Subgroups — C₂×#13129530 #16770348

Order 3328.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129530	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719377	C₂	1	3	yes	maximal, complemented
3	C₂×#11719376	C₂	1	6	yes	maximal, complemented
4	C₂×#11719292	C₂	1	6	yes	maximal, complemented
5	C₂×#11719374	C₂	1	6	yes	maximal, complemented
6	C₂×#11719298	C₂	1	6	yes	maximal, complemented
7	C₂×#11719385	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
10	C₂×C₁₃×#124	C₂²	1	3	yes	—
11	C₂×C₁₃×#124	C₂²	1	6	yes	—
12	C₂×C₁₃×#120	C₂²	1	6	yes	—
13	C₂×#88207	C₂²	1	2	yes	complemented
14	C₂²×C₂²⋊Dic₁₃	C₂²	1	6	yes	complemented
15	C₂×#88200	C₂²	1	3	yes	complemented
16	C₂×Q₈×Dic₁₃	C₂²	1	3	yes	complemented
17	C₂×#88198	C₂²	1	6	yes	complemented
18	C₂×#88193	C₂²	1	6	yes	—
19	C₂×#88192	C₂²	1	3	yes	—
20	C₂×#88190	C₂²	1	6	yes	—
21	C₂×#88189	C₂²	1	6	yes	—
22	C₂×#88189	C₂²	1	6	yes	—
23	C₂×D₄×Dic₁₃	C₂²	1	3	yes	—
24	C₂×D₄×Dic₁₃	C₂²	1	6	yes	—
25	#11719385	C₂²	1	48	yes	complemented
26	#11719377	C₂²	1	48	yes	complemented
27	#11719376	C₂²	1	96	yes	complemented
28	#11719374	C₂²	1	96	yes	complemented
29	#11719298	C₂²	1	96	yes	complemented
30	#11719292	C₂²	1	96	yes	complemented
31	C₂×#88139	C₂²	1	6	yes	complemented
32	C₂×#88137	C₂²	1	6	yes	complemented
33	C₂×#88135	C₂²	1	6	yes	complemented
34	C₂×#88133	C₂²	1	6	yes	complemented
35	C₂×#88133	C₂²	1	6	yes	complemented
36	C₂×#88133	C₂²	1	6	yes	complemented
37	C₂×#88133	C₂²	1	6	yes	complemented
38	C₂×#88132	C₂²	1	6	yes	complemented
39	C₂×#88132	C₂²	1	6	yes	complemented
40	C₂×#88132	C₂²	1	6	yes	complemented
41	C₂×#88131	C₂²	1	6	yes	complemented
42	C₂×#88131	C₂²	1	6	yes	complemented
43	C₂×#88130	C₂²	1	2	yes	complemented
44	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#88124	C₂²	1	3	yes	complemented
46	C₂×C₄×Dic₂₆	C₂²	1	6	yes	complemented
47	C₂⁵×C₁₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
51	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
52	C₂³×Dic₁₃	C₂³	1	6	yes	—
53	C₂³×Dic₁₃	C₂³	1	6	yes	—
54	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
55	C₂²×Dic₂₆	C₂³	1	6	yes	—
56	C₁₃×#124	C₂³	1	48	yes	—
57	C₁₃×#124	C₂³	1	24	yes	—
58	C₁₃×#120	C₂³	1	48	yes	—
59	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
60	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	#88207	C₂³	1	16	yes	complemented
65	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
66	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
67	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
68	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
69	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
70	C₂×C₂²⋊Dic₁₃	C₂³	1	48	yes	complemented
71	#88200	C₂³	1	24	yes	complemented
72	Q₈×Dic₁₃	C₂³	1	24	yes	complemented
73	#88198	C₂³	1	48	yes	complemented
74	#88193	C₂³	1	48	yes	—
75	#88192	C₂³	1	24	yes	—
76	#88190	C₂³	1	48	yes	—
77	#88189	C₂³	1	48	yes	—
78	#88189	C₂³	1	48	yes	—
79	D₄×Dic₁₃	C₂³	1	24	yes	—
80	D₄×Dic₁₃	C₂³	1	48	yes	—
81	C₂×#6103	C₂³	1	6	yes	—
82	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
83	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
84	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
85	C₂×#6101	C₂³	1	6	yes	—
86	C₂×#6101	C₂³	1	6	yes	—
87	C₂×#6101	C₂³	1	6	yes	—
88	C₂×#6101	C₂³	1	6	yes	—
89	C₂×#6101	C₂³	1	6	yes	—
90	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
91	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
92	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
93	#88139	C₂³	1	48	yes	complemented
94	#88137	C₂³	1	48	yes	complemented
95	#88135	C₂³	1	48	yes	complemented
96	#88133	C₂³	1	48	yes	complemented
97	#88133	C₂³	1	48	yes	complemented
98	#88133	C₂³	1	48	yes	complemented
99	#88133	C₂³	1	48	yes	complemented
100	#88132	C₂³	1	48	yes	complemented
101	#88132	C₂³	1	48	yes	complemented
102	#88132	C₂³	1	48	yes	complemented
103	#88131	C₂³	1	48	yes	complemented
104	#88131	C₂³	1	48	yes	complemented
105	#88130	C₂³	1	16	yes	complemented
106	C₄²×D₁₃	C₂³	1	8	yes	complemented
107	#88124	C₂³	1	24	yes	complemented
108	C₄×Dic₂₆	C₂³	1	48	yes	complemented
109	C₂×#3568	—	13	1	no	maximal, Sylow
110	C₂⁴×C₁₃	—	4	12	no	—
111	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
112	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
113	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	—	4	6	no	—
115	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
116	C₂×D₄×C₁₃	—	4	12	no	—
117	C₂×D₄×C₁₃	—	4	6	no	—
118	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
119	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
122	C₂×C₂²⋊D₁₃	—	4	12	no	—
123	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
124	C₂²×Dic₁₃	—	4	12	no	—
125	C₂²×Dic₁₃	—	4	12	no	—
126	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
127	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
128	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
129	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
130	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
131	C₂×C₄×D₁₃	—	4	6	no	—
132	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
133	C₂×Dic₂₆	—	4	12	no	—
134	C₂×Dic₂₆	C₂⁴	1	24	yes	—
135	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
136	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
137	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
138	C₄²×C₁₃	C₂⁴	1	8	yes	—
139	C₄²×C₁₃	C₂⁴	1	4	yes	—
140	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
141	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
142	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
143	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
144	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
145	#6103	C₂⁴	1	24	yes	—
146	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
147	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
148	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
149	#6101	C₂⁴	1	24	yes	—
150	#6101	C₂⁴	1	24	yes	—
151	#6101	C₂⁴	1	24	yes	—
152	#6101	C₂⁴	1	24	yes	—
153	#6101	C₂⁴	1	24	yes	—
154	C₄×Dic₁₃	C₂⁴	1	24	yes	—
155	C₄×Dic₁₃	C₂⁴	1	24	yes	—
156	C₄×Dic₁₃	C₂⁴	1	12	yes	—
157	#3568	—	13	32	no	—
158	C₂×#563	—	13	3	no	—
159	C₂×H(3,𝔽₄)	D₁₃	1	1	yes	characteristic, complemented
160	C₂×#556	—	13	6	no	—
161	C₂×#551	—	13	6	no	—
162	C₂×#542	—	13	6	no	—
163	C₂×#538	—	13	6	no	—
164	C₂×#529	—	13	3	no	—
165	C₂³×C₁₃	—	2	12	no	—
166	C₂³×C₁₃	—	2	12	no	—
167	C₂³×C₁₃	—	2	12	no	—
168	C₂³×C₁₃	—	4	24	no	—
169	C₂³×C₁₃	—	8	16	no	—
170	C₂³×C₁₃	C₂⁵	1	12	yes	—
171	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	6	no	—
173	C₂²×D₁₃	C₂⁵	1	2	yes	—
174	Q₈×C₁₃	—	4	12	no	—
175	D₄×C₁₃	—	4	24	no	—
176	D₄×C₁₃	—	4	12	no	—
177	C₂×C₄×C₁₃	—	2	12	no	—
178	C₂×C₄×C₁₃	—	2	6	no	—
179	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
180	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
181	C₂²⋊D₁₃	—	4	24	no	—
182	C₂×Dic₁₃	—	2	12	no	—
183	C₂×Dic₁₃	—	2	12	no	—
184	C₂×Dic₁₃	—	2	6	no	—
185	C₂×Dic₁₃	—	4	24	no	—
186	C₂×Dic₁₃	—	4	24	no	—
187	C₂×Dic₁₃	C₂⁵	1	6	yes	—
188	C₂×Dic₁₃	C₂⁵	1	12	yes	—
189	C₂×Dic₁₃	C₂⁵	1	12	yes	—
190	C₄×D₁₃	—	4	12	no	—
191	Dic₂₆	—	4	24	no	—
192	#563	—	13	48	no	—
193	H(3,𝔽₄)	C₂×D₁₃	1	16	yes	complemented
194	#556	—	13	96	no	—
195	#551	—	13	96	no	—
196	#542	—	13	96	no	—
197	#538	—	13	96	no	—
198	C₂×C₄⋊Q₈	—	13	6	no	—
199	#529	—	13	48	no	—
200	C₂×#126	—	13	6	no	—
201	C₂×#126	—	13	6	no	—
202	C₂×#126	—	13	6	no	—
203	C₂×#126	—	13	6	no	—
204	C₂×#126	—	13	2	no	—
205	C₂×#125	—	13	3	no	—
206	C₂×#124	—	13	6	no	—
207	C₂×#124	—	13	6	no	—
208	C₂×#124	C₂×D₁₃	1	3	yes	—
209	C₂×#124	C₂×D₁₃	1	6	yes	—
210	C₂×#123	—	13	6	no	—
211	C₂×#123	—	13	6	no	—
212	C₂×#123	—	13	6	no	—
213	C₂×C₂²⋊Q₈	—	13	3	no	—
214	C₂×C₂²⋊Q₈	—	13	6	no	—
215	C₂×C₂²⋊Q₈	—	13	6	no	—
216	C₂×C₂²⋊Q₈	—	13	6	no	—
217	C₂×#121	—	13	3	no	—
218	C₂×#121	—	13	6	no	—
219	C₂×#120	—	13	2	no	—
220	C₂×#120	C₂×D₁₃	1	6	yes	—
221	C₂×C₄×Q₈	—	13	3	no	—
222	C₂×C₄×Q₈	—	13	6	no	—
223	C₂×C₄×D₄	—	13	3	no	—
224	C₂×C₄×D₄	—	13	6	no	—
225	C₂×C₄×D₄	—	13	6	no	—
226	C₂×#117	—	13	6	no	—
227	C₂×#117	—	13	6	no	—
228	C₂²×C₂²⋊C₄	—	13	6	no	—
229	C₂²×C₄²	—	13	1	no	—
230	C₂²×C₁₃	—	2	12	no	—
231	C₂²×C₁₃	—	2	12	no	—
232	C₂²×C₁₃	—	2	12	no	—
233	C₂²×C₁₃	—	4	24	no	—
234	C₂²×C₁₃	—	8	16	no	—
235	C₂²×C₁₃	#585	1	6	yes	—
236	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
237	C₂×D₁₃	—	2	6	no	—
238	C₂×D₁₃	—	4	4	no	—
239	C₄×C₁₃	—	2	12	no	—
240	C₄×C₁₃	—	2	6	no	—
241	Dic₁₃	—	2	12	no	—
242	Dic₁₃	—	2	12	no	—
243	Dic₁₃	—	2	6	no	—
244	C₂⁵	C₂²×D₁₃	1	2	yes	—
245	C₂²×Q₈	—	13	6	no	—
246	C₂²×Q₈	C₂²×D₁₃	1	3	yes	—
247	C₂²×D₄	—	13	6	no	—
248	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
249	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
250	C₂³×C₄	—	13	6	no	—
251	C₂³×C₄	—	13	6	no	—
252	C₂³×C₄	—	13	3	no	—
253	C₄⋊Q₈	—	13	48	no	—
254	#126	—	13	48	no	—
255	#126	—	13	48	no	—
256	#126	—	13	48	no	—
257	#126	—	13	48	no	—
258	#126	—	13	16	no	—
259	#125	—	13	24	no	—
260	#124	—	13	48	no	—
261	#124	—	13	48	no	—
262	#124	C₂²×D₁₃	1	24	yes	—
263	#124	C₂²×D₁₃	1	48	yes	—
264	#123	—	13	48	no	—
265	#123	—	13	48	no	—
266	#123	—	13	48	no	—
267	C₂²⋊Q₈	—	13	24	no	—
268	C₂²⋊Q₈	—	13	48	no	—
269	C₂²⋊Q₈	—	13	48	no	—
270	C₂²⋊Q₈	—	13	48	no	—
271	#121	—	13	24	no	—
272	#121	—	13	48	no	—
273	#120	—	13	16	no	—
274	#120	C₂²×D₁₃	1	48	yes	—
275	C₄×Q₈	—	13	24	no	—
276	C₄×Q₈	—	13	48	no	—
277	C₄×D₄	—	13	24	no	—
278	C₄×D₄	—	13	48	no	—
279	C₄×D₄	—	13	48	no	—
280	#117	—	13	48	no	—
281	#117	—	13	48	no	—
282	C₂×C₄⋊C₄	—	13	6	no	—
283	C₂×C₄⋊C₄	—	13	6	no	—
284	C₂×C₄⋊C₄	—	13	6	no	—
285	C₂×C₄⋊C₄	—	13	6	no	—
286	C₂×C₄⋊C₄	—	13	3	no	—
287	C₂×C₄⋊C₄	—	13	6	no	—
288	C₂×C₄⋊C₄	—	13	3	no	—
289	C₂×C₄⋊C₄	—	13	6	no	—
290	C₂×C₂²⋊C₄	—	13	6	no	—
291	C₂×C₂²⋊C₄	—	13	6	no	—
292	C₂×C₂²⋊C₄	—	13	6	no	—
293	C₂×C₂²⋊C₄	—	13	6	no	—
294	C₂×C₂²⋊C₄	—	13	48	no	—
295	C₂×C₂²⋊C₄	—	13	6	no	—
296	C₂×C₂²⋊C₄	—	13	6	no	—
297	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
300	C₂×C₄²	—	13	6	no	—
301	C₂×C₄²	—	13	3	no	—
302	C₂×C₄²	—	13	6	no	—
303	C₂×C₄²	—	13	8	no	—
304	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
305	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×C₁₃	—	4	12	no	—
307	C₂×C₁₃	#3568	1	4	yes	complemented
308	C₂×C₁₃	C₂×#585	1	3	yes	—
309	D₁₃	—	4	2	no	—
310	C₂⁴	—	4	12	no	—
311	C₂⁴	—	13	1	no	—
312	C₂⁴	C₂³×D₁₃	1	6	yes	—
313	C₂⁴	C₂³×D₁₃	1	8	yes	—
314	C₂×Q₈	—	4	6	no	—
315	C₂×Q₈	—	13	24	no	—
316	C₂×Q₈	—	52	12	no	—
317	C₂×Q₈	C₂³×D₁₃	1	12	yes	—
318	C₂×D₄	—	4	6	no	—
319	C₂×D₄	—	4	12	no	—
320	C₂×D₄	—	13	24	no	—
321	C₂×D₄	—	52	12	no	—
322	C₂×D₄	C₂³×D₁₃	1	12	yes	—
323	C₂×D₄	C₂³×D₁₃	1	24	yes	—
324	C₂²×C₄	—	13	3	no	—
325	C₂²×C₄	—	13	6	no	—
326	C₂²×C₄	—	13	6	no	—
327	C₂²×C₄	—	13	24	no	—
328	C₂²×C₄	—	13	24	no	—
329	C₂²×C₄	—	13	12	no	—
330	C₂²×C₄	—	52	6	no	—
331	C₂²×C₄	—	52	12	no	—
332	C₂²×C₄	—	52	12	no	—
333	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
334	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
335	C₄⋊C₄	—	13	24	no	—
336	C₄⋊C₄	—	13	24	no	—
337	C₄⋊C₄	—	13	24	no	—
338	C₄⋊C₄	—	13	24	no	—
339	C₄⋊C₄	—	13	12	no	—
340	C₄⋊C₄	—	13	24	no	—
341	C₄⋊C₄	—	13	12	no	—
342	C₄⋊C₄	—	13	24	no	—
343	C₂²⋊C₄	—	13	24	no	—
344	C₂²⋊C₄	—	13	24	no	—
345	C₂²⋊C₄	—	13	24	no	—
346	C₂²⋊C₄	—	13	24	no	—
347	C₂²⋊C₄	—	13	24	no	—
348	C₂²⋊C₄	—	13	24	no	—
349	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
350	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
351	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
352	C₄²	—	13	12	no	—
353	C₄²	—	13	24	no	—
354	C₄²	—	13	24	no	—
355	C₄²	C₂³×D₁₃	1	4	yes	—
356	C₄²	C₂³×D₁₃	1	8	yes	—
357	C₁₃	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	2	12	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	4	24	no	—
362	C₂³	—	8	16	no	—
363	C₂³	—	13	2	no	—
364	C₂³	—	26	6	no	—
365	C₂³	C₂⁴×D₁₃	1	12	yes	—
366	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
367	Q₈	—	4	12	no	—
368	Q₈	—	52	24	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	24	no	—
371	D₄	—	52	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	13	6	no	—
375	C₂×C₄	—	13	12	no	—
376	C₂×C₄	—	13	12	no	—
377	C₂×C₄	—	26	6	no	—
378	C₂×C₄	—	26	12	no	—
379	C₂×C₄	—	26	12	no	—
380	C₂×C₄	—	52	12	no	—
381	C₂×C₄	—	52	24	no	—
382	C₂×C₄	—	52	24	no	—
383	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
384	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
385	C₂²	—	2	12	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	26	6	no	—
391	C₂²	—	52	4	no	—
392	C₂²	#11719650	1	6	yes	—
393	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	26	6	no	—
397	C₄	—	26	12	no	—
398	C₄	—	26	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	52	2	no	—
401	C₂	#13129530	1	4	yes	direct product factor
402	C₂	C₂×#11719650	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×H(3,𝔽₄)	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₁₃
hypocenter	C₁₃	C₂×#3568
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #13129530	C₂	direct (N × H)
2. C₂×#11719377	C₂	semidirect
3. C₂×#11719376	C₂	semidirect
4. C₂×#11719292	C₂	semidirect
5. C₂×#11719374	C₂	semidirect
6. C₂×#11719298	C₂	semidirect
7. C₂×#11719385	C₂	semidirect
8. C₂×C₁₃×H(3,𝔽₄)	C₂	semidirect
9. C₁₃×H(3,𝔽₄)	C₂²	semidirect
13. C₂×#88207	C₂²	semidirect
14. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
15. C₂×#88200	C₂²	semidirect
16. C₂×Q₈×Dic₁₃	C₂²	semidirect
17. C₂×#88198	C₂²	semidirect
25. #11719385	C₂²	semidirect
26. #11719377	C₂²	semidirect
27. #11719376	C₂²	semidirect
28. #11719374	C₂²	semidirect
29. #11719298	C₂²	semidirect
30. #11719292	C₂²	semidirect
31. C₂×#88139	C₂²	semidirect
32. C₂×#88137	C₂²	semidirect
33. C₂×#88135	C₂²	semidirect
34. C₂×#88133	C₂²	semidirect
35. C₂×#88133	C₂²	semidirect
36. C₂×#88133	C₂²	semidirect
37. C₂×#88133	C₂²	semidirect
38. C₂×#88132	C₂²	semidirect
39. C₂×#88132	C₂²	semidirect
40. C₂×#88132	C₂²	semidirect
41. C₂×#88131	C₂²	semidirect
42. C₂×#88131	C₂²	semidirect
43. C₂×#88130	C₂²	semidirect
44. C₂×C₄²×D₁₃	C₂²	semidirect
45. C₂×#88124	C₂²	semidirect
46. C₂×C₄×Dic₂₆	C₂²	semidirect
64. #88207	C₂³	semidirect
70. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
71. #88200	C₂³	semidirect
72. Q₈×Dic₁₃	C₂³	semidirect
73. #88198	C₂³	semidirect
93. #88139	C₂³	semidirect
94. #88137	C₂³	semidirect
95. #88135	C₂³	semidirect
96. #88133	C₂³	semidirect
97. #88133	C₂³	semidirect
98. #88133	C₂³	semidirect
99. #88133	C₂³	semidirect
100. #88132	C₂³	semidirect
101. #88132	C₂³	semidirect
102. #88132	C₂³	semidirect
103. #88131	C₂³	semidirect
104. #88131	C₂³	semidirect
105. #88130	C₂³	semidirect
106. C₄²×D₁₃	C₂³	semidirect
107. #88124	C₂³	semidirect
108. C₄×Dic₂₆	C₂³	semidirect
159. C₂×H(3,𝔽₄)	D₁₃	semidirect
193. H(3,𝔽₄)	C₂×D₁₃	semidirect
307. C₂×C₁₃	#3568	semidirect
357. C₁₃	C₂×#3568	semidirect
401. C₂	#13129530	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129530	2
C₂×#11719377	2
C₂×#11719376	2
C₂×#11719292	2
C₂×#11719374	2
C₂×#11719298	2
C₂×#11719385	2
C₂×C₁₃×H(3,𝔽₄)	2
C₂×#3568	13

Subgroups — C2×#13129530 #16770348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129530 #16770348