Subgroups — #15768763

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718121	C₂	1	4	yes	maximal
4	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
6	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂²×C₄×Dic₁₃	—	2	1	no	—
11	C₂³×#1055	C₂²	1	2	yes	—
12	C₁₃×#384	—	2	2	no	—
13	C₁₃×#384	C₄	1	4	yes	complemented
14	C₂×#88071	—	2	1	no	—
15	C₄×C₄⋊Dic₁₃	—	2	2	no	—
16	C₄×C₄⋊Dic₁₃	C₄	1	4	yes	complemented
17	C₂×C₄⋊#1055	—	2	2	no	—
18	C₂×C₄⋊#1055	—	2	2	no	—
19	C₂×C₄⋊#1055	C₄	1	4	yes	complemented
20	#11718121	—	2	8	no	—
21	C₂³×C₄×C₁₃	—	2	2	no	—
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₃	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
32	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
34	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₃	D₄	1	2	yes	—
39	C₂×C₄²×C₁₃	D₄	1	2	yes	—
40	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
41	C₂×C₄⋊Dic₁₃	—	2	2	no	—
42	C₂×C₄⋊Dic₁₃	—	2	2	no	—
43	C₂×C₄⋊Dic₁₃	—	2	2	no	—
44	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊Dic₁₃	D₄	1	4	yes	—
46	C₂×C₄⋊Dic₁₃	Q₈	1	4	yes	—
47	C₂×C₄×Dic₁₃	—	2	4	no	—
48	C₂×C₄×Dic₁₃	—	4	2	no	—
49	C₂×C₄×Dic₁₃	—	4	2	no	—
50	C₂²×#1055	—	2	2	no	—
51	C₂²×#1055	—	2	2	no	—
52	C₂²×#1055	—	2	4	no	—
53	C₂²×#1055	—	2	4	no	—
54	C₂²×#1055	C₂×C₄	1	4	yes	—
55	#88071	—	2	4	no	—
56	C₄⋊#1055	—	2	8	no	—
57	#10849	—	13	1	no	maximal, Sylow
58	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	4	no	—
62	C₂²×C₄×C₁₃	—	4	4	no	—
63	C₂²×C₄×C₁₃	—	4	2	no	—
64	C₂²×C₄×C₁₃	—	4	2	no	—
65	C₂²×C₄×C₁₃	—	4	4	no	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₃	D₈	1	2	yes	—
73	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₁₃	#41	1	2	yes	—
85	C₂²×C₄×C₁₃	#41	1	2	yes	—
86	C₂²×Dic₁₃	—	2	4	no	—
87	C₂²×Dic₁₃	—	2	4	no	—
88	C₂²×Dic₁₃	—	2	4	no	—
89	C₂²×Dic₁₃	—	4	2	no	—
90	C₂²×Dic₁₃	—	4	2	no	—
91	C₂²×Dic₁₃	—	4	2	no	—
92	C₂²×Dic₁₃	—	4	2	no	—
93	C₁₃×C₄⋊C₄	—	2	8	no	—
94	C₁₃×C₄⋊C₄	—	4	8	no	—
95	C₁₃×C₄⋊C₄	—	4	8	no	—
96	C₁₃×C₄⋊C₄	—	4	2	no	—
97	C₁₃×C₄⋊C₄	—	4	2	no	—
98	C₄²×C₁₃	C₄²	1	4	yes	—
99	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
100	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
101	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
102	C₄⋊Dic₁₃	—	2	4	no	—
103	C₄⋊Dic₁₃	—	2	4	no	—
104	C₄⋊Dic₁₃	—	2	4	no	—
105	C₄⋊Dic₁₃	C₄⋊C₄	1	8	yes	complemented
106	C₄×Dic₁₃	—	4	8	no	—
107	C₂×#1055	—	2	4	no	—
108	C₂×#1055	—	2	8	no	—
109	C₂×#1055	—	4	4	no	—
110	C₂×#1055	—	4	2	no	—
111	C₂×#1055	—	4	2	no	—
112	C₂²×C₄⋊C₈	—	13	1	no	—
113	C₂×#384	D₁₃	1	1	yes	characteristic
114	C₂×C₄×C₄⋊C₄	—	13	1	no	—
115	C₂×#340	—	13	4	no	—
116	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₁₃	#121	1	2	yes	—
120	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
121	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
122	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
123	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
124	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
125	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
126	C₂³×C₁₃	#137	1	2	yes	—
127	C₂×C₄×C₁₃	—	2	4	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	4	4	no	—
132	C₂×C₄×C₁₃	—	4	4	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	8	4	no	—
135	C₂×C₄×C₁₃	—	8	4	no	—
136	C₂×C₄×C₁₃	#95	1	4	yes	—
137	C₂×C₄×C₁₃	#95	1	4	yes	—
138	C₂×C₄×C₁₃	#102	1	4	yes	—
139	C₂×C₄×C₁₃	#102	1	4	yes	—
140	C₂×C₄×C₁₃	#103	1	4	yes	—
141	C₂×C₄×C₁₃	#103	1	4	yes	—
142	C₂×C₄×C₁₃	#106	1	4	yes	—
143	C₂×C₄×C₁₃	#107	1	4	yes	—
144	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#117	1	2	yes	—
150	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₁₃	#121	1	2	yes	—
155	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#125	1	2	yes	—
159	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
161	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
162	C₂×Dic₁₃	—	2	8	no	—
163	C₂×Dic₁₃	—	4	4	no	—
164	C₂×Dic₁₃	—	4	4	no	—
165	C₂×Dic₁₃	—	4	4	no	—
166	C₂×Dic₁₃	—	4	4	no	—
167	C₂×Dic₁₃	—	4	4	no	—
168	C₂×Dic₁₃	—	4	4	no	—
169	#1055	—	4	4	no	—
170	C₂³×C₈	—	13	2	no	—
171	C₂²×C₄⋊C₄	—	2	1	no	—
172	C₂²×C₄⋊C₄	—	2	1	no	—
173	C₂²×C₄⋊C₄	—	13	2	no	—
174	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
175	C₂²×C₄²	—	26	1	no	—
176	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
177	C₂×C₄⋊C₈	—	13	4	no	—
178	C₂×C₄⋊C₈	—	26	2	no	—
179	C₂×C₄⋊C₈	—	26	2	no	—
180	#384	—	2	2	no	—
181	#384	Dic₁₃	1	4	yes	complemented
182	C₄×C₄⋊C₄	—	13	4	no	—
183	C₄×C₄⋊C₄	—	26	2	no	—
184	C₂×#95	—	26	1	no	—
185	#340	—	26	8	no	—
186	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
187	C₂²×C₁₃	#380	1	2	yes	—
188	C₂²×C₁₃	#389	1	2	yes	—
189	C₂²×C₁₃	#390	1	1	yes	characteristic
190	C₂²×C₁₃	#391	1	1	yes	characteristic
191	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
192	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
195	C₂²×C₁₃	#417	1	2	yes	—
196	C₂²×C₁₃	#418	1	1	yes	characteristic
197	C₂²×C₁₃	#419	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
200	C₂²×C₁₃	#428	1	2	yes	—
201	C₂²×C₁₃	#459	1	2	yes	—
202	C₂²×C₁₃	#460	1	2	yes	—
203	C₂²×C₁₃	#461	1	2	yes	—
204	C₂²×C₁₃	#462	1	2	yes	—
205	C₂²×C₁₃	#474	1	2	yes	—
206	C₂²×C₁₃	#475	1	2	yes	—
207	C₂²×C₁₃	#476	1	2	yes	—
208	C₂²×C₁₃	#477	1	2	yes	—
209	C₄×C₁₃	—	2	4	no	—
210	C₄×C₁₃	—	8	4	no	—
211	C₄×C₁₃	#340	1	8	yes	complemented
212	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
213	C₄×C₁₃	#382	1	1	yes	characteristic
214	C₄×C₁₃	#384	1	1	yes	characteristic
215	C₄×C₁₃	#389	1	2	yes	—
216	C₄×C₁₃	#390	1	1	yes	characteristic
217	C₄×C₁₃	#391	1	1	yes	characteristic
218	Dic₁₃	—	4	8	no	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	—	26	2	no	—
221	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
224	C₂²×C₈	—	13	4	no	—
225	C₂²×C₈	—	26	2	no	—
226	C₂²×C₈	—	26	4	no	—
227	C₂²×C₈	—	26	4	no	—
228	C₂²×C₈	—	26	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	4	4	no	—
235	C₂×C₄⋊C₄	—	4	2	no	—
236	C₂×C₄⋊C₄	—	4	2	no	—
237	C₂×C₄⋊C₄	—	13	4	no	—
238	C₂×C₄⋊C₄	—	13	4	no	—
239	C₂×C₄⋊C₄	—	13	4	no	—
240	C₂×C₄⋊C₄	—	26	2	no	—
241	C₂×C₄⋊C₄	—	26	2	no	—
242	C₂×C₄⋊C₄	—	26	2	no	—
243	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
244	C₂×C₄²	—	26	4	no	—
245	C₂×C₄²	—	52	2	no	—
246	C₂×C₄²	—	52	2	no	—
247	C₂×C₄²	Dic₂₆	1	2	yes	—
248	C₂×C₄²	C₄×D₁₃	1	2	yes	—
249	C₂×C₄²	C₄×D₁₃	1	2	yes	—
250	C₂×C₄²	D₅₂	1	2	yes	—
251	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
252	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
253	C₄⋊C₈	—	26	8	no	—
254	#95	—	26	4	no	—
255	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
257	C₂×C₁₃	#1736	1	1	yes	characteristic
258	C₂×C₁₃	#1802	1	2	yes	—
259	C₂×C₁₃	#1803	1	2	yes	—
260	C₂×C₁₃	#1947	1	2	yes	—
261	C₂×C₁₃	#1948	1	2	yes	—
262	C₂×C₁₃	#1981	1	1	yes	characteristic
263	C₂×C₁₃	#1982	1	1	yes	characteristic
264	C₂×C₁₃	#1987	1	1	yes	characteristic
265	C₂×C₁₃	#1988	1	1	yes	characteristic
266	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	26	4	no	—
275	C₂²×C₄	—	26	4	no	—
276	C₂²×C₄	—	26	4	no	—
277	C₂²×C₄	—	52	2	no	—
278	C₂²×C₄	—	52	2	no	—
279	C₂²×C₄	—	52	2	no	—
280	C₂²×C₄	—	52	2	no	—
281	C₂²×C₄	#6101	1	2	yes	—
282	C₂²×C₄	#6101	1	2	yes	—
283	C₂²×C₄	#6103	1	2	yes	—
284	C₂²×C₄	#6103	1	2	yes	—
285	C₂²×C₄	#6104	1	2	yes	—
286	C₂²×C₄	#6105	1	2	yes	—
287	C₂²×C₄	#6106	1	2	yes	—
288	C₂²×C₄	#6107	1	2	yes	—
289	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
290	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
291	C₂²×C₄	C₂×Dic₂₆	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×D₅₂	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₁₃	1	2	yes	—
296	C₂²×C₄	#6129	1	2	yes	—
297	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
298	C₂²×C₄	#6131	1	2	yes	—
299	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
301	C₂×C₈	—	26	8	no	—
302	C₂×C₈	—	26	4	no	—
303	C₂×C₈	—	52	4	no	—
304	C₂×C₈	—	52	2	no	—
305	C₂×C₈	—	52	2	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	4	8	no	—
308	C₄⋊C₄	—	4	8	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	13	8	no	—
312	C₄⋊C₄	—	26	4	no	—
313	C₄⋊C₄	—	26	4	no	—
314	C₄⋊C₄	—	26	4	no	—
315	C₄²	—	52	8	no	—
316	C₄²	C₄×Dic₁₃	1	4	yes	—
317	C₄²	#6101	1	4	yes	—
318	C₄²	C₄⋊Dic₁₃	1	4	yes	—
319	C₄²	#6103	1	4	yes	—
320	C₁₃	#10849	1	1	yes	characteristic, complemented, Sylow
321	C₂³	C₂×#6101	1	1	yes	characteristic
322	C₂³	C₂×#6103	1	1	yes	characteristic
323	C₂³	C₂×#6104	1	1	yes	characteristic
324	C₂³	#88186	1	2	yes	—
325	C₂³	C₂×#6105	1	1	yes	characteristic
326	C₂³	#88192	1	2	yes	—
327	C₂³	C₂×#6106	1	1	yes	characteristic
328	C₂³	#88196	1	2	yes	—
329	C₂³	C₂×#6107	1	1	yes	characteristic
330	C₂³	#88200	1	2	yes	—
331	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	4	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	—	26	8	no	—
342	C₂×C₄	—	52	4	no	—
343	C₂×C₄	—	52	4	no	—
344	C₂×C₄	—	52	4	no	—
345	C₂×C₄	—	52	4	no	—
346	C₂×C₄	—	52	4	no	—
347	C₂×C₄	—	52	4	no	—
348	C₂×C₄	#88047	1	4	yes	—
349	C₂×C₄	#88048	1	4	yes	—
350	C₂×C₄	#88049	1	4	yes	—
351	C₂×C₄	#88050	1	4	yes	—
352	C₂×C₄	#88071	1	4	yes	—
353	C₂×C₄	#88071	1	4	yes	—
354	C₂×C₄	#88072	1	4	yes	—
355	C₂×C₄	#88075	1	4	yes	—
356	C₂×C₄	#88141	1	2	yes	—
357	C₂×C₄	#88142	1	2	yes	—
358	C₂×C₄	#88144	1	2	yes	—
359	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
360	C₂×C₄	#88146	1	2	yes	—
361	C₂×C₄	#88147	1	2	yes	—
362	C₂×C₄	#88149	1	2	yes	—
363	C₂×C₄	#88151	1	2	yes	—
364	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂×#6101	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂×#6103	1	1	yes	characteristic
368	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
369	C₂×C₄	#88190	1	1	yes	characteristic
370	C₂×C₄	#88194	1	1	yes	characteristic
371	C₂×C₄	#88198	1	1	yes	characteristic
372	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
373	C₂×C₄	#88201	1	1	yes	characteristic
374	C₈	—	52	4	no	—
375	C₂²	C₂×#88047	1	1	yes	characteristic
376	C₂²	C₂×#88048	1	1	yes	characteristic
377	C₂²	#11718625	1	2	yes	—
378	C₂²	C₂×#88049	1	1	yes	characteristic
379	C₂²	#11718627	1	2	yes	—
380	C₂²	C₂×#88050	1	1	yes	characteristic
381	C₂²	#11718634	1	2	yes	—
382	C₂²	#11718648	1	2	yes	—
383	C₂²	#11718733	1	2	yes	—
384	C₂²	#11718736	1	2	yes	—
385	C₂²	#11718744	1	2	yes	—
386	C₂²	#11718745	1	2	yes	—
387	C₂²	#11718748	1	2	yes	—
388	C₂²	#11718751	1	2	yes	—
389	C₂²	#11718752	1	2	yes	—
390	C₂²	#11718755	1	2	yes	—
391	C₂²	C₂×#88071	1	1	yes	characteristic
392	C₂²	C₂×#88072	1	1	yes	characteristic
393	C₂²	#11718876	1	1	yes	characteristic
394	C₂²	#11718882	1	1	yes	characteristic
395	C₂²	C₂×#88075	1	1	yes	characteristic
396	C₂²	#11718886	1	1	yes	characteristic
397	C₂²	#11718891	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	8	4	no	—
400	C₄	—	52	8	no	—
401	C₄	#11718121	1	8	yes	complemented
402	C₄	#11718635	1	1	yes	characteristic
403	C₄	C₄⋊C₄×Dic₁₃	1	2	yes	—
404	C₄	#11718637	1	1	yes	characteristic
405	C₄	#11718638	1	1	yes	characteristic
406	C₄	#11718646	1	2	yes	—
407	C₄	#11718649	1	1	yes	characteristic
408	C₂	#13113065	1	1	yes	characteristic
409	C₂	C₂×#11718121	1	1	yes	characteristic
410	C₂	#13114555	1	1	yes	characteristic
411	C₂	#13114833	1	2	yes	—
412	C₂	#13114838	1	2	yes	—
413	C₂	#13115592	1	2	yes	—
414	C₂	#13115597	1	2	yes	—
415	C₂	#13115760	1	1	yes	characteristic
416	C₂	#13115764	1	1	yes	characteristic
417	C₂	#13115785	1	1	yes	characteristic
418	C₂	#13115789	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#384	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#384	D₁₃
hypocenter	C₁₃	#10849
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
13. C₁₃×#384	C₄	semidirect
16. C₄×C₄⋊Dic₁₃	C₄	semidirect
19. C₂×C₄⋊#1055	C₄	semidirect
105. C₄⋊Dic₁₃	C₄⋊C₄	semidirect
181. #384	Dic₁₃	semidirect
211. C₄×C₁₃	#340	semidirect
320. C₁₃	#10849	semidirect
401. C₄	#11718121	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#1055	2
C₂×C₄×C₄⋊Dic₁₃	2
C₂×#11718121	2
C₂×C₁₃×#384	2
#10849	13