Subgroups — #14296192

Order 1920.

520 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	C₂×#91221	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
3	#11752345	C₂	1	1	yes	maximal, characteristic
4	D₅⋊(C₄⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic
5	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#11746763	C₂	1	1	yes	maximal, characteristic
7	#11746763	C₂	1	1	yes	maximal, characteristic
8	#10604029	—	3	1	no	maximal, Hall
9	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
10	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
11	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
16	#91235	C₄	1	2	yes	—
17	#91235	C₄	1	2	yes	—
18	#91233	C₄	1	2	yes	complemented
19	C₄⋊(C₃⋊#170)	C₄	1	2	yes	complemented
20	#91221	—	2	2	no	—
21	C₈×ΓL(1,𝔽₁₆)	—	2	2	no	—
22	C₃×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
23	C₃×#3946	C₄	1	1	yes	characteristic, complemented
24	C₃×#3946	C₄	1	1	yes	characteristic, complemented
25	C₃×C₄⋊#168	C₄	1	1	yes	characteristic, complemented
26	#70442	—	5	1	no	maximal, Hall
27	C₂×#3992	—	3	1	no	—
28	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
29	#65686	—	3	1	no	—
30	D₅⋊(C₄⋊C₈)	—	3	1	no	—
31	D₅×C₄⋊C₈	D₃	1	1	yes	characteristic
32	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
33	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
34	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
35	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
36	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
39	C₂×C₃⋊#170	C₂×C₄	1	2	yes	—
40	C₂×C₃⋊#170	C₂×C₄	1	2	yes	—
41	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
42	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
43	C₄×ΓL(1,𝔽₁₆)	D₄	1	2	yes	—
44	C₄×ΓL(1,𝔽₁₆)	Q₈	1	2	yes	—
45	D₅⋊(C₃⋊C₈)	—	2	1	no	—
46	D₅⋊(C₃⋊C₈)	—	2	1	no	—
47	D₅⋊(C₃⋊C₈)	—	2	1	no	—
48	D₅⋊(C₃⋊C₈)	—	2	1	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
57	C₃×C₈×D₅	—	2	1	no	—
58	C₃×C₈×D₅	—	2	1	no	—
59	C₃×C₈×D₅	—	2	1	no	—
60	C₃×C₈×D₅	—	2	1	no	—
61	C₂×C₃×C₄⋊C₈	—	5	1	no	—
62	C₂×#815	—	5	1	no	—
63	C₂×C₈×Dic₃	—	5	1	no	—
64	#4932	—	5	1	no	—
65	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
66	#4550	—	5	1	no	—
67	#4550	—	5	1	no	—
68	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
69	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
70	C₂×D₅⋊C₈	—	3	1	no	—
71	C₂×D₅⋊C₈	—	3	1	no	—
72	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
73	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
74	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
75	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	2	no	—
76	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	2	no	—
77	#4004	—	3	2	no	—
78	C₄⋊#170	—	3	2	no	—
79	#3992	—	6	2	no	—
80	C₈×AGL(1,𝔽₅)	—	6	2	no	—
81	C₅×C₄⋊C₈	Dic₃	1	1	yes	characteristic, complemented
82	#3946	Dic₃	1	1	yes	characteristic, complemented
83	#3946	Dic₃	1	1	yes	characteristic, complemented
84	C₄⋊#168	Dic₃	1	1	yes	characteristic, complemented
85	#1768	—	15	1	no	Sylow
86	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
88	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
89	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
90	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
91	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
92	C₂×ΓL(1,𝔽₁₆)	C₄⋊C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
97	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
98	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
99	C₃×C₄×D₅	—	2	2	no	—
100	C₃×C₄×D₅	—	2	2	no	—
101	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
102	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
103	C₃×C₄×D₅	#41	1	1	yes	characteristic
104	C₃×C₄×D₅	#41	1	1	yes	characteristic
105	C₃⋊#170	—	2	2	no	—
106	C₃⋊#170	—	2	2	no	—
107	C₃×C₅×C₈	—	2	1	no	—
108	C₃×C₅×C₈	—	2	1	no	—
109	C₃×#168	—	2	1	no	—
110	C₃×#168	—	2	1	no	—
111	C₂²×C₃×C₈	—	5	1	no	—
112	C₂²×C₃×C₈	—	5	1	no	—
113	C₂×C₃×C₄²	—	5	1	no	—
114	C₂×C₄×Dic₃	—	5	1	no	—
115	C₂×C₄×Dic₃	—	5	1	no	—
116	C₂²×C₃⋊C₈	—	5	1	no	—
117	C₂²×C₃⋊C₈	—	5	1	no	—
118	C₃×C₄⋊C₈	—	5	1	no	—
119	C₃×C₄⋊C₈	—	5	1	no	—
120	C₃×C₄⋊C₈	—	5	1	no	—
121	C₃×C₄⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
122	C₃⋊#95	—	5	2	no	—
123	C₃⋊#95	—	5	2	no	—
124	#815	—	10	2	no	—
125	C₈×Dic₃	—	10	2	no	—
126	C₄⋊(C₃⋊C₈)	—	5	2	no	—
127	C₄⋊(C₃⋊C₈)	—	5	2	no	—
128	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
129	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
130	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
131	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
133	C₂×#170	—	3	2	no	—
134	C₂×#170	—	3	2	no	—
135	C₄×AGL(1,𝔽₅)	—	3	2	no	—
136	C₄×AGL(1,𝔽₅)	—	3	2	no	—
137	C₄×AGL(1,𝔽₅)	—	6	1	no	—
138	C₄×AGL(1,𝔽₅)	—	6	1	no	—
139	D₅⋊C₈	—	6	1	no	—
140	D₅⋊C₈	—	6	1	no	—
141	D₅⋊C₈	—	6	1	no	—
142	D₅⋊C₈	—	6	1	no	—
143	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
145	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
146	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
147	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
148	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
149	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
150	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
151	C₈×D₅	—	2	1	no	—
152	C₈×D₅	—	2	1	no	—
153	C₈×D₅	—	2	1	no	—
154	C₈×D₅	—	2	1	no	—
155	C₂×C₄⋊C₈	—	5	1	no	—
156	C₂×C₄⋊C₈	—	15	1	no	—
157	C₂×#97	—	15	1	no	—
158	C₂×C₄×C₈	—	15	1	no	—
159	#376	—	15	1	no	—
160	#336	—	15	1	no	—
161	#336	—	15	1	no	—
162	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₃×D₅	#117	1	1	yes	characteristic
165	C₂×C₃×D₅	#131	1	2	yes	—
166	C₂×C₃×D₅	#131	1	2	yes	—
167	ΓL(1,𝔽₁₆)	—	2	4	no	—
168	ΓL(1,𝔽₁₆)	—	4	2	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
172	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
173	C₃×Dic₅	—	2	1	no	—
174	C₃×Dic₅	—	2	1	no	—
175	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
176	C₃×Dic₅	C₄×Q₈	1	1	yes	characteristic
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×Dic₃	—	5	2	no	—
181	C₂²×Dic₃	—	5	2	no	—
182	C₂×C₃×C₈	—	5	1	no	—
183	C₂×C₃×C₈	—	5	1	no	—
184	C₂×C₃×C₈	—	10	1	no	—
185	C₂×C₃×C₈	—	10	1	no	—
186	C₂×C₃×C₈	—	10	1	no	—
187	C₂×C₃×C₈	—	10	1	no	—
188	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
190	C₃×C₄²	—	5	1	no	—
191	C₃×C₄²	—	5	1	no	—
192	C₃×C₄²	—	5	1	no	—
193	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₄×Dic₃	—	5	2	no	—
195	C₄×Dic₃	—	5	2	no	—
196	C₄×Dic₃	—	10	1	no	—
197	C₄×Dic₃	—	10	1	no	—
198	C₂×C₃⋊C₈	—	5	2	no	—
199	C₂×C₃⋊C₈	—	5	2	no	—
200	C₂×C₃⋊C₈	—	10	1	no	—
201	C₂×C₃⋊C₈	—	10	1	no	—
202	C₂×C₃⋊C₈	—	10	1	no	—
203	C₂×C₃⋊C₈	—	10	1	no	—
204	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×AGL(1,𝔽₅)	—	3	4	no	—
206	C₂×AGL(1,𝔽₅)	—	6	2	no	—
207	C₂×AGL(1,𝔽₅)	—	6	2	no	—
208	C₂×AGL(1,𝔽₅)	—	6	2	no	—
209	C₂×AGL(1,𝔽₅)	—	6	2	no	—
210	C₂×AGL(1,𝔽₅)	—	6	2	no	—
211	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
212	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
214	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
215	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
216	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
217	C₄×D₅	—	2	2	no	—
218	C₄×D₅	—	2	2	no	—
219	C₄×D₅	D₃×D₄	1	1	yes	characteristic
220	C₄×D₅	#237	1	1	yes	characteristic
221	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
222	C₄×D₅	#239	1	1	yes	characteristic
223	#170	—	6	2	no	—
224	#170	—	6	2	no	—
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	2	1	no	—
227	#168	—	2	1	no	—
228	#168	—	2	1	no	—
229	C₂²×C₈	—	5	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	15	1	no	—
232	C₂²×C₈	—	15	1	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	15	1	no	—
235	C₂×C₄²	—	15	1	no	—
236	C₄⋊C₈	—	5	1	no	—
237	C₄⋊C₈	—	5	1	no	—
238	C₄⋊C₈	—	5	1	no	—
239	C₄⋊C₈	—	15	2	no	—
240	C₄⋊C₈	—	15	2	no	—
241	C₄⋊C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
242	#97	—	30	2	no	—
243	C₄×C₈	—	30	2	no	—
244	#95	—	15	2	no	—
245	#95	—	15	2	no	—
246	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₅	#405	1	1	yes	characteristic
248	C₂×C₃×C₅	#405	1	1	yes	characteristic
249	C₃×D₅	#424	1	2	yes	—
250	C₃×D₅	#433	1	2	yes	—
251	C₂³×C₃	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	1	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	—	10	2	no	—
261	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₂×Dic₃	—	5	4	no	—
265	C₂×Dic₃	—	10	2	no	—
266	C₂×Dic₃	—	10	2	no	—
267	C₂×Dic₃	—	10	2	no	—
268	C₂×Dic₃	—	10	2	no	—
269	C₂×Dic₃	—	10	2	no	—
270	C₃×C₈	—	2	1	no	—
271	C₃×C₈	—	2	1	no	—
272	C₃×C₈	—	10	1	no	—
273	C₃×C₈	—	10	1	no	—
274	C₃⋊C₈	—	10	2	no	—
275	C₃⋊C₈	—	10	2	no	—
276	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
277	C₂×D₅	D₃×C₄⋊C₄	1	1	yes	characteristic
278	C₂×D₅	#892	1	1	yes	characteristic
279	C₂×D₅	#901	1	2	yes	—
280	C₂×D₅	#907	1	2	yes	—
281	AGL(1,𝔽₅)	—	6	4	no	—
282	AGL(1,𝔽₅)	—	12	2	no	—
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
286	C₄×C₅	Q₈×Dic₃	1	1	yes	characteristic
287	Dic₅	—	2	1	no	—
288	Dic₅	—	2	1	no	—
289	Dic₅	#887	1	1	yes	characteristic
290	Dic₅	#893	1	1	yes	characteristic
291	C₂²×C₄	—	5	1	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	15	2	no	—
295	C₂²×C₄	—	15	2	no	—
296	C₂×C₈	—	5	1	no	—
297	C₂×C₈	—	5	1	no	—
298	C₂×C₈	—	10	1	no	—
299	C₂×C₈	—	10	1	no	—
300	C₂×C₈	—	10	1	no	—
301	C₂×C₈	—	10	1	no	—
302	C₂×C₈	—	15	2	no	—
303	C₂×C₈	—	15	2	no	—
304	C₂×C₈	—	30	1	no	—
305	C₂×C₈	—	30	1	no	—
306	C₂×C₈	—	30	1	no	—
307	C₂×C₈	—	30	1	no	—
308	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
309	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
310	C₄²	—	5	1	no	—
311	C₄²	—	5	1	no	—
312	C₄²	—	5	1	no	—
313	C₄²	—	15	2	no	—
314	C₄²	—	15	2	no	—
315	C₄²	—	30	1	no	—
316	C₄²	—	30	1	no	—
317	C₄²	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
318	C₃×C₅	#1768	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	5	1	no	—
320	C₂²×C₃	—	5	1	no	—
321	C₂²×C₃	—	5	2	no	—
322	C₂²×C₃	—	5	2	no	—
323	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	5	1	no	—
327	C₃×C₄	—	5	1	no	—
328	C₃×C₄	—	10	1	no	—
329	C₃×C₄	—	10	1	no	—
330	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
331	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
332	Dic₃	—	10	4	no	—
333	Dic₃	—	20	2	no	—
334	C₂×C₅	Dic₃×C₄⋊C₄	1	1	yes	characteristic
335	C₂×C₅	#5101	1	1	yes	characteristic
336	C₂×C₅	#5122	1	1	yes	characteristic
337	D₅	#4839	1	2	yes	—
338	D₅	#4840	1	2	yes	—
339	C₂³	—	5	1	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	5	1	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	1	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	5	1	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	10	2	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	15	4	no	—
350	C₂×C₄	—	30	2	no	—
351	C₂×C₄	—	30	2	no	—
352	C₂×C₄	—	30	2	no	—
353	C₂×C₄	—	30	2	no	—
354	C₂×C₄	—	30	2	no	—
355	C₂×C₄	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
356	C₂×C₄	C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
357	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	10	1	no	—
361	C₈	—	10	1	no	—
362	C₈	—	30	2	no	—
363	C₈	—	30	2	no	—
364	C₂×C₃	—	5	2	no	—
365	C₂×C₃	—	5	2	no	—
366	C₂×C₃	C₄⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₂×C₃	#65718	1	1	yes	characteristic
368	C₂×C₃	#65728	1	1	yes	characteristic
369	C₅	#70442	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	5	1	no	—
371	C₂²	—	5	1	no	—
372	C₂²	—	5	2	no	—
373	C₂²	—	5	2	no	—
374	C₂²	C₂×C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	5	1	no	—
378	C₄	—	5	1	no	—
379	C₄	—	10	1	no	—
380	C₄	—	10	1	no	—
381	C₄	—	30	4	no	—
382	C₄	—	60	2	no	—
383	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
384	C₄	Q₈×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
385	C₃	#10604029	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	5	2	no	—
387	C₂	—	5	2	no	—
388	C₂	C₄⋊C₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
389	C₂	#11752377	1	1	yes	characteristic
390	C₂	#11752387	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
commutator, socle	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₃×C₅×C₄⋊C₈	C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄⋊C₈	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1768
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
18. #91233	C₄	semidirect
19. C₄⋊(C₃⋊#170)	C₄	semidirect
22. C₃×C₅×C₄⋊C₈	C₄	semidirect
23. C₃×#3946	C₄	semidirect
24. C₃×#3946	C₄	semidirect
25. C₃×C₄⋊#168	C₄	semidirect
81. C₅×C₄⋊C₈	Dic₃	semidirect
82. #3946	Dic₃	semidirect
83. #3946	Dic₃	semidirect
84. C₄⋊#168	Dic₃	semidirect
121. C₃×C₄⋊C₈	AGL(1,𝔽₅)	semidirect
241. C₄⋊C₈	ΓL(1,𝔽₁₆)	semidirect
318. C₃×C₅	#1768	semidirect
369. C₅	#70442	semidirect
385. C₃	#10604029	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91221	2
C₂×C₈×ΓL(1,𝔽₁₆)	2
#11752345	2
D₅⋊(C₄⋊(C₃⋊C₈))	2
C₃×D₅×C₄⋊C₈	2
#11746763	2
#10604029	3
#70442	5