Subgroups — #15828636

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
3	#13113139	C₂	1	4	yes	maximal, complemented
4	#13113131	C₂	1	4	yes	maximal, complemented
5	#13113129	C₂	1	2	yes	maximal, complemented
6	#13113120	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6099	C₄	1	2	yes	—
10	C₁₃×#432	C₄	1	2	yes	—
11	C₁₃×#432	C₄	1	2	yes	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₁₃×#431	C₂²	1	2	yes	—
14	C₁₃×#423	C₄	1	2	yes	—
15	C₁₃×#407	C₄	1	2	yes	—
16	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
17	#11718868	C₄	1	2	yes	—
18	#11718587	C₄	1	2	yes	—
19	#11718587	C₄	1	2	yes	—
20	#11718586	C₂²	1	2	yes	—
21	#11718586	C₂²	1	2	yes	—
22	#11718585	C₄	1	2	yes	—
23	C₄×#6099	C₄	1	2	yes	—
24	C₄×#6099	C₄	1	2	yes	—
25	C₄×#6099	C₂²	1	2	yes	—
26	C₄×#6099	C₂²	1	2	yes	—
27	C₄×#6099	C₂²	1	2	yes	—
28	C₂×#88043	C₄	1	2	yes	—
29	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
30	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
31	#11718047	C₂²	1	4	yes	complemented
32	#11718046	C₂²	1	4	yes	complemented
33	#11718046	C₂²	1	4	yes	complemented
34	C₈×#1055	C₂²	1	4	yes	complemented
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6099	—	2	8	no	—
52	C₂×#6099	C₂×C₄	1	4	yes	—
53	C₂×#6099	C₂×C₄	1	4	yes	—
54	C₂×#6099	C₂×C₄	1	4	yes	—
55	C₂²×#1055	C₂×C₄	1	2	yes	—
56	C₂²×#1055	C₂×C₄	1	2	yes	—
57	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₁₃×#97	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₁₃	C₂³	1	4	yes	—
63	C₂²⋊#1055	C₂×C₄	1	4	yes	—
64	C₂²⋊#1055	C₂×C₄	1	4	yes	—
65	C₄⋊#1055	C₂×C₄	1	4	yes	—
66	C₄⋊#1055	C₂×C₄	1	4	yes	—
67	#88043	C₂×C₄	1	4	yes	—
68	#88043	C₂×C₄	1	4	yes	—
69	#88043	C₂×C₄	1	4	yes	—
70	C₄×#1055	C₂×C₄	1	2	yes	—
71	C₄×#1055	C₂×C₄	1	2	yes	—
72	C₄×#1055	C₂³	1	2	yes	—
73	C₄×#1055	C₂³	1	4	yes	—
74	C₄×#1055	C₂³	1	2	yes	—
75	#17334	—	13	1	no	maximal, Sylow
76	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	—	2	4	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₁₃×M₁₆	—	4	4	no	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
100	C₄²×C₁₃	C₄²	1	1	yes	characteristic
101	C₄²×C₁₃	C₄²	1	1	yes	characteristic
102	C₄²×C₁₃	C₄²	1	1	yes	characteristic
103	C₄²×C₁₃	C₄²	1	1	yes	characteristic
104	C₄²×C₁₃	C₄²	1	1	yes	characteristic
105	C₄²×C₁₃	C₄²	1	1	yes	characteristic
106	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
116	#6099	—	2	8	no	—
117	#6099	—	2	8	no	—
118	#6099	—	4	4	no	—
119	C₂×#1055	—	2	4	no	—
120	C₂×#1055	M₁₆	1	8	yes	complemented
121	C₂×#1055	C₂²×C₄	1	8	yes	—
122	C₂×#1055	C₂²×C₄	1	4	yes	—
123	C₂×#1055	C₂²×C₄	1	4	yes	—
124	#2920	—	13	1	no	—
125	#2920	D₁₃	1	1	yes	characteristic
126	C₂×C₄×M₁₆	—	13	1	no	—
127	#1455	—	13	4	no	—
128	#1453	—	13	4	no	—
129	#1452	—	13	2	no	—
130	#1450	—	13	2	no	—
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	—	4	1	no	—
134	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
136	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	—	4	1	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₈×C₁₃	—	2	8	no	—
168	#1055	—	2	4	no	—
169	#1055	—	2	8	no	—
170	#1055	C₂×M₁₆	1	8	yes	—
171	C₂²×M₁₆	—	13	2	no	—
172	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
173	#432	—	13	2	no	—
174	#432	—	13	2	no	—
175	#432	Dic₁₃	1	2	yes	—
176	#432	Dic₁₃	1	2	yes	—
177	#431	—	13	2	no	—
178	#431	—	13	2	no	—
179	#431	C₂×D₁₃	1	2	yes	—
180	#431	C₂×D₁₃	1	2	yes	—
181	#423	—	13	2	no	—
182	#423	Dic₁₃	1	2	yes	—
183	#407	—	13	2	no	—
184	#407	Dic₁₃	1	2	yes	—
185	C₄×M₁₆	—	13	2	no	—
186	C₄×M₁₆	—	13	2	no	—
187	C₄×M₁₆	—	13	2	no	—
188	C₄×M₁₆	—	13	2	no	—
189	C₄×M₁₆	—	13	2	no	—
190	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
191	C₂×#97	—	13	2	no	—
192	C₂×C₄×C₈	—	13	1	no	—
193	C₂×C₄×C₈	—	13	1	no	—
194	#322	—	13	4	no	—
195	#322	—	13	4	no	—
196	#322	—	13	4	no	—
197	C₈²	—	13	4	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	4	4	no	—
207	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
208	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
218	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
219	C₄×C₁₃	#568	1	2	yes	—
220	C₄×C₁₃	#568	1	2	yes	—
221	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
224	C₂×M₁₆	—	13	4	no	—
225	C₂×M₁₆	—	13	4	no	—
226	C₂×M₁₆	—	13	4	no	—
227	C₂×M₁₆	—	26	8	no	—
228	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
229	C₂²×C₈	—	13	2	no	—
230	C₂²×C₈	—	13	2	no	—
231	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
239	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
243	C₄⋊C₈	—	13	4	no	—
244	C₄⋊C₈	—	13	4	no	—
245	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
246	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
247	C₂²⋊C₈	—	13	4	no	—
248	C₂²⋊C₈	—	13	4	no	—
249	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
250	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
251	#97	—	13	4	no	—
252	#97	—	13	4	no	—
253	#97	—	13	4	no	—
254	#97	C₂×Dic₁₃	1	4	yes	—
255	C₄×C₈	—	13	2	no	—
256	C₄×C₈	—	13	2	no	—
257	C₄×C₈	—	13	2	no	—
258	C₄×C₈	—	13	4	no	—
259	C₄×C₈	—	13	2	no	—
260	C₄×C₈	C₂²×D₁₃	1	4	yes	—
261	C₂×C₁₃	—	2	2	no	—
262	C₂×C₁₃	—	4	1	no	—
263	C₂×C₁₃	—	4	1	no	—
264	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
265	C₂×C₁₃	#2873	1	1	yes	characteristic
266	C₂×C₁₃	#2873	1	1	yes	characteristic
267	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
289	M₁₆	—	4	4	no	—
290	M₁₆	—	26	8	no	—
291	M₁₆	—	26	8	no	—
292	M₁₆	—	52	4	no	—
293	C₂×C₈	—	13	8	no	—
294	C₂×C₈	—	13	4	no	—
295	C₂×C₈	—	13	4	no	—
296	C₂×C₈	—	13	8	no	—
297	C₂×C₈	—	26	4	no	—
298	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
299	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
300	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
301	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
302	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
303	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
304	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
305	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
307	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
310	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
312	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
313	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
314	C₄²	C₂³×D₁₃	1	1	yes	characteristic
315	C₁₃	#17334	1	1	yes	characteristic, complemented, Sylow
316	C₂³	—	2	2	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
320	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
321	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
340	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
351	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
352	C₈	—	2	8	no	—
353	C₈	—	13	8	no	—
354	C₈	—	26	4	no	—
355	C₈	—	26	8	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	4	4	no	—
365	C₂²	M₁₆×Dic₁₃	1	2	yes	—
366	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	M₁₆×Dic₁₃	1	2	yes	—
376	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
377	C₄	#11719450	1	2	yes	—
378	C₄	#11719524	1	2	yes	—
379	C₂	—	2	2	no	—
380	C₂	—	4	1	no	—
381	C₂	—	4	1	no	—
382	C₂	C₂×M₁₆×Dic₁₃	1	1	yes	characteristic
383	C₂	#13123254	1	1	yes	characteristic
384	C₂	#13123255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#2920	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17334
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13113139	C₂	semidirect
4. #13113131	C₂	semidirect
5. #13113129	C₂	semidirect
6. #13113120	C₂	semidirect
31. #11718047	C₂²	semidirect
32. #11718046	C₂²	semidirect
33. #11718046	C₂²	semidirect
34. C₈×#1055	C₂²	semidirect
120. C₂×#1055	M₁₆	semidirect
315. C₁₃	#17334	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
C₂×C₄×#6099	2
#13113139	2
#13113131	2
#13113129	2
#13113120	2
C₁₃×#2920	2
#17334	13