₅)	—	3	4	no	—
119	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
121	C₂×C₄×D₅	—	2	2	no	—
122	C₂×C₄×D₅	—	2	2	no	—
123	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
124	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
125	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
127	C₂²⋊AGL(1,𝔽₅)	—	3	8	no	—
128	C₂×#170	—	3	4	no	—
129	C₄×AGL(1,𝔽₅)	—	6	2	no	—
130	C₄×AGL(1,𝔽₅)	—	6	2	no	—
131	D₅⋊C₈	—	6	2	no	—
132	D₅⋊C₈	—	6	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
136	C₂×#168	—	2	2	no	—
137	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
138	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
139	C₈×D₅	—	2	2	no	—
140	C₈×D₅	—	2	2	no	—
141	C₈×D₅	—	2	2	no	—
142	C₈×D₅	#67	1	4	yes	—
143	C₂³×C₈	—	5	1	no	—
144	C₂×C₂²⋊C₈	—	15	1	no	—
145	C₂×C₄×C₈	—	15	2	no	—
146	C₄×C₂²⋊C₄	—	15	1	no	—
147	#336	—	15	2	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	C₄×C₈	1	2	yes	complemented
151	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₃×D₅	—	2	1	no	—
153	C₂×C₃×D₅	—	2	1	no	—
154	C₂×C₃×D₅	—	2	8	no	—
155	C₂×C₃×D₅	C₄×C₈	1	2	yes	complemented
156	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
157	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
158	C₂×C₃×D₅	#131	1	2	yes	—
159	ΓL(1,𝔽₁₆)	—	2	8	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₃×C₄×C₅	#117	1	1	yes	characteristic
163	C₃×Dic₅	—	2	1	no	—
164	C₃×Dic₅	C₄×D₄	1	2	yes	—
165	C₂⁴×C₃	—	5	1	no	—
166	C₂²×C₃×C₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	5	1	no	—
168	C₂²×C₃×C₄	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	10	2	no	—
172	C₂²×C₃×C₄	—	10	2	no	—
173	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
174	C₂²×Dic₃	—	5	4	no	—
175	C₂×C₃×C₈	—	2	2	no	—
176	C₂×C₃×C₈	—	5	1	no	—
177	C₂×C₃×C₈	—	5	4	no	—
178	C₂×C₃×C₈	—	5	1	no	—
179	C₂×C₃×C₈	—	10	2	no	—
180	C₂×C₃×C₈	—	10	2	no	—
181	C₂×C₃×C₈	—	10	2	no	—
182	C₂×C₃×C₈	—	10	2	no	—
183	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
184	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
185	#217	—	5	8	no	—
186	C₄×Dic₃	—	10	2	no	—
187	C₄×Dic₃	—	10	2	no	—
188	C₂×C₃⋊C₈	—	5	4	no	—
189	C₂×C₃⋊C₈	—	10	2	no	—
190	C₂×C₃⋊C₈	—	10	2	no	—
191	C₂³×C₅	C₄×Dic₃	1	1	yes	characteristic
192	C₂²×D₅	—	2	2	no	—
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	D₃×C₈	1	4	yes	—
195	C₂²×D₅	C₄×Dic₃	1	1	yes	characteristic
196	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
197	C₂×AGL(1,𝔽₅)	—	3	8	no	—
198	C₂×AGL(1,𝔽₅)	—	6	4	no	—
199	C₂×AGL(1,𝔽₅)	—	6	4	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
204	C₂×Dic₅	—	2	2	no	—
205	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
206	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
207	C₄×D₅	—	2	2	no	—
208	C₄×D₅	—	2	1	no	—
209	C₄×D₅	—	2	1	no	—
210	C₄×D₅	—	2	2	no	—
211	C₄×D₅	#235	1	2	yes	—
212	C₄×D₅	C₂×#67	1	2	yes	—
213	#170	—	6	4	no	—
214	C₅×C₈	—	2	1	no	—
215	C₅×C₈	#217	1	2	yes	complemented
216	#168	—	2	1	no	—
217	#168	#217	1	2	yes	complemented
218	C₂³×C₄	—	5	1	no	—
219	C₂²×C₈	—	5	1	no	—
220	C₂²×C₈	—	5	1	no	—
221	C₂²×C₈	—	5	1	no	—
222	C₂²×C₈	—	5	1	no	—
223	C₂²×C₈	—	5	1	no	—
224	C₂²×C₈	—	10	4	no	—
225	C₂²×C₈	—	15	2	no	—
226	C₂²×C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
227	C₂×C₂²⋊C₄	—	15	2	no	—
228	C₂×C₄²	—	15	2	no	—
229	C₂²⋊C₈	—	15	2	no	—
230	C₂²⋊C₈	—	15	2	no	—
231	C₄×C₈	—	30	4	no	—
232	#95	—	15	2	no	—
233	C₂×C₃×C₅	—	2	2	no	—
234	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
236	C₂×C₃×C₅	#405	1	1	yes	characteristic
237	C₃×D₅	—	2	2	no	—
238	C₃×D₅	C₈×D₄	1	4	yes	—
239	C₂³×C₃	—	5	1	no	—
240	C₂³×C₃	—	5	1	no	—
241	C₂³×C₃	—	5	4	no	—
242	C₂³×C₃	—	10	2	no	—
243	C₂³×C₃	—	10	2	no	—
244	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	5	1	no	—
248	C₂×C₃×C₄	—	5	2	no	—
249	C₂×C₃×C₄	—	5	2	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	10	2	no	—
252	C₂×C₃×C₄	—	10	2	no	—
253	C₂×C₃×C₄	—	10	2	no	—
254	C₂×C₃×C₄	—	10	1	no	—
255	C₂×C₃×C₄	—	10	1	no	—
256	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
258	C₂×Dic₃	—	5	8	no	—
259	C₂×Dic₃	—	10	4	no	—
260	C₂×Dic₃	—	10	4	no	—
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	5	2	no	—
263	C₃×C₈	—	10	1	no	—
264	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
265	C₃⋊C₈	—	10	4	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	C₈×Dic₃	1	2	yes	complemented
269	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
270	C₂×D₅	—	2	1	no	—
271	C₂×D₅	—	2	1	no	—
272	C₂×D₅	—	2	8	no	—
273	C₂×D₅	C₈×Dic₃	1	2	yes	complemented
274	C₂×D₅	C₂×D₃×C₈	1	2	yes	—
275	C₂×D₅	#901	1	2	yes	—
276	C₂×D₅	C₄×#67	1	2	yes	—
277	AGL(1,𝔽₅)	—	6	8	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	#926	1	1	yes	characteristic
280	C₄×C₅	C₂×#217	1	1	yes	characteristic
281	Dic₅	—	2	1	no	—
282	Dic₅	C₄×#67	1	2	yes	—
283	C₂⁴	—	5	1	no	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	1	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	—	10	2	no	—
290	C₂²×C₄	—	10	2	no	—
291	C₂²×C₄	—	15	4	no	—
292	C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	5	1	no	—
295	C₂×C₈	—	5	4	no	—
296	C₂×C₈	—	5	1	no	—
297	C₂×C₈	—	10	2	no	—
298	C₂×C₈	—	10	2	no	—
299	C₂×C₈	—	10	2	no	—
300	C₂×C₈	—	10	2	no	—
301	C₂×C₈	—	15	4	no	—
302	C₂×C₈	—	30	2	no	—
303	C₂×C₈	—	30	2	no	—
304	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
305	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
306	C₂²⋊C₄	—	15	8	no	—
307	C₄²	—	30	2	no	—
308	C₄²	—	30	2	no	—
309	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	5	2	no	—
313	C₂²×C₃	—	5	2	no	—
314	C₂²×C₃	—	5	2	no	—
315	C₂²×C₃	—	5	2	no	—
316	C₂²×C₃	—	10	8	no	—
317	C₂²×C₃	—	10	1	no	—
318	C₂²×C₃	—	10	1	no	—
319	C₂²×C₃	C₈×AGL(1,𝔽₅)	1	2	yes	complemented
320	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	5	2	no	—
323	C₃×C₄	—	10	1	no	—
324	C₃×C₄	#4130	1	1	yes	characteristic
325	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
326	Dic₃	—	10	8	no	—
327	C₂×C₅	—	2	2	no	—
328	C₂×C₅	C₂×C₈×Dic₃	1	1	yes	characteristic
329	C₂×C₅	#5101	1	1	yes	characteristic
330	C₂×C₅	C₄×#217	1	1	yes	characteristic
331	D₅	—	2	2	no	—
332	D₅	C₈×#67	1	4	yes	—
333	C₂³	—	5	1	no	—
334	C₂³	—	5	1	no	—
335	C₂³	—	5	4	no	—
336	C₂³	—	10	2	no	—
337	C₂³	—	10	2	no	—
338	C₂³	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	5	1	no	—
342	C₂×C₄	—	5	2	no	—
343	C₂×C₄	—	5	2	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	10	2	no	—
347	C₂×C₄	—	10	2	no	—
348	C₂×C₄	—	10	1	no	—
349	C₂×C₄	—	10	1	no	—
350	C₂×C₄	—	15	8	no	—
351	C₂×C₄	—	30	4	no	—
352	C₂×C₄	—	30	4	no	—
353	C₂×C₄	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
354	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	5	2	no	—
357	C₈	—	10	1	no	—
358	C₈	—	30	4	no	—
359	C₈	#6763	1	2	yes	direct product factor
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	5	4	no	—
362	C₂×C₃	—	10	2	no	—
363	C₂×C₃	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×C₃	#65718	1	1	yes	characteristic
365	C₂×C₃	C₄×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₅	C₈×#217	1	1	yes	characteristic, complemented, Sylow
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	5	2	no	—
370	C₂²	—	5	2	no	—
371	C₂²	—	5	2	no	—
372	C₂²	—	5	2	no	—
373	C₂²	—	10	8	no	—
374	C₂²	—	10	1	no	—
375	C₂²	—	10	1	no	—
376	C₂²	C₈×ΓL(1,𝔽₁₆)	1	2	yes	complemented
377	C₂²	C₂×C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	5	2	no	—
380	C₄	—	10	1	no	—
381	C₄	—	30	8	no	—
382	C₄	#91989	1	1	yes	characteristic
383	C₄	C₂×#6763	1	1	yes	characteristic
384	C₃	C₈×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
385	C₂	—	2	2	no	—
386	C₂	—	5	4	no	—
387	C₂	—	10	2	no	—
388	C₂	C₂×C₈×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
389	C₂	#11752377	1	1	yes	characteristic
390	C₂	C₄×#6763	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₅	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₂²×C₃×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂²×C₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₈×ΓL(1,𝔽₁₆)	C₂	semidirect
5. #11746763	C₂	semidirect
11. C₂²×C₃×C₅×C₈	C₄	semidirect
12. C₂²×C₃×#168	C₄	semidirect
14. C₂×C₃×C₈×D₅	C₄	semidirect
15. C₂×C₃×C₈×D₅	C₄	semidirect
18. #91241	C₄	semidirect
20. #91232	C₄	semidirect
38. #6763	C₈	direct (N × H)
63. C₂²×C₅×C₈	Dic₃	semidirect
64. C₂²×#168	Dic₃	semidirect
66. C₂×C₈×D₅	Dic₃	semidirect
67. C₂×C₈×D₅	Dic₃	semidirect
83. C₂×ΓL(1,𝔽₁₆)	C₂×C₈	semidirect
99. C₃×C₅×C₈	C₂²⋊C₄	semidirect
101. C₃×#168	C₂²⋊C₄	semidirect
109. C₂²×C₃×C₈	AGL(1,𝔽₅)	semidirect
150. C₂²×C₃×C₅	C₄×C₈	semidirect
155. C₂×C₃×D₅	C₄×C₈	semidirect
215. C₅×C₈	#217	semidirect
217. #168	#217	semidirect
226. C₂²×C₈	ΓL(1,𝔽₁₆)	semidirect
264. C₃×C₈	C₂²⋊AGL(1,𝔽₅)	semidirect
268. C₂²×C₅	C₈×Dic₃	semidirect
273. C₂×D₅	C₈×Dic₃	semidirect
309. C₃×C₅	C₈×C₂²⋊C₄	semidirect
319. C₂²×C₃	C₈×AGL(1,𝔽₅)	semidirect
359. C₈	#6763	direct (N × H)
366. C₅	C₈×#217	semidirect
376. C₂²	C₈×ΓL(1,𝔽₁₆)	semidirect
384. C₃	C₈×C₂²⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×D₅	2
C₄×#6763	2
D₅⋊#830	2
C₂×C₈×ΓL(1,𝔽₁₆)	2
#11746763	2
C₈×C₂²⋊AGL(1,𝔽₅)	3
C₈×#217	5

Subgroups — C8×#6763 #14295155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6763 #14295155