Subgroups — #14296447

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₃×#65676	C₂	1	1	yes	maximal, characteristic
3	C₂×#91150	C₂	1	1	yes	maximal, characteristic
4	C₂×ΓL(1,𝔽₁₆)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	D₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	#11746517	C₂	1	1	yes	maximal, characteristic
7	#11746517	C₂	1	1	yes	maximal, characteristic
8	#10604035	—	3	1	no	maximal, Hall
9	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₄	1	2	yes	—
10	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
11	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
14	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	#91235	C₄	1	2	yes	—
18	C₃×#4002	C₄	1	2	yes	complemented
19	C₃×#4002	C₄	1	2	yes	complemented
20	#91150	—	2	2	no	—
21	ΓL(1,𝔽₁₆)⋊C₈	—	2	2	no	—
22	C₄⋊(C₃⋊#168)	C₄	1	1	yes	characteristic, complemented
23	C₅×C₄⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic, complemented
24	#90982	C₄	1	1	yes	characteristic, complemented
25	#90982	C₄	1	1	yes	characteristic, complemented
26	#69810	—	5	1	no	maximal, Hall
27	C₂×#3992	—	3	1	no	—
28	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
29	C₄×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
30	#65676	D₃	1	1	yes	characteristic
31	D₅×C₄⋊C₈	—	3	1	no	—
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	C₄⋊ΓL(1,𝔽₁₆)	—	2	4	no	—
40	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
41	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
42	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
43	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
44	C₂×C₃×#170	C₂×C₄	1	2	yes	—
45	C₂×C₃×#170	C₂×C₄	1	2	yes	—
46	C₃×D₅⋊C₈	—	2	1	no	—
47	C₃×D₅⋊C₈	—	2	1	no	—
48	C₃×D₅⋊C₈	D₄	1	2	yes	—
49	C₃×D₅⋊C₈	Q₈	1	2	yes	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
53	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
58	D₅×C₃⋊C₈	—	2	1	no	—
59	D₅×C₃⋊C₈	—	2	1	no	—
60	D₅×C₃⋊C₈	—	2	1	no	—
61	D₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₃×#97	—	5	1	no	—
63	C₂×#815	—	5	1	no	—
64	C₂×C₈×Dic₃	—	5	1	no	—
65	C₄×C₄⋊Dic₃	—	5	1	no	—
66	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
67	#4550	—	5	1	no	—
68	#4550	—	5	1	no	—
69	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
70	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
71	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
72	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₈×D₅	—	3	1	no	—
75	C₂×C₈×D₅	—	3	1	no	—
76	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
77	(C₂×AGL(1,𝔽₅))⋊C₄	—	3	2	no	—
78	#4002	Dic₃	1	2	yes	complemented
79	#4002	Dic₃	1	2	yes	complemented
80	#3992	—	6	2	no	—
81	C₈×AGL(1,𝔽₅)	—	6	2	no	—
82	C₅×C₄⋊C₈	—	3	1	no	—
83	#3946	—	3	1	no	—
84	#3946	—	3	1	no	—
85	C₄⋊#168	—	3	1	no	—
86	#1771	—	15	1	no	Sylow
87	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
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)	—	2	2	no	—
93	C₂×ΓL(1,𝔽₁₆)	M₁₆	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
98	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
99	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
100	C₃×C₄×D₅	—	2	2	no	—
101	C₃×C₄×D₅	—	2	2	no	—
102	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
103	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
104	C₃×C₄×D₅	#41	1	1	yes	characteristic
105	C₃×C₄×D₅	#41	1	1	yes	characteristic
106	C₃×#170	—	2	2	no	—
107	C₃×#170	C₄⋊C₄	1	4	yes	complemented
108	C₃⋊#168	—	2	1	no	—
109	C₃⋊#168	—	2	1	no	—
110	C₅×C₃⋊C₈	—	2	1	no	—
111	C₅×C₃⋊C₈	—	2	1	no	—
112	C₂²×C₃×C₈	—	5	1	no	—
113	C₂²×C₃×C₈	—	5	1	no	—
114	C₂×C₃×C₄²	—	5	1	no	—
115	C₂×C₄⋊Dic₃	—	5	2	no	—
116	C₂×C₄×Dic₃	—	5	1	no	—
117	C₂×C₄×Dic₃	—	5	1	no	—
118	C₂²×C₃⋊C₈	—	5	1	no	—
119	C₂²×C₃⋊C₈	—	5	1	no	—
120	C₃×#97	—	5	2	no	—
121	C₃×#97	—	5	2	no	—
122	C₃⋊#95	—	5	2	no	—
123	#815	—	10	2	no	—
124	C₈×Dic₃	—	10	2	no	—
125	C₄⋊(C₃⋊C₈)	—	5	1	no	—
126	C₄⋊(C₃⋊C₈)	—	5	1	no	—
127	C₄⋊(C₃⋊C₈)	—	5	1	no	—
128	C₄⋊(C₃⋊C₈)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
129	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
130	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
131	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
132	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
134	C₂×#170	C₂×Dic₃	1	2	yes	—
135	C₂×#170	C₂×Dic₃	1	2	yes	—
136	C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
137	C₄×AGL(1,𝔽₅)	—	6	1	no	—
138	C₄×AGL(1,𝔽₅)	—	6	1	no	—
139	C₄×AGL(1,𝔽₅)	—	6	1	no	—
140	C₄×AGL(1,𝔽₅)	—	6	1	no	—
141	D₅⋊C₈	—	2	1	no	—
142	D₅⋊C₈	—	2	1	no	—
143	D₅⋊C₈	Dic₆	1	2	yes	—
144	D₅⋊C₈	D₁₂	1	2	yes	—
145	C₂×C₅×C₈	—	3	1	no	—
146	C₂×C₅×C₈	—	3	1	no	—
147	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
148	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
149	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
150	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
151	C₂×#168	—	3	1	no	—
152	C₂×#168	—	3	1	no	—
153	C₈×D₅	—	6	1	no	—
154	C₈×D₅	—	6	1	no	—
155	C₈×D₅	—	6	1	no	—
156	C₈×D₅	—	6	1	no	—
157	C₂×C₄⋊C₈	—	15	1	no	—
158	C₂×#97	—	5	1	no	—
159	C₂×#97	—	15	1	no	—
160	C₂×C₄×C₈	—	15	1	no	—
161	C₄×C₄⋊C₄	—	15	1	no	—
162	#336	—	15	1	no	—
163	#336	—	15	1	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
166	C₂×C₃×D₅	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
168	C₂×C₃×D₅	#131	1	2	yes	—
169	ΓL(1,𝔽₁₆)	—	2	4	no	—
170	ΓL(1,𝔽₁₆)	—	4	2	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₃×C₄×C₅	—	2	1	no	—
173	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
175	C₃×Dic₅	—	2	1	no	—
176	C₃×Dic₅	—	2	1	no	—
177	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₃×Dic₅	#117	1	1	yes	characteristic
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	1	no	—
182	C₂²×Dic₃	—	5	2	no	—
183	C₂²×Dic₃	—	5	2	no	—
184	C₂×C₃×C₈	—	5	2	no	—
185	C₂×C₃×C₈	—	5	2	no	—
186	C₂×C₃×C₈	—	5	2	no	—
187	C₂×C₃×C₈	—	5	2	no	—
188	C₂×C₃×C₈	—	10	1	no	—
189	C₂×C₃×C₈	—	10	1	no	—
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	—	10	4	no	—
195	C₄×Dic₃	—	10	1	no	—
196	C₄×Dic₃	—	10	1	no	—
197	C₄×Dic₃	—	10	1	no	—
198	C₄×Dic₃	—	10	1	no	—
199	C₂×C₃⋊C₈	—	5	1	no	—
200	C₂×C₃⋊C₈	—	5	1	no	—
201	C₂×C₃⋊C₈	—	10	1	no	—
202	C₂×C₃⋊C₈	—	10	1	no	—
203	C₂×C₃⋊C₈	—	10	1	no	—
204	C₂×C₃⋊C₈	—	10	1	no	—
205	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
206	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
207	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
208	C₂×AGL(1,𝔽₅)	—	3	4	no	—
209	C₂×AGL(1,𝔽₅)	—	6	2	no	—
210	C₂×AGL(1,𝔽₅)	—	6	2	no	—
211	C₂×AGL(1,𝔽₅)	—	6	2	no	—
212	C₂×AGL(1,𝔽₅)	—	6	2	no	—
213	C₂×AGL(1,𝔽₅)	—	6	2	no	—
214	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
215	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
217	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
218	C₂×Dic₅	C₄×Dic₃	1	1	yes	characteristic
219	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
220	C₄×D₅	—	2	2	no	—
221	C₄×D₅	—	2	2	no	—
222	C₄×D₅	C₂×Dic₆	1	1	yes	characteristic
223	C₄×D₅	C₂×D₁₂	1	1	yes	characteristic
224	C₄×D₅	#235	1	1	yes	characteristic
225	C₄×D₅	#235	1	1	yes	characteristic
226	#170	—	2	2	no	—
227	#170	C₄⋊Dic₃	1	4	yes	complemented
228	C₅×C₈	—	6	1	no	—
229	C₅×C₈	—	6	1	no	—
230	#168	—	6	1	no	—
231	#168	—	6	1	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	15	1	no	—
235	C₂²×C₈	—	15	1	no	—
236	C₂×C₄⋊C₄	—	15	2	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	15	1	no	—
239	C₂×C₄²	—	15	1	no	—
240	C₄⋊C₈	—	3	1	no	—
241	C₄⋊C₈	—	15	1	no	—
242	C₄⋊C₈	—	15	1	no	—
243	C₄⋊C₈	—	15	1	no	—
244	#97	—	5	2	no	—
245	#97	—	5	2	no	—
246	#97	—	30	2	no	—
247	C₄×C₈	—	30	2	no	—
248	#95	—	15	2	no	—
249	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
250	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
251	C₂×C₃×C₅	#405	1	1	yes	characteristic
252	C₃×D₅	#435	1	2	yes	—
253	C₃×D₅	#446	1	2	yes	—
254	C₂³×C₃	—	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	—	5	1	no	—
260	C₂×C₃×C₄	—	5	1	no	—
261	C₂×C₃×C₄	—	5	1	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	2	no	—
264	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
265	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₂×Dic₃	—	5	4	no	—
268	C₂×Dic₃	—	10	2	no	—
269	C₂×Dic₃	—	10	2	no	—
270	C₂×Dic₃	—	10	2	no	—
271	C₂×Dic₃	—	10	2	no	—
272	C₂×Dic₃	—	10	2	no	—
273	C₃×C₈	—	5	4	no	—
274	C₃×C₈	—	10	2	no	—
275	C₃⋊C₈	—	2	1	no	—
276	C₃⋊C₈	—	2	1	no	—
277	C₃⋊C₈	—	10	1	no	—
278	C₃⋊C₈	—	10	1	no	—
279	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
280	C₂×D₅	C₄×Dic₆	1	1	yes	characteristic
281	C₂×D₅	C₄×D₁₂	1	1	yes	characteristic
282	C₂×D₅	D₃×M₁₆	1	2	yes	—
283	C₂×D₅	#907	1	2	yes	—
284	AGL(1,𝔽₅)	—	6	4	no	—
285	AGL(1,𝔽₅)	—	12	2	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	C₄×Dic₆	1	1	yes	characteristic
289	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
290	Dic₅	—	2	1	no	—
291	Dic₅	—	2	1	no	—
292	Dic₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
293	Dic₅	#926	1	1	yes	characteristic
294	C₂²×C₄	—	5	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	15	2	no	—
298	C₂²×C₄	—	15	2	no	—
299	C₂×C₈	—	3	1	no	—
300	C₂×C₈	—	3	1	no	—
301	C₂×C₈	—	5	2	no	—
302	C₂×C₈	—	5	2	no	—
303	C₂×C₈	—	5	2	no	—
304	C₂×C₈	—	5	2	no	—
305	C₂×C₈	—	10	1	no	—
306	C₂×C₈	—	10	1	no	—
307	C₂×C₈	—	15	1	no	—
308	C₂×C₈	—	15	1	no	—
309	C₂×C₈	—	30	1	no	—
310	C₂×C₈	—	30	1	no	—
311	C₂×C₈	—	30	1	no	—
312	C₂×C₈	—	30	1	no	—
313	C₄⋊C₄	—	30	4	no	—
314	C₄²	—	5	1	no	—
315	C₄²	—	5	1	no	—
316	C₄²	—	5	1	no	—
317	C₄²	—	30	1	no	—
318	C₄²	—	30	1	no	—
319	C₄²	—	30	1	no	—
320	C₄²	—	30	1	no	—
321	C₄²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₃×C₅	#1771	1	1	yes	characteristic, complemented, Hall
323	C₂²×C₃	—	5	1	no	—
324	C₂²×C₃	—	5	1	no	—
325	C₂²×C₃	—	5	2	no	—
326	C₂²×C₃	—	5	2	no	—
327	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	5	1	no	—
331	C₃×C₄	—	5	1	no	—
332	C₃×C₄	—	10	1	no	—
333	C₃×C₄	—	10	1	no	—
334	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
336	Dic₃	—	10	4	no	—
337	Dic₃	—	20	2	no	—
338	C₂×C₅	C₄×C₄⋊Dic₃	1	1	yes	characteristic
339	C₂×C₅	Dic₃×M₁₆	1	1	yes	characteristic
340	C₂×C₅	#5122	1	1	yes	characteristic
341	D₅	#4701	1	2	yes	—
342	D₅	#4706	1	2	yes	—
343	C₂³	—	5	1	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	5	1	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	5	1	no	—
348	C₂×C₄	—	5	1	no	—
349	C₂×C₄	—	5	1	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	—	15	4	no	—
354	C₂×C₄	—	30	2	no	—
355	C₂×C₄	—	30	2	no	—
356	C₂×C₄	—	30	2	no	—
357	C₂×C₄	—	30	2	no	—
358	C₂×C₄	—	30	2	no	—
359	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
362	C₈	—	5	4	no	—
363	C₈	—	6	1	no	—
364	C₈	—	6	1	no	—
365	C₈	—	10	2	no	—
366	C₈	—	30	1	no	—
367	C₈	—	30	1	no	—
368	C₂×C₃	—	5	2	no	—
369	C₂×C₃	—	5	2	no	—
370	C₂×C₃	C₄⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₂×C₃	#65718	1	1	yes	characteristic
372	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₅	#69810	1	1	yes	characteristic, complemented, Sylow
374	C₂²	—	5	2	no	—
375	C₂²	—	5	2	no	—
376	C₂²	—	5	1	no	—
377	C₂²	—	5	1	no	—
378	C₂²	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	5	1	no	—
382	C₄	—	5	1	no	—
383	C₄	—	10	1	no	—
384	C₄	—	10	1	no	—
385	C₄	—	30	4	no	—
386	C₄	—	60	2	no	—
387	C₄	AGL(1,𝔽₅)×Dic₆	1	1	yes	characteristic
388	C₄	AGL(1,𝔽₅)×D₁₂	1	1	yes	characteristic
389	C₃	#10604035	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	5	2	no	—
391	C₂	—	5	2	no	—
392	C₂	#11751696	1	1	yes	characteristic
393	C₂	#11751698	1	1	yes	characteristic
394	C₂	AGL(1,𝔽₅)×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₃×C₄²×C₅	C₂×C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄²	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1771
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
18. C₃×#4002	C₄	semidirect
19. C₃×#4002	C₄	semidirect
22. C₄⋊(C₃⋊#168)	C₄	semidirect
23. C₅×C₄⋊(C₃⋊C₈)	C₄	semidirect
24. #90982	C₄	semidirect
25. #90982	C₄	semidirect
78. #4002	Dic₃	semidirect
79. #4002	Dic₃	semidirect
107. C₃×#170	C₄⋊C₄	semidirect
128. C₄⋊(C₃⋊C₈)	AGL(1,𝔽₅)	semidirect
227. #170	C₄⋊Dic₃	semidirect
322. C₃×C₅	#1771	semidirect
373. C₅	#69810	semidirect
389. C₃	#10604035	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊ΓL(1,𝔽₁₆)	2
C₃×#65676	2
C₂×#91150	2
C₂×ΓL(1,𝔽₁₆)⋊C₈	2
D₅×C₄⋊(C₃⋊C₈)	2
#11746517	2
#10604035	3
#69810	5