Subgroups — #15828577

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 400 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	#13113131	C₂	1	4	yes	maximal, complemented
4	#13113126	C₂	1	2	yes	maximal, complemented
5	#13113125	C₂	1	2	yes	maximal, complemented
6	#13113117	C₂	1	2	yes	maximal, complemented
7	C₈×#6099	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₄	1	2	yes	—
11	C₁₃×#431	C₄	1	2	yes	—
12	C₁₃×#431	C₄	1	2	yes	—
13	C₁₃×#431	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
19	#11718868	C₄	1	2	yes	—
20	#11718587	C₄	1	2	yes	—
21	#11718587	C₄	1	2	yes	—
22	#11718586	C₂²	1	2	yes	—
23	#11718586	C₂²	1	2	yes	—
24	#11718585	C₄	1	2	yes	—
25	C₄×#6099	C₄	1	2	yes	—
26	C₄×#6099	C₄	1	2	yes	—
27	C₄×#6099	C₂²	1	1	yes	characteristic
28	C₄×#6099	C₂²	1	2	yes	—
29	C₄×#6099	C₂²	1	1	yes	characteristic
30	C₄×#6099	C₂²	1	2	yes	—
31	C₂×#88043	C₄	1	2	yes	—
32	C₂×C₄×#1055	C₂²	1	2	yes	—
33	#11718047	C₂²	1	4	yes	complemented
34	#11718046	C₂²	1	4	yes	complemented
35	#11718046	C₂²	1	4	yes	complemented
36	C₈×#1055	C₂²	1	4	yes	complemented
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×#6099	—	2	8	no	—
54	C₂×#6099	C₂×C₄	1	2	yes	—
55	C₂×#6099	C₂×C₄	1	4	yes	—
56	C₂×#6099	C₂×C₄	1	4	yes	—
57	C₂×#6099	C₂×C₄	1	2	yes	—
58	C₂²×#1055	C₂×C₄	1	4	yes	—
59	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
63	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
66	C₄×C₈×C₁₃	C₂³	1	2	yes	—
67	C₄×C₈×C₁₃	C₂³	1	2	yes	—
68	C₂²⋊#1055	C₂×C₄	1	4	yes	—
69	C₂²⋊#1055	C₂×C₄	1	4	yes	—
70	C₄⋊#1055	C₂×C₄	1	4	yes	—
71	C₄⋊#1055	C₂×C₄	1	4	yes	—
72	#88043	C₂×C₄	1	2	yes	—
73	#88043	C₂×C₄	1	4	yes	—
74	#88043	C₂×C₄	1	2	yes	—
75	#88043	C₂×C₄	1	4	yes	—
76	C₄×#1055	C₂×C₄	1	4	yes	—
77	C₄×#1055	C₂³	1	2	yes	—
78	C₄×#1055	C₂³	1	4	yes	—
79	C₄×#1055	C₂³	1	2	yes	—
80	#17327	—	13	1	no	maximal, Sylow
81	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄²	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	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	4	4	no	—
104	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
105	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
106	C₄²×C₁₃	C₄²	1	1	yes	characteristic
107	C₄²×C₁₃	C₄²	1	1	yes	characteristic
108	C₄²×C₁₃	C₄²	1	1	yes	characteristic
109	C₄²×C₁₃	C₄²	1	1	yes	characteristic
110	C₄²×C₁₃	C₄²	1	1	yes	characteristic
111	C₄²×C₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
122	#6099	—	2	4	no	—
123	#6099	—	2	8	no	—
124	#6099	—	2	8	no	—
125	#6099	M₁₆	1	8	yes	complemented
126	C₂×#1055	—	2	8	no	—
127	C₂×#1055	C₂²×C₄	1	8	yes	—
128	C₂×#1055	C₂²×C₄	1	4	yes	—
129	C₂×#1055	C₂²×C₄	1	4	yes	—
130	#2920	—	13	1	no	—
131	C₂×#431	D₁₃	1	1	yes	characteristic
132	C₂×C₄×M₁₆	—	13	1	no	—
133	#1453	—	13	4	no	—
134	#1451	—	13	2	no	—
135	#1451	—	13	2	no	—
136	C₈×M₁₆	—	13	2	no	—
137	C₈×M₁₆	—	13	2	no	—
138	C₂³×C₁₃	—	2	2	no	—
139	C₂³×C₁₃	—	2	2	no	—
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
143	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
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	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
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×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
170	C₂×C₄×C₁₃	#131	1	4	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₈×C₁₃	—	2	4	no	—
175	C₈×C₁₃	—	2	4	no	—
176	#1055	—	2	4	no	—
177	#1055	—	2	8	no	—
178	#1055	C₂×M₁₆	1	8	yes	—
179	C₂²×M₁₆	—	13	2	no	—
180	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
181	#432	—	13	2	no	—
182	#432	—	13	2	no	—
183	#431	—	13	2	no	—
184	#431	—	13	2	no	—
185	#431	Dic₁₃	1	2	yes	—
186	#431	Dic₁₃	1	2	yes	—
187	#431	C₂×D₁₃	1	1	yes	characteristic
188	#431	C₂×D₁₃	1	1	yes	characteristic
189	#431	C₂×D₁₃	1	2	yes	—
190	#423	—	13	2	no	—
191	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
192	#407	—	13	2	no	—
193	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
194	C₄×M₁₆	—	13	2	no	—
195	C₄×M₁₆	—	13	2	no	—
196	C₄×M₁₆	—	13	1	no	—
197	C₄×M₁₆	—	13	1	no	—
198	C₄×M₁₆	—	13	2	no	—
199	C₄×M₁₆	—	13	2	no	—
200	C₂×#97	—	13	2	no	—
201	C₂×C₄×C₈	—	13	2	no	—
202	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
203	#322	—	13	4	no	—
204	#322	—	13	4	no	—
205	#322	—	13	4	no	—
206	C₈²	—	13	4	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	4	4	no	—
215	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
216	C₂²×C₁₃	#405	1	2	yes	—
217	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
226	C₄×C₁₃	#405	1	2	yes	—
227	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
228	C₄×C₁₃	C₂×#131	1	2	yes	—
229	C₄×C₁₃	#568	1	2	yes	—
230	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂×M₁₆	—	13	2	no	—
234	C₂×M₁₆	—	13	4	no	—
235	C₂×M₁₆	—	13	2	no	—
236	C₂×M₁₆	—	13	4	no	—
237	C₂×M₁₆	—	26	8	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
240	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
248	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
252	C₄⋊C₈	—	13	4	no	—
253	C₄⋊C₈	—	13	4	no	—
254	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
255	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
256	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
257	C₂²⋊C₈	—	13	4	no	—
258	C₂²⋊C₈	—	13	4	no	—
259	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
260	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
261	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
262	#97	—	13	2	no	—
263	#97	—	13	4	no	—
264	#97	—	13	2	no	—
265	#97	—	13	4	no	—
266	C₄×C₈	—	13	4	no	—
267	C₄×C₈	—	13	2	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	2	no	—
270	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
271	C₄×C₈	C₂²×D₁₃	1	2	yes	—
272	C₄×C₈	C₂²×D₁₃	1	2	yes	—
273	C₂×C₁₃	—	2	2	no	—
274	C₂×C₁₃	—	2	2	no	—
275	C₂×C₁₃	—	4	1	no	—
276	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
278	C₂×C₁₃	#2873	1	1	yes	characteristic
279	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
301	M₁₆	—	13	8	no	—
302	M₁₆	—	26	8	no	—
303	M₁₆	—	26	8	no	—
304	M₁₆	—	26	4	no	—
305	C₂×C₈	—	4	4	no	—
306	C₂×C₈	—	13	4	no	—
307	C₂×C₈	—	13	4	no	—
308	C₂×C₈	—	13	8	no	—
309	C₂×C₈	—	26	8	no	—
310	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
311	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
312	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
313	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
314	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
315	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
316	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
317	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
318	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
320	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
321	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
322	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
324	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
325	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
326	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
327	C₄²	C₂³×D₁₃	1	1	yes	characteristic
328	C₁₃	#17327	1	1	yes	characteristic, complemented, Sylow
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
333	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
334	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	#88155	1	4	yes	—
352	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
353	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	2	4	no	—
367	C₈	—	13	8	no	—
368	C₈	—	26	8	no	—
369	C₈	—	26	4	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	4	no	—
378	C₂²	#11718762	1	2	yes	—
379	C₂²	M₁₆×Dic₁₃	1	2	yes	—
380	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	#11718762	1	2	yes	—
389	C₄	M₁₆×Dic₁₃	1	2	yes	—
390	C₄	C₂×#88155	1	2	yes	—
391	C₄	C₂×M₁₆×D₁₃	1	2	yes	—
392	C₄	#11719524	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	—	4	1	no	—
396	C₂	C₂×M₁₆×Dic₁₃	1	1	yes	characteristic
397	C₂	C₂×#11718762	1	1	yes	characteristic
398	C₂	#13123255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₁₃×#431	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17327
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13113131	C₂	semidirect
4. #13113126	C₂	semidirect
5. #13113125	C₂	semidirect
6. #13113117	C₂	semidirect
7. C₈×#6099	C₂	semidirect
33. #11718047	C₂²	semidirect
34. #11718046	C₂²	semidirect
35. #11718046	C₂²	semidirect
36. C₈×#1055	C₂²	semidirect
125. #6099	M₁₆	semidirect
328. C₁₃	#17327	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
#13113131	2
#13113126	2
#13113125	2
#13113117	2
C₈×#6099	2
C₂×C₁₃×#431	2
#17327	13