Subgroups — #15832113

Order 3328.

664 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×#11718587	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	#13113621	C₂	1	4	yes	maximal, complemented
4	#13113611	C₂	1	2	yes	maximal, complemented
5	#13113607	C₂	1	2	yes	maximal, complemented
6	#13113603	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6099	—	2	1	no	—
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	C₂×C₂²⋊#1055	—	2	1	no	—
18	#11718587	—	2	1	no	—
19	#11718587	—	2	1	no	—
20	#11718587	C₂²	1	2	yes	—
21	#11718587	C₂²	1	2	yes	—
22	#11718585	—	2	1	no	—
23	#11718585	—	2	1	no	—
24	#11718585	C₂²	1	2	yes	—
25	#11718585	C₂²	1	2	yes	—
26	C₂×C₄⋊#1055	—	2	1	no	—
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	C₂×#88043	—	2	1	no	—
31	#11718050	C₂²	1	8	yes	complemented
32	#11718049	C₂²	1	8	yes	complemented
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
36	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6099	—	2	2	no	—
50	C₂×#6099	—	2	2	no	—
51	C₂×#6099	—	4	4	no	—
52	C₂²×#1055	—	2	2	no	—
53	C₂²×#1055	—	2	1	no	—
54	C₂²×#1055	—	2	1	no	—
55	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
58	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
59	C₁₃×#97	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₁₃	C₂³	1	4	yes	—
61	C₂²⋊#1055	—	2	2	no	—
62	C₂²⋊#1055	—	2	2	no	—
63	C₄⋊#1055	—	2	2	no	—
64	C₄⋊#1055	—	2	2	no	—
65	C₄⋊#1055	—	2	2	no	—
66	C₄⋊#1055	—	2	1	no	—
67	C₄⋊#1055	—	2	1	no	—
68	C₄⋊#1055	C₂³	1	2	yes	—
69	C₄⋊#1055	C₂³	1	4	yes	—
70	C₄⋊#1055	C₂³	1	2	yes	—
71	#88043	—	2	2	no	—
72	#88043	—	2	2	no	—
73	#17822	—	13	1	no	maximal, Sylow
74	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
79	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₁₃×M₁₆	—	4	4	no	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
115	#6099	—	4	4	no	—
116	#6099	—	4	4	no	—
117	C₂×#1055	—	2	2	no	—
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	—	2	4	no	—
120	C₂×#1055	—	4	4	no	—
121	C₂×#1055	—	4	2	no	—
122	C₂×#1055	—	4	2	no	—
123	#2920	D₁₃	1	1	yes	characteristic
124	C₂×#432	—	13	1	no	—
125	C₂×#423	—	13	1	no	—
126	#1573	—	13	4	no	—
127	#1571	—	13	2	no	—
128	#1570	—	13	2	no	—
129	#1569	—	13	4	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	—	2	2	no	—
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	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₃	#137	1	2	yes	—
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
169	C₈×C₁₃	—	2	8	no	—
170	#1055	—	4	2	no	—
171	#1055	—	4	4	no	—
172	#1055	—	4	2	no	—
173	C₂²×M₁₆	—	26	1	no	—
174	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
175	#432	—	13	2	no	—
176	#432	—	13	2	no	—
177	#432	—	26	1	no	—
178	#432	—	26	1	no	—
179	#432	Dic₁₃	1	2	yes	—
180	#432	Dic₁₃	1	2	yes	—
181	#431	C₂×D₁₃	1	2	yes	—
182	#431	C₂×D₁₃	1	2	yes	—
183	#423	—	13	2	no	—
184	#423	—	13	2	no	—
185	#423	—	26	1	no	—
186	#423	—	26	1	no	—
187	#423	Dic₁₃	1	2	yes	—
188	C₂×C₄⋊C₈	—	13	1	no	—
189	C₂×C₄⋊C₈	—	13	1	no	—
190	C₂×C₄⋊C₈	—	13	2	no	—
191	C₂×C₄⋊C₈	—	26	1	no	—
192	#407	Dic₁₃	1	2	yes	—
193	C₂×C₂²⋊C₈	—	26	1	no	—
194	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
195	C₂×#97	—	26	1	no	—
196	#335	—	13	8	no	—
197	#334	—	13	8	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	—	4	4	no	—
206	C₂²×C₁₃	#428	1	2	yes	—
207	C₂²×C₁₃	#430	1	2	yes	—
208	C₂²×C₁₃	C₂²×C₄⋊C₄	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	—	2	1	no	—
218	C₄×C₁₃	#428	1	2	yes	—
219	C₄×C₁₃	#568	1	2	yes	—
220	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
222	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
223	C₂³×C₄	D₅₂	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
225	C₂×M₁₆	—	26	2	no	—
226	C₂×M₁₆	—	26	2	no	—
227	C₂×M₁₆	—	52	4	no	—
228	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
229	C₂²×C₈	—	26	2	no	—
230	C₂²×C₈	—	26	1	no	—
231	C₂²×C₈	—	26	1	no	—
232	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
233	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
234	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
235	C₂×C₄²	D₅₂	1	1	yes	characteristic
236	C₂×C₄²	D₅₂	1	1	yes	characteristic
237	C₂×C₄²	D₅₂	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	C₂×Dic₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
244	C₄⋊C₈	—	13	2	no	—
245	C₄⋊C₈	—	13	4	no	—
246	C₄⋊C₈	—	13	2	no	—
247	C₄⋊C₈	—	26	2	no	—
248	C₄⋊C₈	—	26	1	no	—
249	C₄⋊C₈	—	26	1	no	—
250	C₄⋊C₈	—	26	2	no	—
251	C₄⋊C₈	—	26	2	no	—
252	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
253	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
254	C₂²⋊C₈	—	26	2	no	—
255	C₂²⋊C₈	—	26	2	no	—
256	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
257	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
258	#97	—	26	2	no	—
259	#97	—	26	2	no	—
260	#97	C₂×Dic₁₃	1	4	yes	—
261	C₄×C₈	C₂²×D₁₃	1	4	yes	—
262	C₂×C₁₃	—	2	2	no	—
263	C₂×C₁₃	—	2	2	no	—
264	C₂×C₁₃	—	4	1	no	—
265	C₂×C₁₃	#2905	1	1	yes	characteristic
266	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
267	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
268	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
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	C₄⋊Dic₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
283	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
284	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
291	M₁₆	—	4	4	no	—
292	M₁₆	—	52	4	no	—
293	M₁₆	—	52	4	no	—
294	C₂×C₈	—	26	2	no	—
295	C₂×C₈	—	26	2	no	—
296	C₂×C₈	—	26	4	no	—
297	C₂×C₈	—	52	4	no	—
298	C₂×C₈	—	52	2	no	—
299	C₂×C₈	—	52	2	no	—
300	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
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	C₄⋊Dic₁₃	1	1	yes	characteristic
306	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
307	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
308	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
309	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
310	C₄²	C₂×D₅₂	1	1	yes	characteristic
311	C₄²	C₂×D₅₂	1	1	yes	characteristic
312	C₄²	C₂×D₅₂	1	1	yes	characteristic
313	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
314	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
315	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
316	C₄²	C₂³×D₁₃	1	1	yes	characteristic
317	C₁₃	#17822	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
322	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
323	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	#88162	1	2	yes	—
344	C₂×C₄	#88163	1	2	yes	—
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	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
356	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
357	C₈	—	2	8	no	—
358	C₈	—	52	2	no	—
359	C₈	—	52	4	no	—
360	C₈	—	52	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	4	no	—
369	C₂²	#11718782	1	2	yes	—
370	C₂²	#11718786	1	2	yes	—
371	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	#11718782	1	2	yes	—
382	C₄	C₂×#88162	1	1	yes	characteristic
383	C₄	C₂×#88163	1	1	yes	characteristic
384	C₄	#11719524	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	#13123400	1	1	yes	characteristic
389	C₂	C₂×#11718782	1	1	yes	characteristic
390	C₂	C₂×#11718786	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2920	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17822
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13113621	C₂	semidirect
4. #13113611	C₂	semidirect
5. #13113607	C₂	semidirect
6. #13113603	C₂	semidirect
31. #11718050	C₂²	semidirect
32. #11718049	C₂²	semidirect
317. C₁₃	#17822	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718587	2
C₂×#11718585	2
#13113621	2
#13113611	2
#13113607	2
#13113603	2
C₁₃×#2920	2
#17822	13