Subgroups — #14417550

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756991	C₂	1	2	yes	maximal
2	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	#11752441	C₂	1	2	yes	maximal
4	#11752398	C₂	1	4	yes	maximal, complemented
5	Q₁₆×ΓL(1,𝔽₁₆)	C₂	1	4	yes	maximal, complemented
6	#11752380	C₂	1	1	yes	maximal, characteristic
7	#11752377	C₂	1	1	yes	maximal, characteristic
8	#10617434	—	3	1	no	maximal, Hall
9	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
10	Q₈×ΓL(1,𝔽₁₆)	—	2	4	no	—
11	Q₈×ΓL(1,𝔽₁₆)	C₂²	1	8	yes	—
12	#91989	—	2	4	no	—
13	#91989	C₂²	1	2	yes	—
14	#91989	C₂²	1	1	yes	characteristic
15	D₅⋊#208	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#689	C₄	1	2	yes	complemented
18	C₃×D₅×Q₁₆	C₄	1	2	yes	complemented
19	C₃×D₅×Q₁₆	C₄	1	2	yes	complemented
20	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
21	C₃×D₅×Q₁₆	C₂²	1	2	yes	—
22	C₂×C₃×Dic₂₀	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	#91238	C₂²	1	8	yes	—
25	#91223	C₂²	1	2	yes	—
26	#91222	C₂²	1	2	yes	—
27	#91221	C₂²	1	2	yes	—
28	C₈×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
29	#83874	—	5	1	no	maximal, Hall
30	#66262	—	3	2	no	—
31	C₂×D₅×Q₁₆	D₃	1	1	yes	characteristic
32	#65782	—	3	2	no	—
33	#65739	—	3	4	no	—
34	Q₁₆×AGL(1,𝔽₅)	—	3	4	no	—
35	#65721	—	3	1	no	—
36	#65718	—	3	1	no	—
37	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
38	C₃×Q₈×D₅	—	2	2	no	—
39	C₃×Q₈×D₅	—	2	2	no	—
40	C₃×Q₈×D₅	C₂×C₄	1	4	yes	—
41	C₃×Q₈×D₅	C₂³	1	4	yes	—
42	C₂×C₃×C₄×D₅	—	2	2	no	—
43	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×Dic₁₀	—	2	2	no	—
45	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
46	#6763	—	2	2	no	—
47	#6763	D₄	1	2	yes	—
48	#6762	—	2	1	no	—
49	C₄⋊ΓL(1,𝔽₁₆)	—	2	8	no	—
50	C₄⋊ΓL(1,𝔽₁₆)	D₄	1	2	yes	—
51	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	4	yes	—
52	C₄×ΓL(1,𝔽₁₆)	—	2	8	no	—
53	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
54	C₄×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
55	#6758	—	2	1	no	—
56	D₅⋊(C₃⋊C₈)	C₂³	1	2	yes	—
57	C₃×C₅×Q₁₆	C₂×C₄	1	2	yes	—
58	C₃×C₅×Q₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
60	C₃×#689	C₂×C₄	1	4	yes	—
61	C₃×#689	C₂×C₄	1	4	yes	—
62	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
63	C₃×Dic₂₀	C₂×C₄	1	2	yes	—
64	C₃×Dic₂₀	C₂×C₄	1	2	yes	—
65	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×Q₁₆	—	5	1	no	—
70	#5812	—	5	2	no	—
71	#5225	—	5	2	no	—
72	#5184	—	5	4	no	—
73	Dic₃×Q₁₆	—	5	4	no	—
74	#5106	—	5	1	no	—
75	#5101	—	5	1	no	—
76	C₂×Q₈×D₅	C₂×D₃	1	2	yes	—
77	Q₈×AGL(1,𝔽₅)	—	3	8	no	—
78	Q₈×AGL(1,𝔽₅)	—	6	4	no	—
79	#4130	—	3	1	no	—
80	#4130	—	3	2	no	—
81	#4130	—	6	4	no	—
82	D₅⋊M₁₆	—	3	1	no	—
83	C₂×C₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
84	C₂×#689	Dic₃	1	2	yes	complemented
85	D₅×Q₁₆	Dic₃	1	2	yes	complemented
86	D₅×Q₁₆	Dic₃	1	2	yes	complemented
87	D₅×Q₁₆	C₂×D₃	1	2	yes	—
88	D₅×Q₁₆	C₂×D₃	1	2	yes	—
89	C₂×Dic₂₀	Dic₃	1	1	yes	characteristic, complemented
90	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
91	#4009	—	3	8	no	—
92	#3994	—	3	2	no	—
93	#3993	—	3	2	no	—
94	#3992	—	3	2	no	—
95	C₈×AGL(1,𝔽₅)	—	3	2	no	—
96	#2950	—	15	1	no	Sylow
97	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
98	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
99	C₂×ΓL(1,𝔽₁₆)	C₂×D₄	1	4	yes	—
100	C₃×C₅×Q₈	—	2	2	no	—
101	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
106	C₃×C₄×D₅	—	2	4	no	—
107	C₃×C₄×D₅	—	2	4	no	—
108	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
109	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₄×D₅	#41	1	1	yes	characteristic
111	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
112	C₃×Dic₁₀	—	2	2	no	—
113	C₃×Dic₁₀	—	2	4	no	—
114	C₃×Dic₁₀	—	2	4	no	—
115	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
116	C₃⋊#170	—	2	2	no	—
117	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
118	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₃×#168	C₂²×C₄	1	1	yes	characteristic
120	C₃×#168	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₃×Q₈	—	5	2	no	—
122	C₂×C₃×Q₁₆	—	5	2	no	—
123	C₂×C₃×Q₁₆	—	5	2	no	—
124	C₂×C₃×Q₁₆	—	5	2	no	—
125	C₂×C₃×Q₁₆	—	5	2	no	—
126	C₂×C₃×Q₁₆	—	5	2	no	—
127	C₂×C₃×Q₁₆	—	5	1	no	—
128	C₂×C₃×Q₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
129	C₂²×C₃×C₈	—	5	1	no	—
130	Q₈×Dic₃	—	5	8	no	—
131	Q₈×Dic₃	—	10	4	no	—
132	#926	—	5	1	no	—
133	#926	—	5	2	no	—
134	#926	—	10	4	no	—
135	C₂×#208	—	5	1	no	—
136	#835	—	5	8	no	—
137	#818	—	5	2	no	—
138	#817	—	5	2	no	—
139	#815	—	5	2	no	—
140	C₈×Dic₃	—	5	2	no	—
141	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
142	Q₈×D₅	—	2	2	no	—
143	Q₈×D₅	—	2	2	no	—
144	Q₈×D₅	C₂×Dic₃	1	4	yes	—
145	Q₈×D₅	C₂²×D₃	1	4	yes	—
146	C₂×C₄×D₅	—	2	2	no	—
147	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
148	C₂×Dic₁₀	—	2	2	no	—
149	C₂×Dic₁₀	C₂×Dic₃	1	2	yes	—
150	C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
151	C₂²⋊AGL(1,𝔽₅)	—	6	2	no	—
152	#704	—	6	1	no	—
153	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
154	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
155	C₄⋊AGL(1,𝔽₅)	—	6	8	no	—
156	C₄×AGL(1,𝔽₅)	—	3	2	no	—
157	C₄×AGL(1,𝔽₅)	—	6	8	no	—
158	C₄×AGL(1,𝔽₅)	—	6	2	no	—
159	#700	—	6	1	no	—
160	D₅⋊C₈	—	3	2	no	—
161	C₅×Q₁₆	C₂×Dic₃	1	2	yes	—
162	C₅×Q₁₆	C₂×Dic₃	1	2	yes	—
163	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
164	#689	C₂×Dic₃	1	4	yes	—
165	#689	C₂×Dic₃	1	4	yes	—
166	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
167	Dic₂₀	C₂×Dic₃	1	2	yes	—
168	Dic₂₀	C₂×Dic₃	1	2	yes	—
169	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
170	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
171	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
172	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×Q₁₆	—	5	1	no	—
174	#519	—	15	2	no	—
175	#441	—	15	4	no	—
176	C₄×Q₁₆	—	15	4	no	—
177	#427	—	15	1	no	—
178	#419	—	15	2	no	—
179	#405	—	15	1	no	—
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₂×C₃×D₅	—	2	2	no	—
182	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
183	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
184	ΓL(1,𝔽₁₆)	—	2	4	no	—
185	ΓL(1,𝔽₁₆)	—	4	4	no	—
186	C₃×C₄×C₅	—	2	4	no	—
187	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
189	C₃×Dic₅	—	2	4	no	—
190	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
191	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
192	C₂×C₃×Q₈	—	5	4	no	—
193	C₂×C₃×Q₈	—	5	4	no	—
194	C₂×C₃×Q₈	—	5	2	no	—
195	C₂×C₃×Q₈	—	10	2	no	—
196	C₂×C₃×Q₈	—	10	2	no	—
197	C₂×C₃×Q₈	—	10	2	no	—
198	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	10	2	no	—
201	C₃×Q₁₆	—	5	4	no	—
202	C₃×Q₁₆	—	5	4	no	—
203	C₃×Q₁₆	—	5	2	no	—
204	C₃×Q₁₆	—	5	2	no	—
205	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	—
206	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	—
207	C₂×C₃×C₈	—	5	1	no	—
208	C₂×C₃×C₈	—	5	1	no	—
209	C₂×C₃×C₈	—	5	1	no	—
210	C₂×C₃×C₈	—	5	1	no	—
211	C₂×C₃×C₈	—	5	1	no	—
212	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
213	#217	—	5	2	no	—
214	#217	—	10	2	no	—
215	C₄⋊Dic₃	—	5	2	no	—
216	C₄⋊Dic₃	—	5	4	no	—
217	C₄⋊Dic₃	—	10	8	no	—
218	C₄×Dic₃	—	5	2	no	—
219	C₄×Dic₃	—	10	8	no	—
220	C₄×Dic₃	—	10	2	no	—
221	#208	—	10	1	no	—
222	#208	—	10	1	no	—
223	C₂×C₃⋊C₈	—	5	2	no	—
224	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
225	C₂×AGL(1,𝔽₅)	—	3	4	no	—
226	C₂×AGL(1,𝔽₅)	—	6	4	no	—
227	C₅×Q₈	—	2	2	no	—
228	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	#237	1	1	yes	characteristic
233	C₄×D₅	—	2	4	no	—
234	C₄×D₅	—	2	4	no	—
235	C₄×D₅	D₃×D₄	1	1	yes	characteristic
236	C₄×D₅	#237	1	1	yes	characteristic
237	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
238	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
239	Dic₁₀	—	2	2	no	—
240	Dic₁₀	—	2	4	no	—
241	Dic₁₀	—	2	4	no	—
242	Dic₁₀	C₂²×Dic₃	1	4	yes	—
243	#170	—	6	2	no	—
244	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
245	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
246	#168	C₂²×Dic₃	1	1	yes	characteristic
247	#168	C₂²×Dic₃	1	1	yes	characteristic
248	C₂²×Q₈	—	5	2	no	—
249	C₂×Q₁₆	—	5	2	no	—
250	C₂×Q₁₆	—	5	2	no	—
251	C₂×Q₁₆	—	5	2	no	—
252	C₂×Q₁₆	—	5	2	no	—
253	C₂×Q₁₆	—	5	2	no	—
254	C₂×Q₁₆	—	5	1	no	—
255	C₂×Q₁₆	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
256	C₂×M₁₆	—	15	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₄×Q₈	—	15	8	no	—
259	C₄×Q₈	—	30	4	no	—
260	#117	—	15	1	no	—
261	#117	—	15	2	no	—
262	#117	—	30	4	no	—
263	#107	—	15	2	no	—
264	#106	—	15	2	no	—
265	#103	—	15	8	no	—
266	#97	—	15	2	no	—
267	C₄×C₈	—	15	2	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
270	C₃×D₅	—	2	1	no	—
271	C₃×D₅	#578	1	2	yes	—
272	C₂³×C₃	—	5	1	no	—
273	C₃×Q₈	—	2	2	no	—
274	C₃×Q₈	—	5	4	no	—
275	C₃×Q₈	—	10	4	no	—
276	C₃×Q₈	—	10	4	no	—
277	C₃×Q₈	—	10	2	no	—
278	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	5	1	no	—
281	C₂×C₃×C₄	—	5	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	5	1	no	—
285	C₂×C₃×C₄	—	10	4	no	—
286	C₂×C₃×C₄	—	10	4	no	—
287	C₂×C₃×C₄	—	10	2	no	—
288	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₂×Dic₃	—	5	4	no	—
290	C₂×Dic₃	—	10	4	no	—
291	C₃×C₈	—	5	1	no	—
292	C₃×C₈	—	5	1	no	—
293	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
294	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₃⋊C₈	—	10	2	no	—
296	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
297	C₂×D₅	—	2	2	no	—
298	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
299	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
300	AGL(1,𝔽₅)	—	6	4	no	—
301	AGL(1,𝔽₅)	—	12	4	no	—
302	C₄×C₅	—	2	4	no	—
303	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
304	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
305	Dic₅	—	2	4	no	—
306	Dic₅	D₄×Dic₃	1	1	yes	characteristic
307	Dic₅	C₂×#237	1	1	yes	characteristic
308	C₂×Q₈	—	5	4	no	—
309	C₂×Q₈	—	5	4	no	—
310	C₂×Q₈	—	5	2	no	—
311	C₂×Q₈	—	10	2	no	—
312	C₂×Q₈	—	10	2	no	—
313	C₂×Q₈	—	10	2	no	—
314	C₂×Q₈	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	10	2	no	—
317	Q₁₆	—	5	4	no	—
318	Q₁₆	—	5	4	no	—
319	Q₁₆	—	5	2	no	—
320	Q₁₆	—	5	2	no	—
321	Q₁₆	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
322	Q₁₆	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
323	M₁₆	—	30	1	no	—
324	M₁₆	—	30	1	no	—
325	C₂×C₈	—	5	1	no	—
326	C₂×C₈	—	5	1	no	—
327	C₂×C₈	—	5	1	no	—
328	C₂×C₈	—	5	1	no	—
329	C₂×C₈	—	5	1	no	—
330	C₂×C₈	—	15	2	no	—
331	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
332	C₄⋊C₄	—	15	2	no	—
333	C₄⋊C₄	—	15	4	no	—
334	C₄⋊C₄	—	30	8	no	—
335	C₂²⋊C₄	—	15	2	no	—
336	C₂²⋊C₄	—	30	2	no	—
337	C₄²	—	15	2	no	—
338	C₄²	—	30	2	no	—
339	C₄²	—	30	8	no	—
340	C₃×C₅	#2950	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	5	1	no	—
342	C₂²×C₃	—	5	1	no	—
343	C₂²×C₃	—	10	2	no	—
344	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	5	1	no	—
347	C₃×C₄	—	5	1	no	—
348	C₃×C₄	—	10	4	no	—
349	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
351	Dic₃	—	10	4	no	—
352	Dic₃	—	20	4	no	—
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
355	D₅	—	2	1	no	—
356	D₅	#5766	1	2	yes	—
357	C₂³	—	5	1	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	5	4	no	—
360	Q₈	—	10	4	no	—
361	Q₈	—	10	4	no	—
362	Q₈	—	10	2	no	—
363	Q₈	C₂²×ΓL(1,𝔽₁₆)	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	5	1	no	—
366	C₂×C₄	—	5	1	no	—
367	C₂×C₄	—	5	1	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	5	1	no	—
370	C₂×C₄	—	10	4	no	—
371	C₂×C₄	—	10	4	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	15	4	no	—
374	C₂×C₄	—	30	4	no	—
375	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
376	C₈	—	5	1	no	—
377	C₈	—	5	1	no	—
378	C₈	—	30	2	no	—
379	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
380	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	5	2	no	—
383	C₂×C₃	—	10	1	no	—
384	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₅	#83874	1	1	yes	characteristic, complemented, Sylow
386	C₂²	—	5	1	no	—
387	C₂²	—	5	1	no	—
388	C₂²	—	10	2	no	—
389	C₂²	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
390	C₄	—	2	4	no	—
391	C₄	—	5	1	no	—
392	C₄	—	5	1	no	—
393	C₄	—	10	4	no	—
394	C₄	—	30	4	no	—
395	C₄	—	60	4	no	—
396	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
397	C₄	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
398	C₃	#10617434	1	1	yes	characteristic, complemented, Sylow
399	C₂	—	2	1	no	—
400	C₂	—	5	2	no	—
401	C₂	—	10	1	no	—
402	C₂	C₂×D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×ΓL(1,𝔽₁₆)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₅×Q₁₆	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×Q₁₆	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#2950
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #11752398	C₂	semidirect
5. Q₁₆×ΓL(1,𝔽₁₆)	C₂	semidirect
16. C₂×C₃×C₅×Q₁₆	C₄	semidirect
17. C₂×C₃×#689	C₄	semidirect
18. C₃×D₅×Q₁₆	C₄	semidirect
19. C₃×D₅×Q₁₆	C₄	semidirect
22. C₂×C₃×Dic₂₀	C₄	semidirect
83. C₂×C₅×Q₁₆	Dic₃	semidirect
84. C₂×#689	Dic₃	semidirect
85. D₅×Q₁₆	Dic₃	semidirect
86. D₅×Q₁₆	Dic₃	semidirect
89. C₂×Dic₂₀	Dic₃	semidirect
128. C₂×C₃×Q₁₆	AGL(1,𝔽₅)	semidirect
255. C₂×Q₁₆	ΓL(1,𝔽₁₆)	semidirect
340. C₃×C₅	#2950	semidirect
385. C₅	#83874	semidirect
398. C₃	#10617434	semidirect

Maximal subgroups

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

subgroup	index
#11756991	2
C₂×C₃×D₅×Q₁₆	2
#11752441	2
#11752398	2
Q₁₆×ΓL(1,𝔽₁₆)	2
#11752380	2
#11752377	2
#10617434	3
#83874	5