Subgroups — C₂×#11719407 #13128379

Order 1664.

1112 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×C₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719407	C₂	1	16	yes	maximal, direct product factor
3	C₂×#88152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88142	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#88141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88141	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#88139	C₂	1	1	yes	maximal, characteristic
10	C₂×#88139	C₂	1	1	yes	maximal, characteristic
11	C₂×#88135	C₂	1	1	yes	maximal, characteristic
12	C₂×#88133	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#88132	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#88131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#88126	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
21	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
22	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
23	C₁₃×#126	C₂²	1	8	yes	complemented
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂×#6103	C₂²	1	1	yes	characteristic
34	C₂×#6103	C₂²	1	1	yes	characteristic
35	C₂×#6103	C₂²	1	1	yes	characteristic
36	C₂×#6103	C₂²	1	1	yes	characteristic
37	C₂×#6103	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
40	C₂×#6101	C₂²	1	1	yes	characteristic
41	C₂×#6101	C₂²	1	1	yes	characteristic
42	C₂×#6101	C₂²	1	1	yes	characteristic
43	C₂×#6101	C₂²	1	1	yes	characteristic
44	C₂×#6101	C₂²	1	1	yes	characteristic
45	C₂×#6101	C₂²	1	1	yes	characteristic
46	C₂×#6101	C₂²	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
53	#88152	C₂²	1	8	yes	complemented
54	#88152	C₂²	1	8	yes	complemented
55	#88150	C₂²	1	8	yes	complemented
56	#88142	C₂²	1	8	yes	complemented
57	#88141	C₂²	1	8	yes	complemented
58	#88141	C₂²	1	8	yes	complemented
59	#88139	C₂²	1	8	yes	—
60	#88139	C₂²	1	8	yes	—
61	#88135	C₂²	1	8	yes	—
62	#88133	C₂²	1	8	yes	complemented
63	#88132	C₂²	1	8	yes	complemented
64	#88131	C₂²	1	8	yes	complemented
65	#88126	C₂²	1	8	yes	complemented
66	C₄×Dic₂₆	C₂²	1	8	yes	complemented
67	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×D₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₃	—	2	4	no	—
76	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
77	C₂²×Dic₁₃	—	2	4	no	—
78	C₂²×Dic₁₃	C₂³	1	4	yes	—
79	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₁₃	—	2	4	no	—
87	C₂×C₄×D₁₃	C₂³	1	4	yes	—
88	C₂×Dic₂₆	—	2	4	no	—
89	C₂×Dic₂₆	—	2	4	no	—
90	C₂×Dic₂₆	—	2	4	no	—
91	C₂×Dic₂₆	C₂³	1	4	yes	—
92	C₂×Dic₂₆	C₂³	1	4	yes	—
93	C₂×Dic₂₆	C₂³	1	4	yes	—
94	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₄²×C₁₃	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
103	#6103	C₂³	1	4	yes	—
104	#6103	C₂³	1	4	yes	—
105	#6103	C₂³	1	4	yes	—
106	#6103	C₂³	1	4	yes	—
107	#6103	C₂³	1	4	yes	—
108	C₄⋊Dic₁₃	C₂³	1	4	yes	—
109	C₄⋊Dic₁₃	C₂³	1	4	yes	—
110	#6101	C₂³	1	4	yes	—
111	#6101	C₂³	1	4	yes	—
112	#6101	C₂³	1	4	yes	—
113	#6101	C₂³	1	4	yes	—
114	#6101	C₂³	1	4	yes	—
115	#6101	C₂³	1	4	yes	—
116	#6101	C₂³	1	4	yes	—
117	C₄×Dic₁₃	C₂³	1	4	yes	—
118	C₄×Dic₁₃	C₂³	1	4	yes	—
119	C₄×Dic₁₃	C₂³	1	4	yes	—
120	C₄×Dic₁₃	C₂³	1	4	yes	—
121	C₄×Dic₁₃	C₂³	1	4	yes	—
122	C₄×Dic₁₃	C₂³	1	4	yes	—
123	C₂×#556	—	13	1	no	maximal, Sylow
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	C₂⁴	1	2	yes	—
128	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂²×D₁₃	—	2	2	no	—
130	C₂²×D₁₃	—	2	2	no	—
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	C₂⁴	1	2	yes	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
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	C₂⁴	1	2	yes	—
140	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
141	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²⋊D₁₃	—	2	8	no	—
146	C₂×Dic₁₃	—	2	2	no	—
147	C₂×Dic₁₃	—	2	2	no	—
148	C₂×Dic₁₃	—	2	2	no	—
149	C₂×Dic₁₃	—	2	2	no	—
150	C₂×Dic₁₃	—	2	2	no	—
151	C₂×Dic₁₃	—	2	8	no	—
152	C₂×Dic₁₃	#41	1	4	yes	—
153	C₂×Dic₁₃	#41	1	4	yes	—
154	C₂×Dic₁₃	C₂⁴	1	2	yes	—
155	C₂×Dic₁₃	C₂⁴	1	2	yes	—
156	C₂×Dic₁₃	C₂⁴	1	2	yes	—
157	C₂×Dic₁₃	C₂⁴	1	2	yes	—
158	C₂×Dic₁₃	C₂⁴	1	2	yes	—
159	C₂×Dic₁₃	C₂⁴	1	2	yes	—
160	C₂×Dic₁₃	C₂⁴	1	2	yes	—
161	C₄×D₁₃	—	2	8	no	—
162	Dic₂₆	—	2	8	no	—
163	Dic₂₆	—	2	8	no	—
164	Dic₂₆	—	2	8	no	—
165	#556	—	13	16	no	—
166	C₂×C₄⋊Q₈	—	13	1	no	—
167	C₂×#126	—	13	1	no	—
168	C₂×#126	—	13	1	no	—
169	C₂×#126	—	13	1	no	—
170	C₂×#126	D₁₃	1	1	yes	characteristic, complemented
171	C₂×#124	—	13	1	no	—
172	C₂×#124	—	13	1	no	—
173	C₂×C₂²⋊Q₈	—	13	1	no	—
174	C₂×C₂²⋊Q₈	—	13	1	no	—
175	C₂×C₄×Q₈	—	13	1	no	—
176	C₂×C₄×Q₈	—	13	1	no	—
177	C₂×C₄×Q₈	—	13	1	no	—
178	C₂×C₄×D₄	—	13	1	no	—
179	C₂×#117	—	13	1	no	—
180	C₂×#117	—	13	1	no	—
181	C₂²×C₁₃	—	2	2	no	—
182	C₂²×C₁₃	—	2	2	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	4	4	no	—
185	C₂²×C₁₃	C₂×#41	1	2	yes	—
186	C₂²×C₁₃	C₂×#41	1	2	yes	—
187	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
188	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
189	C₂×D₁₃	—	2	2	no	—
190	C₂×D₁₃	—	2	2	no	—
191	C₂×D₁₃	—	2	2	no	—
192	C₂×D₁₃	—	4	4	no	—
193	C₄×C₁₃	—	2	2	no	—
194	C₄×C₁₃	—	2	2	no	—
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	2	no	—
199	Dic₁₃	—	2	2	no	—
200	Dic₁₃	—	2	2	no	—
201	Dic₁₃	—	2	2	no	—
202	Dic₁₃	—	2	2	no	—
203	Dic₁₃	—	2	2	no	—
204	Dic₁₃	C₂×#41	1	4	yes	—
205	Dic₁₃	C₂×#41	1	4	yes	—
206	C₂²×Q₈	—	13	1	no	—
207	C₂²×Q₈	—	13	1	no	—
208	C₂²×Q₈	—	13	1	no	—
209	C₂²×D₄	—	13	1	no	—
210	C₂³×C₄	—	13	1	no	—
211	C₂³×C₄	—	13	1	no	—
212	C₄⋊Q₈	—	13	8	no	—
213	#126	—	13	8	no	—
214	#126	—	13	8	no	—
215	#126	—	13	8	no	—
216	#126	C₂×D₁₃	1	8	yes	complemented
217	#124	—	13	8	no	—
218	#124	—	13	8	no	—
219	C₂²⋊Q₈	—	13	8	no	—
220	C₂²⋊Q₈	—	13	8	no	—
221	C₄×Q₈	—	13	8	no	—
222	C₄×Q₈	—	13	8	no	—
223	C₄×Q₈	—	13	8	no	—
224	C₄×D₄	—	13	8	no	—
225	#117	—	13	8	no	—
226	#117	—	13	8	no	—
227	C₂×C₄⋊C₄	—	13	1	no	—
228	C₂×C₄⋊C₄	—	13	1	no	—
229	C₂×C₄⋊C₄	—	13	1	no	—
230	C₂×C₄⋊C₄	—	13	1	no	—
231	C₂×C₄⋊C₄	—	13	1	no	—
232	C₂×C₄⋊C₄	—	13	1	no	—
233	C₂×C₄⋊C₄	—	13	1	no	—
234	C₂×C₄⋊C₄	—	13	1	no	—
235	C₂×C₄⋊C₄	—	13	1	no	—
236	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	13	1	no	—
240	C₂×C₂²⋊C₄	—	13	1	no	—
241	C₂×C₂²⋊C₄	—	13	1	no	—
242	C₂×C₂²⋊C₄	—	13	1	no	—
243	C₂×C₂²⋊C₄	—	13	1	no	—
244	C₂×C₂²⋊C₄	—	13	1	no	—
245	C₂×C₂²⋊C₄	—	13	1	no	—
246	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
256	C₂×C₁₃	—	4	2	no	—
257	C₂×C₁₃	#556	1	4	yes	complemented
258	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
259	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
260	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
261	D₁₃	—	4	2	no	—
262	C₂⁴	—	13	1	no	—
263	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
264	C₂×Q₈	—	13	4	no	—
265	C₂×Q₈	—	13	4	no	—
266	C₂×Q₈	—	13	4	no	—
267	C₂×Q₈	—	26	4	no	—
268	C₂×Q₈	—	26	4	no	—
269	C₂×Q₈	—	26	4	no	—
270	C₂×D₄	—	13	4	no	—
271	C₂×D₄	—	26	4	no	—
272	C₂²×C₄	—	13	1	no	—
273	C₂²×C₄	—	13	1	no	—
274	C₂²×C₄	—	13	4	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	4	no	—
281	C₂²×C₄	—	26	4	no	—
282	C₂²×C₄	—	26	4	no	—
283	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
289	C₄⋊C₄	—	13	4	no	—
290	C₄⋊C₄	—	13	4	no	—
291	C₄⋊C₄	—	13	4	no	—
292	C₄⋊C₄	—	13	4	no	—
293	C₄⋊C₄	—	13	4	no	—
294	C₄⋊C₄	—	13	4	no	—
295	C₄⋊C₄	—	13	4	no	—
296	C₄⋊C₄	—	13	4	no	—
297	C₄⋊C₄	—	13	4	no	—
298	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
299	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
300	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
301	C₂²⋊C₄	—	13	4	no	—
302	C₂²⋊C₄	—	13	4	no	—
303	C₂²⋊C₄	—	13	4	no	—
304	C₂²⋊C₄	—	13	4	no	—
305	C₂²⋊C₄	—	13	4	no	—
306	C₂²⋊C₄	—	13	4	no	—
307	C₂²⋊C₄	—	13	4	no	—
308	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
309	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
310	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
311	C₄²	—	13	4	no	—
312	C₄²	—	13	4	no	—
313	C₄²	—	13	4	no	—
314	C₄²	—	13	4	no	—
315	C₄²	—	13	4	no	—
316	C₄²	—	13	4	no	—
317	C₄²	C₂²×D₁₃	1	4	yes	—
318	C₁₃	C₂×#556	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	13	2	no	—
323	C₂³	—	26	2	no	—
324	C₂³	—	26	2	no	—
325	C₂³	—	26	2	no	—
326	C₂³	C₂³×D₁₃	1	2	yes	—
327	C₂³	C₂³×D₁₃	1	1	yes	characteristic
328	Q₈	—	26	8	no	—
329	Q₈	—	26	8	no	—
330	Q₈	—	26	8	no	—
331	D₄	—	26	8	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	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	13	4	no	—
339	C₂×C₄	—	13	4	no	—
340	C₂×C₄	—	13	2	no	—
341	C₂×C₄	—	13	2	no	—
342	C₂×C₄	—	13	2	no	—
343	C₂×C₄	—	13	2	no	—
344	C₂×C₄	—	13	2	no	—
345	C₂×C₄	—	13	2	no	—
346	C₂×C₄	—	13	2	no	—
347	C₂×C₄	—	26	8	no	—
348	C₂×C₄	—	26	8	no	—
349	C₂×C₄	—	26	2	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	C₂³×D₁₃	1	2	yes	—
355	C₂×C₄	C₂³×D₁₃	1	2	yes	—
356	C₂×C₄	C₂³×D₁₃	1	2	yes	—
357	C₂×C₄	C₂³×D₁₃	1	2	yes	—
358	C₂×C₄	C₂³×D₁₃	1	2	yes	—
359	C₂×C₄	C₂³×D₁₃	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	26	2	no	—
365	C₂²	—	26	2	no	—
366	C₂²	—	26	2	no	—
367	C₂²	—	52	4	no	—
368	C₂²	#41×D₁₃	1	2	yes	—
369	C₂²	#41×D₁₃	1	2	yes	—
370	C₂²	#88257	1	2	yes	—
371	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	13	4	no	—
379	C₄	—	13	4	no	—
380	C₄	—	26	2	no	—
381	C₄	—	26	2	no	—
382	C₄	—	26	2	no	—
383	C₄	—	26	2	no	—
384	C₄	—	26	2	no	—
385	C₂	—	4	2	no	—
386	C₂	—	52	2	no	—
387	C₂	#11719407	1	4	yes	direct product factor
388	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
389	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
390	C₂	C₂×#88257	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#126	C₂
socle	C₂³×C₁₃	C₂⁴
prime radical	C₂²×C₂²⋊D₁₃	C₂²
hypercenter	C₂×#126	D₁₃
hypocenter	C₁₃	C₂×#556
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#126	C₂	semidirect
2. #11719407	C₂	direct (N × H)
3. C₂×#88152	C₂	semidirect
4. C₂×#88152	C₂	semidirect
5. C₂×#88150	C₂	semidirect
6. C₂×#88142	C₂	semidirect
7. C₂×#88141	C₂	semidirect
8. C₂×#88141	C₂	semidirect
12. C₂×#88133	C₂	semidirect
13. C₂×#88132	C₂	semidirect
14. C₂×#88131	C₂	semidirect
15. C₂×#88126	C₂	semidirect
16. C₂×C₄×Dic₂₆	C₂	semidirect
23. C₁₃×#126	C₂²	semidirect
53. #88152	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88150	C₂²	semidirect
56. #88142	C₂²	semidirect
57. #88141	C₂²	semidirect
58. #88141	C₂²	semidirect
62. #88133	C₂²	semidirect
63. #88132	C₂²	semidirect
64. #88131	C₂²	semidirect
65. #88126	C₂²	semidirect
66. C₄×Dic₂₆	C₂²	semidirect
170. C₂×#126	D₁₃	semidirect
216. #126	C₂×D₁₃	semidirect
257. C₂×C₁₃	#556	semidirect
318. C₁₃	C₂×#556	semidirect
387. C₂	#11719407	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#126	2
#11719407	2
C₂×#88152	2
C₂×#88150	2
C₂×#88142	2
C₂×#88141	2
C₂×#88139	2
C₂×#88135	2
C₂×#88133	2
C₂×#88132	2
C₂×#88131	2
C₂×#88126	2
C₂×C₄×Dic₂₆	2
C₂×#556	13

Subgroups — C2×#11719407 #13128379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719407 #13128379