Subgroups — C₂×#13112720 #15753003

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#11718596	C₂	1	1	yes	maximal, characteristic
3	#13112720	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	—	2	1	no	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
8	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
9	C₂²×C₄⋊Dic₁₃	C₄	1	2	yes	—
10	C₂³×#1055	—	2	1	no	—
11	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
13	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	complemented
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	#11718596	—	2	1	no	—
16	#11718596	—	2	1	no	—
17	#11718596	C₄	1	2	yes	—
18	#11718596	C₂²	1	2	yes	—
19	C₂×C₄⋊#1055	—	2	2	no	—
20	C₂×C₄⋊#1055	—	2	1	no	—
21	C₂×C₄⋊#1055	C₄	1	4	yes	complemented
22	C₂×C₄⋊#1055	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×Dic₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₃	—	2	4	no	—
28	C₂²×C₈×C₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	4	2	no	—
30	C₂²×C₈×C₁₃	—	4	2	no	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	D₄	1	2	yes	—
37	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
38	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₃	—	2	2	no	—
40	C₂×C₄⋊Dic₁₃	—	2	2	no	—
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	—	4	2	no	—
45	C₂×C₄⋊Dic₁₃	—	4	2	no	—
46	C₂×C₄⋊Dic₁₃	—	4	2	no	—
47	C₂×C₄⋊Dic₁₃	—	4	2	no	—
48	C₂×C₄⋊Dic₁₃	—	4	4	no	—
49	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
50	C₂²×#1055	—	2	4	no	—
51	C₂²×#1055	—	2	2	no	—
52	C₂²×#1055	—	4	2	no	—
53	C₂²×#1055	—	4	2	no	—
54	C₁₃×C₄⋊C₈	—	2	4	no	—
55	C₁₃×C₄⋊C₈	—	2	2	no	—
56	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
57	C₄⋊#1055	—	2	4	no	—
58	C₄⋊#1055	—	2	2	no	—
59	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
60	C₂×#1296	—	13	1	no	maximal, Sylow
61	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₃	D₈	1	2	yes	—
74	C₂²×C₄×C₁₃	D₈	1	2	yes	—
75	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
76	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
80	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	—	2	4	no	—
85	C₂²×Dic₁₃	—	4	4	no	—
86	C₂²×Dic₁₃	—	4	4	no	—
87	C₂²×Dic₁₃	—	4	4	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	4	8	no	—
90	C₂×C₈×C₁₃	—	4	2	no	—
91	C₂×C₈×C₁₃	—	4	2	no	—
92	C₄²×C₁₃	C₄²	1	2	yes	—
93	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
98	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
102	C₄⋊Dic₁₃	—	4	4	no	—
103	C₄⋊Dic₁₃	—	4	4	no	—
104	C₄⋊Dic₁₃	—	4	4	no	—
105	C₄⋊Dic₁₃	—	4	2	no	—
106	C₄⋊Dic₁₃	—	4	2	no	—
107	C₄⋊Dic₁₃	—	4	2	no	—
108	C₄⋊Dic₁₃	—	4	2	no	—
109	C₄⋊Dic₁₃	—	4	4	no	—
110	C₂×#1055	—	2	4	no	—
111	C₂×#1055	—	4	8	no	—
112	C₂×#1055	—	4	2	no	—
113	C₂×#1055	—	4	2	no	—
114	C₂²×C₄⋊C₈	—	13	1	no	—
115	C₂²×C₄⋊C₈	D₁₃	1	1	yes	characteristic
116	C₂×#384	—	13	1	no	—
117	#1296	—	13	4	no	—
118	C₂³×C₁₃	#95	1	2	yes	—
119	C₂³×C₁₃	#100	1	2	yes	—
120	C₂³×C₁₃	#101	1	2	yes	—
121	C₂³×C₁₃	#102	1	2	yes	—
122	C₂³×C₁₃	#102	1	2	yes	—
123	C₂³×C₁₃	#103	1	2	yes	—
124	C₂³×C₁₃	#103	1	2	yes	—
125	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃	—	2	4	no	—
127	C₂×C₄×C₁₃	—	2	4	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	#95	1	2	yes	—
133	C₂×C₄×C₁₃	#95	1	2	yes	—
134	C₂×C₄×C₁₃	#95	1	2	yes	—
135	C₂×C₄×C₁₃	#102	1	2	yes	—
136	C₂×C₄×C₁₃	#102	1	2	yes	—
137	C₂×C₄×C₁₃	#102	1	4	yes	—
138	C₂×C₄×C₁₃	#102	1	4	yes	—
139	C₂×C₄×C₁₃	#103	1	2	yes	—
140	C₂×C₄×C₁₃	#103	1	2	yes	—
141	C₂×C₄×C₁₃	#103	1	4	yes	—
142	C₂×C₄×C₁₃	#103	1	4	yes	—
143	C₂×C₄×C₁₃	#106	1	4	yes	—
144	C₂×C₄×C₁₃	#106	1	4	yes	—
145	C₂×C₄×C₁₃	#107	1	4	yes	—
146	C₂×C₄×C₁₃	#107	1	4	yes	—
147	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
161	C₂×Dic₁₃	—	4	4	no	—
162	C₂×Dic₁₃	—	4	4	no	—
163	C₂×Dic₁₃	—	4	4	no	—
164	C₂×Dic₁₃	—	8	8	no	—
165	C₈×C₁₃	—	4	4	no	—
166	#1055	—	4	4	no	—
167	C₂³×C₈	—	2	1	no	—
168	C₂³×C₈	—	26	1	no	—
169	C₂²×C₄⋊C₄	—	13	2	no	—
170	C₂²×C₄⋊C₄	—	26	1	no	—
171	C₂²×C₄⋊C₄	—	26	1	no	—
172	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
173	C₂×C₄⋊C₈	—	2	1	no	—
174	C₂×C₄⋊C₈	—	2	2	no	—
175	C₂×C₄⋊C₈	—	13	4	no	—
176	C₂×C₄⋊C₈	—	13	2	no	—
177	C₂×C₄⋊C₈	—	26	1	no	—
178	C₂×C₄⋊C₈	—	26	2	no	—
179	C₂×C₄⋊C₈	Dic₁₃	1	4	yes	complemented
180	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
181	#384	—	13	2	no	—
182	#384	—	13	2	no	—
183	#384	—	26	1	no	—
184	#384	—	26	1	no	—
185	C₂²×C₁₃	#331	1	4	yes	—
186	C₂²×C₁₃	#332	1	4	yes	—
187	C₂²×C₁₃	#332	1	4	yes	—
188	C₂²×C₁₃	#333	1	4	yes	—
189	C₂²×C₁₃	#340	1	4	yes	—
190	C₂²×C₁₃	#340	1	4	yes	—
191	C₂²×C₁₃	#343	1	4	yes	—
192	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×#101	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	#340	1	4	yes	—
203	C₄×C₁₃	#340	1	4	yes	—
204	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
205	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
206	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
207	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
208	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
209	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
210	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
211	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
212	Dic₁₃	—	8	4	no	—
213	C₂³×C₄	—	26	2	no	—
214	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
215	C₂³×C₄	D₅₂	1	1	yes	characteristic
216	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	—	4	2	no	—
220	C₂²×C₈	—	4	2	no	—
221	C₂²×C₈	—	26	4	no	—
222	C₂²×C₈	—	26	2	no	—
223	C₂²×C₈	—	52	2	no	—
224	C₂²×C₈	—	52	2	no	—
225	C₂×C₄⋊C₄	—	13	4	no	—
226	C₂×C₄⋊C₄	—	26	2	no	—
227	C₂×C₄⋊C₄	—	26	2	no	—
228	C₂×C₄⋊C₄	—	26	2	no	—
229	C₂×C₄⋊C₄	—	26	2	no	—
230	C₂×C₄⋊C₄	—	26	2	no	—
231	C₂×C₄⋊C₄	—	52	4	no	—
232	C₂×C₄⋊C₄	—	52	2	no	—
233	C₂×C₄⋊C₄	—	52	2	no	—
234	C₂×C₄⋊C₄	—	52	2	no	—
235	C₂×C₄⋊C₄	—	52	2	no	—
236	C₂×C₄²	Dic₂₆	1	2	yes	—
237	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₁₃	1	2	yes	—
239	C₂×C₄²	D₅₂	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
241	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
243	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
244	C₄⋊C₈	—	2	4	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	13	4	no	—
247	C₄⋊C₈	—	26	4	no	—
248	C₄⋊C₈	—	26	2	no	—
249	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	complemented
250	C₂×C₁₃	#1296	1	8	yes	complemented
251	C₂×C₁₃	C₂×#331	1	1	yes	characteristic
252	C₂×C₁₃	C₂×#332	1	1	yes	characteristic
253	C₂×C₁₃	C₂×#332	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#333	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
257	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
258	C₂⁴	#6103	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	26	4	no	—
262	C₂²×C₄	—	52	4	no	—
263	C₂²×C₄	—	52	4	no	—
264	C₂²×C₄	—	52	4	no	—
265	C₂²×C₄	#6095	1	2	yes	—
266	C₂²×C₄	#6095	1	2	yes	—
267	C₂²×C₄	D₁₀₄	1	2	yes	—
268	C₂²×C₄	Dic₅₂	1	2	yes	—
269	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
270	C₂²×C₄	#6101	1	2	yes	—
271	C₂²×C₄	#6101	1	2	yes	—
272	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
273	C₂²×C₄	#6103	1	1	yes	characteristic
274	C₂²×C₄	#6103	1	1	yes	characteristic
275	C₂²×C₄	#6103	1	1	yes	characteristic
276	C₂²×C₄	#6103	1	2	yes	—
277	C₂²×C₄	#6104	1	2	yes	—
278	C₂²×C₄	#6105	1	2	yes	—
279	C₂²×C₄	#6106	1	2	yes	—
280	C₂²×C₄	#6107	1	2	yes	—
281	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
282	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	8	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	26	4	no	—
290	C₂×C₈	—	52	2	no	—
291	C₂×C₈	—	52	2	no	—
292	C₂×C₈	—	52	8	no	—
293	C₄⋊C₄	—	52	4	no	—
294	C₄⋊C₄	—	52	4	no	—
295	C₄⋊C₄	—	52	2	no	—
296	C₄⋊C₄	—	52	2	no	—
297	C₄⋊C₄	—	52	2	no	—
298	C₄⋊C₄	—	52	2	no	—
299	C₄⋊C₄	—	52	4	no	—
300	C₄⋊C₄	—	52	4	no	—
301	C₄²	C₄×Dic₁₃	1	2	yes	—
302	C₄²	#6101	1	2	yes	—
303	C₄²	#6101	1	2	yes	—
304	C₄²	C₄⋊Dic₁₃	1	2	yes	—
305	C₄²	#6103	1	2	yes	—
306	C₄²	C₂²⋊Dic₁₃	1	2	yes	—
307	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
309	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
311	C₁₃	C₂×#1296	1	1	yes	characteristic, complemented, Sylow
312	C₂³	#88049	1	2	yes	—
313	C₂³	#88050	1	2	yes	—
314	C₂³	#88056	1	2	yes	—
315	C₂³	#88061	1	2	yes	—
316	C₂³	#88063	1	2	yes	—
317	C₂³	#88064	1	2	yes	—
318	C₂³	#88071	1	2	yes	—
319	C₂³	C₂×#6103	1	1	yes	characteristic
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	52	4	no	—
327	C₂×C₄	—	52	4	no	—
328	C₂×C₄	—	52	4	no	—
329	C₂×C₄	—	104	8	no	—
330	C₂×C₄	#88047	1	4	yes	—
331	C₂×C₄	#88048	1	4	yes	—
332	C₂×C₄	#88049	1	2	yes	—
333	C₂×C₄	#88050	1	2	yes	—
334	C₂×C₄	#88056	1	4	yes	—
335	C₂×C₄	#88056	1	2	yes	—
336	C₂×C₄	#88057	1	4	yes	—
337	C₂×C₄	#88058	1	4	yes	—
338	C₂×C₄	#88061	1	4	yes	—
339	C₂×C₄	#88061	1	2	yes	—
340	C₂×C₄	#88071	1	2	yes	—
341	C₂×C₄	#88071	1	2	yes	—
342	C₂×C₄	#88071	1	2	yes	—
343	C₂×C₄	#88072	1	4	yes	—
344	C₂×C₄	#88075	1	4	yes	—
345	C₂×C₄	C₂×#6095	1	1	yes	characteristic
346	C₂×C₄	C₂×#6095	1	1	yes	characteristic
347	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂×#6101	1	1	yes	characteristic
351	C₂×C₄	C₂×#6101	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂×#6103	1	1	yes	characteristic
354	C₂×C₄	C₂×#6104	1	1	yes	characteristic
355	C₂×C₄	C₂×#6105	1	1	yes	characteristic
356	C₂×C₄	C₂×#6106	1	1	yes	characteristic
357	C₂×C₄	C₂×#6107	1	1	yes	characteristic
358	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	52	4	no	—
361	C₂²	#11718073	1	4	yes	—
362	C₂²	#11718074	1	4	yes	—
363	C₂²	#11718077	1	4	yes	—
364	C₂²	#11718078	1	4	yes	—
365	C₂²	#11718121	1	4	yes	—
366	C₂²	#11718143	1	4	yes	—
367	C₂²	#11718146	1	4	yes	—
368	C₂²	C₂×#88049	1	1	yes	characteristic
369	C₂²	C₂×#88050	1	1	yes	characteristic
370	C₂²	C₂×#88056	1	1	yes	characteristic
371	C₂²	C₂×#88061	1	1	yes	characteristic
372	C₂²	C₂×#88063	1	1	yes	characteristic
373	C₂²	C₂×#88064	1	1	yes	characteristic
374	C₂²	C₂×#88071	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	104	4	no	—
379	C₄	#11718121	1	4	yes	—
380	C₄	#11718143	1	4	yes	—
381	C₄	C₂×#88047	1	1	yes	characteristic
382	C₄	C₂×#88048	1	1	yes	characteristic
383	C₄	C₂×#88056	1	1	yes	characteristic
384	C₄	C₂×#88057	1	1	yes	characteristic
385	C₄	C₂×#88058	1	1	yes	characteristic
386	C₄	C₂×#88061	1	1	yes	characteristic
387	C₄	C₂×#88072	1	1	yes	characteristic
388	C₄	C₂×#88075	1	1	yes	characteristic
389	C₂	#13112720	1	8	yes	direct product factor
390	C₂	C₂×#11718077	1	1	yes	characteristic
391	C₂	C₂×#11718078	1	1	yes	characteristic
392	C₂	C₂×#11718074	1	1	yes	characteristic
393	C₂	C₂×#11718073	1	1	yes	characteristic
394	C₂	C₂×#11718121	1	1	yes	characteristic
395	C₂	C₂×#11718143	1	1	yes	characteristic
396	C₂	C₂×#11718146	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	#6103
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂²×C₁₃×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂²×C₄⋊C₈	D₁₃
hypocenter	C₁₃	C₂×#1296
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13112720	C₂	direct (N × H)
13. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
21. C₂×C₄⋊#1055	C₄	semidirect
56. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
59. C₄⋊#1055	C₂×C₄	semidirect
179. C₂×C₄⋊C₈	Dic₁₃	semidirect
249. C₄⋊C₈	C₂×Dic₁₃	semidirect
250. C₂×C₁₃	#1296	semidirect
311. C₁₃	C₂×#1296	semidirect
389. C₂	#13112720	direct (N × H)

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×#11718596	2
#13112720	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×#1296	13

Subgroups — C2×#13112720 #15753003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112720 #15753003