Subgroups — C₂×#13123859 #16727640

Order 3328.

2890 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
2	#13123859	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₈×D₅₂	C₂	1	4	yes	maximal, complemented
4	C₂×#11718495	C₂	1	4	yes	maximal, complemented
5	C₂×#11718586	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₃×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₅₂	C₄	1	1	yes	characteristic
9	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6103	C₄	1	2	yes	—
12	C₂²×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	8	yes	complemented
14	C₂×C₄×D₅₂	C₄	1	8	yes	—
15	C₂×C₄×D₅₂	C₄	1	2	yes	—
16	C₂×C₄×D₅₂	C₄	1	2	yes	—
17	C₂×C₄×D₅₂	C₂²	1	8	yes	—
18	C₂×C₄×D₅₂	C₂²	1	2	yes	—
19	C₂×C₄×D₅₂	C₂²	1	2	yes	—
20	C₁₃×#431	C₂²	1	8	yes	complemented
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
25	C₂×#88060	C₂²	1	8	yes	complemented
26	#11718586	C₂²	1	8	yes	complemented
27	C₂×C₄⋊#1055	C₂²	1	2	yes	complemented
28	C₂×C₄×#1055	C₂²	1	2	yes	complemented
29	#11718495	C₂²	1	32	yes	complemented
30	D₁₃×C₂²⋊C₈	C₂²	1	32	yes	complemented
31	C₈×D₅₂	C₂²	1	32	yes	complemented
32	C₂⁴×D₁₃	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
37	C₂²×D₅₂	C₈	1	16	yes	complemented
38	C₂²×D₅₂	C₂×C₄	1	2	yes	—
39	C₂²×D₅₂	C₂×C₄	1	2	yes	—
40	C₂²×D₅₂	C₂×C₄	1	8	yes	—
41	C₂²×C₄×D₁₃	—	4	8	no	—
42	C₂²×C₄×D₁₃	C₂×C₄	1	8	yes	—
43	C₂²×C₄×D₁₃	C₂×C₄	1	4	yes	—
44	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
45	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
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	4	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
53	C₂×#6103	C₂×C₄	1	4	yes	—
54	C₂×#6103	C₂×C₄	1	4	yes	—
55	C₂×#6103	C₂×C₄	1	16	yes	—
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	—
59	C₂²×#1055	C₂³	1	4	yes	—
60	C₂×C₈×D₁₃	—	4	16	no	—
61	C₂×C₈×D₁₃	C₂³	1	32	yes	complemented
62	C₄×D₅₂	C₂×C₄	1	8	yes	—
63	C₄×D₅₂	C₂×C₄	1	8	yes	—
64	C₄×D₅₂	C₂×C₄	1	16	yes	—
65	C₄×D₅₂	C₂×C₄	1	16	yes	—
66	C₄×D₅₂	C₂³	1	8	yes	—
67	C₄×D₅₂	C₂³	1	8	yes	—
68	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
69	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
70	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
71	C₂²⋊#1055	C₂³	1	8	yes	—
72	#88060	C₂³	1	32	yes	complemented
73	C₄⋊#1055	C₂³	1	8	yes	complemented
74	C₄×#1055	C₂³	1	8	yes	complemented
75	C₂×#2972	—	13	1	no	maximal, Sylow
76	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂³×D₁₃	—	4	4	no	—
78	C₂³×D₁₃	—	4	4	no	—
79	C₂³×D₁₃	C₂×C₈	1	16	yes	complemented
80	C₂³×D₁₃	C₂²×C₄	1	4	yes	—
81	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	4	2	no	—
84	C₂²×C₄×C₁₃	C₂×C₈	1	8	yes	complemented
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
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	4	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₁₃	—	4	4	no	—
96	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
97	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
98	C₂×D₅₂	C₂×C₈	1	16	yes	complemented
99	C₂×D₅₂	C₂×C₈	1	16	yes	complemented
100	C₂×D₅₂	C₂×C₈	1	64	yes	complemented
101	C₂×D₅₂	C₂²×C₄	1	8	yes	—
102	C₂×D₅₂	C₂²×C₄	1	8	yes	—
103	C₂×C₄×D₁₃	—	2	16	no	—
104	C₂×C₄×D₁₃	—	4	16	no	—
105	C₂×C₄×D₁₃	—	4	16	no	—
106	C₂×C₄×D₁₃	—	4	8	no	—
107	C₂×C₄×D₁₃	C₂²×C₄	1	8	yes	—
108	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	—
109	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
110	C₂×C₈×C₁₃	—	2	8	no	—
111	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
112	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
113	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
114	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₃	C₂⁴	1	2	yes	—
117	C₄²×C₁₃	C₂⁴	1	2	yes	—
118	#6103	C₂²×C₄	1	16	yes	—
119	#6103	C₂²×C₄	1	16	yes	—
120	C₄⋊Dic₁₃	C₂²×C₄	1	8	yes	—
121	C₄⋊Dic₁₃	C₂²×C₄	1	8	yes	—
122	C₂×#1055	—	2	8	no	—
123	C₂×#1055	C₂⁴	1	8	yes	—
124	C₈×D₁₃	—	4	32	no	—
125	C₂²×C₄×D₄	—	13	1	no	—
126	#2972	—	13	16	no	—
127	C₂×C₈×D₄	—	13	4	no	—
128	C₂×C₈×D₄	—	13	4	no	—
129	C₂×#431	—	13	1	no	—
130	C₂×#431	D₁₃	1	1	yes	characteristic, complemented
131	C₂²×C₂²⋊C₈	—	13	4	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
135	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
136	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
137	C₂²×D₁₃	—	2	8	no	—
138	C₂²×D₁₃	—	2	8	no	—
139	C₂²×D₁₃	—	4	8	no	—
140	C₂²×D₁₃	—	4	32	no	—
141	C₂²×D₁₃	—	4	8	no	—
142	C₂²×D₁₃	C₂²×C₈	1	16	yes	—
143	C₂²×D₁₃	C₂²×C₈	1	32	yes	complemented
144	C₂²×D₁₃	C₂³×C₄	1	8	yes	—
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	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
152	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
153	C₂×C₄×C₁₃	C₂²×C₈	1	16	yes	complemented
154	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
155	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
156	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
160	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
161	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
162	C₂×Dic₁₃	—	2	8	no	—
163	C₂×Dic₁₃	—	4	8	no	—
164	C₂×Dic₁₃	C₂³×C₄	1	8	yes	—
165	D₅₂	C₂²×C₈	1	32	yes	complemented
166	D₅₂	C₂²×C₈	1	32	yes	complemented
167	C₄×D₁₃	—	2	16	no	—
168	C₄×D₁₃	—	2	16	no	—
169	C₄×D₁₃	—	4	16	no	—
170	C₈×C₁₃	—	2	8	no	—
171	#1055	—	2	8	no	—
172	C₂³×D₄	—	13	1	no	—
173	C₂⁴×C₄	—	13	2	no	—
174	C₂³×C₈	—	13	8	no	—
175	C₂×C₄×D₄	—	13	2	no	—
176	C₂×C₄×D₄	—	13	2	no	—
177	C₂×C₄×D₄	—	13	8	no	—
178	C₂×C₄×D₄	—	13	2	no	—
179	C₂×C₄×D₄	—	13	2	no	—
180	C₂×C₄×D₄	—	13	8	no	—
181	C₂²×C₄⋊C₄	—	13	1	no	—
182	C₂²×C₂²⋊C₄	—	13	2	no	—
183	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
184	C₈×D₄	—	13	32	no	—
185	C₈×D₄	—	13	32	no	—
186	#431	—	13	8	no	—
187	#431	C₂×D₁₃	1	8	yes	complemented
188	C₂×C₄⋊C₈	—	13	2	no	—
189	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
190	C₂×C₂²⋊C₈	—	13	2	no	—
191	C₂×C₂²⋊C₈	—	13	8	no	—
192	C₂×C₂²⋊C₈	—	13	32	no	—
193	C₂×C₂²⋊C₈	C₂×D₁₃	1	2	yes	—
194	C₂×C₄×C₈	—	13	2	no	—
195	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	2	8	no	—
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	#518	1	2	yes	—
200	C₂²×C₁₃	C₂³×C₈	1	4	yes	—
201	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
202	C₂²×C₁₃	#568	1	2	yes	—
203	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
204	C₂×D₁₃	—	2	8	no	—
205	C₂×D₁₃	—	2	32	no	—
206	C₂×D₁₃	—	2	8	no	—
207	C₂×D₁₃	—	4	32	no	—
208	C₂×D₁₃	C₂³×C₈	1	16	yes	—
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	#518	1	2	yes	—
213	C₄×C₁₃	C₂³×C₈	1	4	yes	—
214	C₄×C₁₃	C₂³×C₈	1	4	yes	—
215	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
216	Dic₁₃	—	2	8	no	—
217	C₂⁵	—	13	2	no	—
218	C₂²×D₄	—	13	16	no	—
219	C₂²×D₄	—	13	2	no	—
220	C₂²×D₄	—	13	2	no	—
221	C₂²×D₄	—	13	8	no	—
222	C₂³×C₄	—	13	2	no	—
223	C₂³×C₄	—	13	4	no	—
224	C₂³×C₄	—	13	4	no	—
225	C₂³×C₄	—	13	8	no	—
226	C₂³×C₄	—	13	8	no	—
227	C₂³×C₄	—	52	8	no	—
228	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
229	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
230	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
231	C₂²×C₈	—	13	4	no	—
232	C₂²×C₈	—	13	32	no	—
233	C₂²×C₈	—	52	16	no	—
234	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
235	C₄×D₄	—	13	8	no	—
236	C₄×D₄	—	13	8	no	—
237	C₄×D₄	—	13	16	no	—
238	C₄×D₄	—	13	16	no	—
239	C₄×D₄	—	13	8	no	—
240	C₄×D₄	—	13	8	no	—
241	C₂×C₄⋊C₄	—	13	2	no	—
242	C₂×C₄⋊C₄	—	13	2	no	—
243	C₂×C₄⋊C₄	—	13	8	no	—
244	C₂×C₂²⋊C₄	—	13	4	no	—
245	C₂×C₂²⋊C₄	—	13	4	no	—
246	C₂×C₂²⋊C₄	—	13	16	no	—
247	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
249	C₂×C₄²	C₄×D₁₃	1	4	yes	—
250	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
251	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
253	C₄⋊C₈	—	13	8	no	—
254	C₄⋊C₈	C₂²×D₁₃	1	8	yes	complemented
255	C₂²⋊C₈	—	13	8	no	—
256	C₂²⋊C₈	—	13	32	no	—
257	C₂²⋊C₈	C₂²×D₁₃	1	8	yes	—
258	C₄×C₈	—	13	8	no	—
259	C₄×C₈	C₂²×D₁₃	1	8	yes	complemented
260	C₂×C₁₃	—	2	4	no	—
261	C₂×C₁₃	#2972	1	4	yes	complemented
262	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
263	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
264	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
265	D₁₃	—	2	16	no	—
266	C₂⁴	—	13	4	no	—
267	C₂⁴	—	13	16	no	—
268	C₂⁴	—	13	8	no	—
269	C₂⁴	—	52	4	no	—
270	C₂⁴	—	52	4	no	—
271	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
272	C₂×D₄	—	13	16	no	—
273	C₂×D₄	—	13	16	no	—
274	C₂×D₄	—	13	64	no	—
275	C₂×D₄	—	13	8	no	—
276	C₂×D₄	—	13	8	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	13	4	no	—
280	C₂²×C₄	—	13	8	no	—
281	C₂²×C₄	—	13	8	no	—
282	C₂²×C₄	—	13	8	no	—
283	C₂²×C₄	—	13	16	no	—
284	C₂²×C₄	—	26	16	no	—
285	C₂²×C₄	—	52	16	no	—
286	C₂²×C₄	—	52	16	no	—
287	C₂²×C₄	—	52	8	no	—
288	C₂²×C₄	—	52	4	no	—
289	C₂²×C₄	C₈×D₁₃	1	8	yes	complemented
290	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
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	4	yes	—
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	4	yes	—
298	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
299	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
300	C₂×C₈	—	2	8	no	—
301	C₂×C₈	—	13	8	no	—
302	C₂×C₈	—	26	8	no	—
303	C₂×C₈	—	52	32	no	—
304	C₂×C₈	C₂³×D₁₃	1	8	yes	—
305	C₄⋊C₄	—	13	8	no	—
306	C₄⋊C₄	—	13	8	no	—
307	C₂²⋊C₄	—	13	16	no	—
308	C₂²⋊C₄	—	13	16	no	—
309	C₄²	C₂×C₄×D₁₃	1	4	yes	—
310	C₄²	C₂×C₄×D₁₃	1	4	yes	—
311	C₄²	C₂×C₄×D₁₃	1	2	yes	—
312	C₄²	C₂×C₄×D₁₃	1	2	yes	—
313	C₄²	C₂³×D₁₃	1	2	yes	—
314	C₄²	C₂³×D₁₃	1	2	yes	—
315	C₁₃	C₂×#2972	1	1	yes	characteristic, complemented, Sylow
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	13	16	no	—
319	C₂³	—	13	8	no	—
320	C₂³	—	13	32	no	—
321	C₂³	—	26	8	no	—
322	C₂³	—	26	8	no	—
323	C₂³	—	52	8	no	—
324	C₂³	—	52	32	no	—
325	C₂³	—	52	8	no	—
326	C₂³	C₂×C₈×D₁₃	1	4	yes	—
327	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
328	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
329	D₄	—	13	32	no	—
330	D₄	—	13	32	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	13	8	no	—
338	C₂×C₄	—	26	8	no	—
339	C₂×C₄	—	26	16	no	—
340	C₂×C₄	—	26	16	no	—
341	C₂×C₄	—	52	16	no	—
342	C₂×C₄	—	52	8	no	—
343	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
344	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
345	C₂×C₄	C₂×C₈×D₁₃	1	16	yes	complemented
346	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
347	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
350	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
351	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
352	C₂×C₄	#88256	1	4	yes	—
353	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
354	C₈	—	2	8	no	—
355	C₈	—	26	8	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	13	16	no	—
360	C₂²	—	26	32	no	—
361	C₂²	—	26	8	no	—
362	C₂²	—	26	8	no	—
363	C₂²	—	52	32	no	—
364	C₂²	#11719226	1	2	yes	—
365	C₂²	C₂²×C₈×D₁₃	1	4	yes	—
366	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
367	C₂²	#11719450	1	2	yes	—
368	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	26	8	no	—
373	C₄	#11719226	1	2	yes	—
374	C₄	C₂²×C₈×D₁₃	1	4	yes	—
375	C₄	C₂²×C₈×D₁₃	1	4	yes	—
376	C₄	C₂×#88256	1	2	yes	—
377	C₂	—	2	4	no	—
378	C₂	—	26	16	no	—
379	C₂	#13123859	1	4	yes	direct product factor
380	C₂	C₂×#11719226	1	1	yes	characteristic
381	C₂	C₂³×C₈×D₁₃	1	1	yes	characteristic
382	C₂	C₂×#11719450	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₅₂	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	C₂×#2972
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #13123859	C₂	direct (N × H)
3. C₂×C₈×D₅₂	C₂	semidirect
4. C₂×#11718495	C₂	semidirect
5. C₂×#11718586	C₂	semidirect
6. C₂×D₁₃×C₂²⋊C₈	C₂	semidirect
7. C₂×C₁₃×#431	C₂	semidirect
13. C₂²×C₈×D₁₃	C₂²	semidirect
20. C₁₃×#431	C₂²	semidirect
21. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
23. C₂×C₄×C₈×C₁₃	C₂²	semidirect
25. C₂×#88060	C₂²	semidirect
26. #11718586	C₂²	semidirect
27. C₂×C₄⋊#1055	C₂²	semidirect
28. C₂×C₄×#1055	C₂²	semidirect
29. #11718495	C₂²	semidirect
30. D₁₃×C₂²⋊C₈	C₂²	semidirect
31. C₈×D₅₂	C₂²	semidirect
37. C₂²×D₅₂	C₈	semidirect
61. C₂×C₈×D₁₃	C₂³	semidirect
68. C₁₃×C₄⋊C₈	C₂³	semidirect
70. C₄×C₈×C₁₃	C₂³	semidirect
72. #88060	C₂³	semidirect
73. C₄⋊#1055	C₂³	semidirect
74. C₄×#1055	C₂³	semidirect
79. C₂³×D₁₃	C₂×C₈	semidirect
84. C₂²×C₄×C₁₃	C₂×C₈	semidirect
98. C₂×D₅₂	C₂×C₈	semidirect
99. C₂×D₅₂	C₂×C₈	semidirect
100. C₂×D₅₂	C₂×C₈	semidirect
130. C₂×#431	D₁₃	semidirect
143. C₂²×D₁₃	C₂²×C₈	semidirect
153. C₂×C₄×C₁₃	C₂²×C₈	semidirect
165. D₅₂	C₂²×C₈	semidirect
166. D₅₂	C₂²×C₈	semidirect
187. #431	C₂×D₁₃	semidirect
189. C₂×C₄⋊C₈	C₂×D₁₃	semidirect
195. C₂×C₄×C₈	C₂×D₁₃	semidirect
254. C₄⋊C₈	C₂²×D₁₃	semidirect
259. C₄×C₈	C₂²×D₁₃	semidirect
261. C₂×C₁₃	#2972	semidirect
289. C₂²×C₄	C₈×D₁₃	semidirect
315. C₁₃	C₂×#2972	semidirect
345. C₂×C₄	C₂×C₈×D₁₃	semidirect
379. C₂	#13123859	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×D₅₂	2
#13123859	2
C₂×C₈×D₅₂	2
C₂×#11718495	2
C₂×#11718586	2
C₂×D₁₃×C₂²⋊C₈	2
C₂×C₁₃×#431	2
C₂×#2972	13

Subgroups — C2×#13123859 #16727640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123859 #16727640