Subgroups — #13128504

Order 1664.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88256	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719539	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719422	C₂	1	3	yes	maximal, complemented
7	#11719420	C₂	1	3	yes	maximal, complemented
8	#11719317	C₂	1	3	yes	maximal, complemented
9	#11719314	C₂	1	3	yes	maximal, complemented
10	#11719313	C₂	1	3	yes	maximal, complemented
11	D₁₃×#121	C₂	1	3	yes	maximal, complemented
12	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719255	C₂	1	3	yes	maximal, complemented
15	#11719252	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
18	#88256	—	2	8	no	—
19	#41×D₁₃	—	2	8	no	—
20	C₂×#6131	C₂²	1	1	yes	characteristic
21	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#6129	C₂²	1	3	yes	complemented
24	C₂×D₄×D₁₃	C₂²	1	3	yes	complemented
25	C₂×D₄×D₁₃	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₃	C₂²	1	3	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	6	yes	complemented
28	C₂×#6127	C₂²	1	3	yes	complemented
29	C₂×#6127	C₂²	1	3	yes	complemented
30	C₂²×D₅₂	C₂²	1	3	yes	complemented
31	C₂²×C₄×D₁₃	C₂²	1	3	yes	complemented
32	C₁₃×#127	C₂²	1	3	yes	complemented
33	C₁₃×#121	C₂²	1	3	yes	complemented
34	C₁₃×#121	C₂²	1	3	yes	complemented
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
37	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
38	#88194	C₂²	1	3	yes	complemented
39	#88193	C₂²	1	3	yes	complemented
40	#88193	C₂²	1	6	yes	complemented
41	#88192	C₂²	1	3	yes	complemented
42	#88192	C₂²	1	3	yes	complemented
43	#88192	C₂²	1	6	yes	complemented
44	#88191	C₂²	1	3	yes	complemented
45	#88191	C₂²	1	6	yes	complemented
46	#88191	C₂²	1	6	yes	complemented
47	#88190	C₂²	1	3	yes	complemented
48	#88184	C₂²	1	3	yes	complemented
49	C₄×C₂²⋊D₁₃	C₂²	1	3	yes	complemented
50	C₄×C₂²⋊D₁₃	C₂²	1	3	yes	complemented
51	#88178	C₂²	1	3	yes	complemented
52	#88151	C₂²	1	3	yes	complemented
53	#88150	C₂²	1	1	yes	characteristic, complemented
54	#88149	C₂²	1	3	yes	complemented
55	#88148	C₂²	1	3	yes	complemented
56	#88147	C₂²	1	3	yes	complemented
57	C₄⋊C₄×D₁₃	C₂²	1	3	yes	complemented
58	#88138	C₂²	1	3	yes	complemented
59	#88138	C₂²	1	6	yes	complemented
60	#88137	C₂²	1	3	yes	complemented
61	#88136	C₂²	1	3	yes	complemented
62	C₂²⋊C₄×D₁₃	C₂²	1	6	yes	complemented
63	#88132	C₂²	1	3	yes	complemented
64	#88129	C₂²	1	3	yes	complemented
65	C₄×D₅₂	C₂²	1	3	yes	complemented
66	C₄×D₅₂	C₂²	1	3	yes	complemented
67	#88126	C₂²	1	3	yes	complemented
68	C₂³×D₁₃	C₂³	1	3	yes	—
69	C₂³×D₁₃	C₂³	1	6	yes	—
70	C₁₃×#41	—	2	4	no	—
71	C₁₃×#41	—	2	4	no	—
72	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₁₃	C₂³	1	3	yes	—
74	C₂×D₄×C₁₃	C₂³	1	3	yes	—
75	C₂×D₄×C₁₃	C₂³	1	3	yes	—
76	C₂×D₄×C₁₃	C₂³	1	6	yes	—
77	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
78	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₁₃	C₂³	1	3	yes	—
80	C₂×C₂²⋊D₁₃	C₂³	1	3	yes	—
81	C₂×C₂²⋊D₁₃	C₂³	1	6	yes	—
82	C₂×C₂²⋊D₁₃	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₁₃	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₁₃	C₂³	1	6	yes	—
85	C₂²×Dic₁₃	C₂³	1	3	yes	—
86	#6131	—	2	4	no	—
87	#6131	D₄	1	8	yes	complemented
88	Q₈×D₁₃	—	2	4	no	—
89	#6129	—	2	12	no	—
90	D₄×D₁₃	—	2	12	no	—
91	D₄×D₁₃	—	2	12	no	—
92	D₄×D₁₃	—	2	12	no	—
93	D₄×D₁₃	—	4	12	no	—
94	#6127	—	2	12	no	—
95	#6127	—	2	12	no	—
96	C₂×D₅₂	—	2	12	no	—
97	C₂×D₅₂	C₂³	1	3	yes	—
98	C₂×D₅₂	C₂³	1	3	yes	—
99	C₂×D₅₂	C₂³	1	3	yes	—
100	C₂×D₅₂	C₂³	1	3	yes	—
101	C₂×C₄×D₁₃	—	2	12	no	—
102	C₂×C₄×D₁₃	C₂³	1	3	yes	—
103	C₂×C₄×D₁₃	C₂³	1	3	yes	—
104	C₂×C₄×D₁₃	C₂³	1	3	yes	—
105	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂³	1	6	yes	—
107	C₂×C₄×D₁₃	C₂³	1	3	yes	—
108	C₂×Dic₂₆	C₂³	1	3	yes	—
109	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
113	C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
114	C₄²×C₁₃	C₂³	1	3	yes	—
115	C₂²⋊Dic₁₃	C₂³	1	3	yes	—
116	C₂²⋊Dic₁₃	C₂³	1	6	yes	—
117	C₂²⋊Dic₁₃	C₂³	1	3	yes	—
118	#6103	C₂³	1	3	yes	—
119	#6103	C₂³	1	3	yes	—
120	#6103	C₂³	1	1	yes	characteristic
121	#6103	C₂³	1	3	yes	—
122	#6103	C₂³	1	6	yes	—
123	#6103	C₂³	1	3	yes	—
124	#6103	C₂³	1	1	yes	characteristic
125	C₄⋊Dic₁₃	C₂³	1	3	yes	—
126	C₄⋊Dic₁₃	C₂³	1	3	yes	—
127	#6101	C₂³	1	1	yes	characteristic
128	#6101	C₂³	1	3	yes	—
129	#6101	C₂³	1	3	yes	—
130	#6101	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂³	1	3	yes	—
132	#3488	—	13	1	no	maximal, Sylow
133	C₂³×C₁₃	C₂⁴	1	3	yes	—
134	C₂³×C₁₃	C₂⁴	1	3	yes	—
135	C₂²×D₁₃	—	2	6	no	—
136	C₂²×D₁₃	—	2	6	no	—
137	C₂²×D₁₃	—	2	12	no	—
138	C₂²×D₁₃	—	4	3	no	—
139	C₂²×D₁₃	—	4	6	no	—
140	C₂²×D₁₃	—	4	6	no	—
141	C₂²×D₁₃	C₂⁴	1	3	yes	—
142	C₂²×D₁₃	C₂⁴	1	3	yes	—
143	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
144	Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
145	D₄×C₁₃	—	2	6	no	—
146	D₄×C₁₃	—	2	6	no	—
147	D₄×C₁₃	—	4	6	no	—
148	D₄×C₁₃	—	4	3	no	—
149	C₂×C₄×C₁₃	—	2	6	no	—
150	C₂×C₄×C₁₃	—	2	6	no	—
151	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
156	C₂²⋊D₁₃	—	2	6	no	—
157	C₂²⋊D₁₃	—	2	12	no	—
158	C₂²⋊D₁₃	—	2	6	no	—
159	C₂²⋊D₁₃	—	2	6	no	—
160	C₂²⋊D₁₃	—	4	6	no	—
161	C₂²⋊D₁₃	—	4	3	no	—
162	C₂×Dic₁₃	—	2	6	no	—
163	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂⁴	1	3	yes	—
165	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂⁴	1	3	yes	—
167	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
168	D₅₂	—	2	6	no	—
169	D₅₂	—	2	6	no	—
170	D₅₂	—	2	6	no	—
171	D₅₂	C₂×D₄	1	12	yes	complemented
172	C₄×D₁₃	—	2	6	no	—
173	C₄×D₁₃	—	2	6	no	—
174	C₄×D₁₃	—	2	6	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	4	6	no	—
177	C₄×D₁₃	C₂×D₄	1	12	yes	complemented
178	Dic₂₆	—	2	6	no	—
179	Dic₂₆	—	2	2	no	—
180	C₂×H(5,𝔽₂)	—	13	1	no	—
181	C₂²×#41	—	13	1	no	—
182	#550	—	13	1	no	—
183	#550	D₁₃	1	1	yes	characteristic, complemented
184	#548	—	13	1	no	—
185	#548	—	13	1	no	—
186	#546	—	13	3	no	—
187	#546	—	13	3	no	—
188	D₄²	—	13	3	no	—
189	D₄²	—	13	3	no	—
190	#537	—	13	3	no	—
191	#535	—	13	3	no	—
192	#525	—	13	3	no	—
193	C₂×#121	—	13	3	no	—
194	#520	—	13	1	no	—
195	C₂²×C₁₃	—	2	3	no	—
196	C₂²×C₁₃	—	2	3	no	—
197	C₂²×C₁₃	—	2	3	no	—
198	C₂²×C₁₃	—	2	3	no	—
199	C₂²×C₁₃	—	2	3	no	—
200	C₂²×C₁₃	—	2	3	no	—
201	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₃	—	2	1	no	—
203	C₂×D₁₃	—	2	3	no	—
204	C₂×D₁₃	—	2	1	no	—
205	C₂×D₁₃	—	2	3	no	—
206	C₂×D₁₃	—	2	3	no	—
207	C₂×D₁₃	—	2	3	no	—
208	C₂×D₁₃	—	2	3	no	—
209	C₂×D₁₃	—	4	12	no	—
210	C₂×D₁₃	—	8	12	no	—
211	C₂×D₁₃	C₂²×D₄	1	6	yes	—
212	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	complemented
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	3	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	C₂²×D₄	1	6	yes	—
218	Dic₁₃	—	2	3	no	—
219	Dic₁₃	—	2	1	no	—
220	Dic₁₃	—	2	3	no	—
221	Dic₁₃	—	2	1	no	—
222	Dic₁₃	C₂²×D₄	1	2	yes	—
223	H(5,𝔽₂)	—	26	8	no	—
224	C₂×#41	—	13	1	no	—
225	C₂×#41	—	13	1	no	—
226	C₂×#41	—	13	3	no	—
227	C₂×#41	—	13	3	no	—
228	C₂×#41	—	13	3	no	—
229	C₂×#41	—	26	8	no	—
230	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
231	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
232	C₂²×Q₈	—	13	1	no	—
233	C₂²×D₄	—	13	3	no	—
234	C₂²×D₄	—	13	3	no	—
235	C₂²×D₄	—	13	3	no	—
236	C₂²×D₄	—	13	6	no	—
237	C₂²×D₄	—	13	3	no	—
238	C₂³×C₄	—	13	3	no	—
239	#127	—	13	3	no	—
240	#127	C₂×D₁₃	1	3	yes	complemented
241	#124	—	13	3	no	—
242	#124	—	13	3	no	—
243	#123	—	13	3	no	—
244	#123	—	13	3	no	—
245	C₂²⋊Q₈	—	13	3	no	—
246	C₂²⋊Q₈	—	13	1	no	—
247	C₂²⋊Q₈	—	13	3	no	—
248	C₂²⋊Q₈	—	13	3	no	—
249	#121	—	13	6	no	—
250	#121	—	13	3	no	—
251	#121	—	13	3	no	—
252	#121	—	13	6	no	—
253	#121	—	13	3	no	—
254	#121	—	13	3	no	—
255	#121	—	13	3	no	—
256	#121	—	13	3	no	—
257	#121	—	13	6	no	—
258	#121	C₂×D₁₃	1	3	yes	complemented
259	#121	C₂×D₁₃	1	3	yes	complemented
260	#120	—	13	3	no	—
261	#120	—	13	6	no	—
262	#120	—	13	6	no	—
263	#120	—	13	3	no	—
264	C₄×Q₈	—	13	1	no	—
265	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
266	C₄×D₄	—	13	3	no	—
267	C₄×D₄	—	13	3	no	—
268	C₄×D₄	—	13	3	no	—
269	C₄×D₄	—	13	3	no	—
270	C₄×D₄	—	13	3	no	—
271	C₄×D₄	C₂×D₁₃	1	3	yes	complemented
272	#117	—	13	3	no	—
273	C₂×C₄⋊C₄	—	13	3	no	—
274	C₂×C₂²⋊C₄	—	13	6	no	—
275	C₂×C₁₃	—	4	3	no	—
276	C₂×C₁₃	—	4	3	no	—
277	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₁₃	#585	1	1	yes	characteristic
280	D₁₃	—	2	2	no	—
281	D₁₃	—	2	6	no	—
282	D₁₃	—	4	3	no	—
283	C₂⁴	—	13	3	no	—
284	C₂⁴	—	13	6	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	13	8	no	—
288	#41	—	26	12	no	—
289	#41	—	26	12	no	—
290	#41	—	26	12	no	—
291	#41	—	26	4	no	—
292	C₂×Q₈	—	13	1	no	—
293	C₂×Q₈	—	13	3	no	—
294	C₂×Q₈	—	26	4	no	—
295	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×D₄	—	13	3	no	—
297	C₂×D₄	—	13	6	no	—
298	C₂×D₄	—	13	3	no	—
299	C₂×D₄	—	13	3	no	—
300	C₂×D₄	—	13	3	no	—
301	C₂×D₄	—	13	6	no	—
302	C₂×D₄	—	13	3	no	—
303	C₂×D₄	—	13	3	no	—
304	C₂×D₄	—	13	3	no	—
305	C₂×D₄	—	13	3	no	—
306	C₂×D₄	—	26	12	no	—
307	C₂×D₄	—	26	12	no	—
308	C₂×D₄	—	26	12	no	—
309	C₂×D₄	—	26	12	no	—
310	C₂×D₄	—	52	12	no	—
311	C₂×D₄	C₂²×D₁₃	1	3	yes	—
312	C₂×D₄	C₂²×D₁₃	1	3	yes	—
313	C₂×D₄	C₂²×D₁₃	1	3	yes	—
314	C₂×D₄	C₂²×D₁₃	1	6	yes	—
315	C₂²×C₄	—	13	3	no	—
316	C₂²×C₄	—	13	3	no	—
317	C₂²×C₄	—	13	3	no	—
318	C₂²×C₄	—	13	3	no	—
319	C₂²×C₄	—	13	3	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	6	no	—
322	C₂²×C₄	—	26	12	no	—
323	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
324	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
325	C₄⋊C₄	—	13	3	no	—
326	C₄⋊C₄	—	13	3	no	—
327	C₄⋊C₄	—	13	1	no	—
328	C₄⋊C₄	—	13	1	no	—
329	C₄⋊C₄	—	13	3	no	—
330	C₄⋊C₄	—	13	3	no	—
331	C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
332	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
333	C₂²⋊C₄	—	13	6	no	—
334	C₂²⋊C₄	—	13	3	no	—
335	C₂²⋊C₄	—	13	3	no	—
336	C₂²⋊C₄	—	13	3	no	—
337	C₂²⋊C₄	—	13	6	no	—
338	C₂²⋊C₄	—	13	3	no	—
339	C₂²⋊C₄	—	13	3	no	—
340	C₂²⋊C₄	—	13	1	no	—
341	C₂²⋊C₄	—	13	1	no	—
342	C₂²⋊C₄	—	13	3	no	—
343	C₂²⋊C₄	C₂²×D₁₃	1	3	yes	—
344	C₂²⋊C₄	C₂²×D₁₃	1	3	yes	—
345	C₄²	—	13	3	no	—
346	C₄²	C₂²×D₁₃	1	3	yes	—
347	C₁₃	#3488	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	13	3	no	—
349	C₂³	—	13	1	no	—
350	C₂³	—	13	3	no	—
351	C₂³	—	26	6	no	—
352	C₂³	—	26	6	no	—
353	C₂³	—	26	12	no	—
354	C₂³	—	52	3	no	—
355	C₂³	—	52	6	no	—
356	C₂³	—	52	6	no	—
357	C₂³	C₂³×D₁₃	1	3	yes	—
358	C₂³	C₂³×D₁₃	1	3	yes	—
359	Q₈	—	26	2	no	—
360	Q₈	—	26	6	no	—
361	Q₈	D₄×D₁₃	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	4	6	no	—
365	D₄	—	4	3	no	—
366	D₄	—	13	12	no	—
367	D₄	—	26	6	no	—
368	D₄	—	26	6	no	—
369	D₄	—	26	6	no	—
370	D₄	—	26	6	no	—
371	D₄	—	26	12	no	—
372	D₄	—	26	6	no	—
373	D₄	—	26	6	no	—
374	D₄	—	52	3	no	—
375	D₄	—	52	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	12	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	3	no	—
382	C₂×C₄	—	13	3	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	6	no	—
386	C₂×C₄	—	26	6	no	—
387	C₂×C₄	—	26	6	no	—
388	C₂×C₄	—	26	6	no	—
389	C₂×C₄	—	52	6	no	—
390	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₃	1	3	yes	—
392	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₃	1	3	yes	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	13	6	no	—
402	C₂²	—	13	2	no	—
403	C₂²	—	26	1	no	—
404	C₂²	—	26	1	no	—
405	C₂²	—	26	3	no	—
406	C₂²	—	26	3	no	—
407	C₂²	—	26	3	no	—
408	C₂²	—	26	3	no	—
409	C₂²	—	26	3	no	—
410	C₂²	—	52	12	no	—
411	C₂²	—	104	12	no	—
412	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	3	no	—
417	C₄	—	13	2	no	—
418	C₄	—	26	1	no	—
419	C₄	—	26	3	no	—
420	C₄	—	26	1	no	—
421	C₄	—	26	3	no	—
422	C₄	C₂×D₄×D₁₃	1	6	yes	—
423	C₂	—	4	3	no	—
424	C₂	—	4	3	no	—
425	C₂	—	26	2	no	—
426	C₂	—	26	6	no	—
427	C₂	—	52	3	no	—
428	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
429	C₂	#11719648	1	1	yes	characteristic
430	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#550	C₂
hypercenter	#550	D₁₃
hypocenter	C₁₃	#3488
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. C₂×#88256	C₂	semidirect
2. C₂×#41×D₁₃	C₂	semidirect
3. C₁₃×#550	C₂	semidirect
4. #11719539	C₂	semidirect
5. #11719536	C₂	semidirect
6. #11719422	C₂	semidirect
7. #11719420	C₂	semidirect
8. #11719317	C₂	semidirect
9. #11719314	C₂	semidirect
10. #11719313	C₂	semidirect
11. D₁₃×#121	C₂	semidirect
12. #11719281	C₂	semidirect
13. #11719279	C₂	semidirect
14. #11719255	C₂	semidirect
15. #11719252	C₂	semidirect
16. C₂×C₁₃×#41	C₂²	semidirect
17. C₂×C₁₃×#41	C₂²	semidirect
21. C₂×#6131	C₂²	semidirect
22. C₂×Q₈×D₁₃	C₂²	semidirect
23. C₂×#6129	C₂²	semidirect
24. C₂×D₄×D₁₃	C₂²	semidirect
25. C₂×D₄×D₁₃	C₂²	semidirect
26. C₂×D₄×D₁₃	C₂²	semidirect
27. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
29. C₂×#6127	C₂²	semidirect
30. C₂²×D₅₂	C₂²	semidirect
31. C₂²×C₄×D₁₃	C₂²	semidirect
32. C₁₃×#127	C₂²	semidirect
33. C₁₃×#121	C₂²	semidirect
34. C₁₃×#121	C₂²	semidirect
35. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. Q₈×Dic₁₃	C₂²	semidirect
38. #88194	C₂²	semidirect
39. #88193	C₂²	semidirect
40. #88193	C₂²	semidirect
41. #88192	C₂²	semidirect
42. #88192	C₂²	semidirect
43. #88192	C₂²	semidirect
44. #88191	C₂²	semidirect
45. #88191	C₂²	semidirect
46. #88191	C₂²	semidirect
47. #88190	C₂²	semidirect
48. #88184	C₂²	semidirect
49. C₄×C₂²⋊D₁₃	C₂²	semidirect
50. C₄×C₂²⋊D₁₃	C₂²	semidirect
51. #88178	C₂²	semidirect
52. #88151	C₂²	semidirect
53. #88150	C₂²	semidirect
54. #88149	C₂²	semidirect
55. #88148	C₂²	semidirect
56. #88147	C₂²	semidirect
57. C₄⋊C₄×D₁₃	C₂²	semidirect
58. #88138	C₂²	semidirect
59. #88138	C₂²	semidirect
60. #88137	C₂²	semidirect
61. #88136	C₂²	semidirect
62. C₂²⋊C₄×D₁₃	C₂²	semidirect
63. #88132	C₂²	semidirect
64. #88129	C₂²	semidirect
65. C₄×D₅₂	C₂²	semidirect
66. C₄×D₅₂	C₂²	semidirect
67. #88126	C₂²	semidirect
87. #6131	D₄	semidirect
144. Q₈×C₁₃	C₂×D₄	semidirect
171. D₅₂	C₂×D₄	semidirect
177. C₄×D₁₃	C₂×D₄	semidirect
183. #550	D₁₃	semidirect
212. C₂×D₁₃	H(5,𝔽₂)	semidirect
230. C₂×#41	C₂×D₁₃	semidirect
231. C₂×#41	C₂×D₁₃	semidirect
240. #127	C₂×D₁₃	semidirect
258. #121	C₂×D₁₃	semidirect
259. #121	C₂×D₁₃	semidirect
265. C₄×Q₈	C₂×D₁₃	semidirect
271. C₄×D₄	C₂×D₁₃	semidirect
347. C₁₃	#3488	semidirect
361. Q₈	D₄×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88256	2
C₂×#41×D₁₃	2
C₁₃×#550	2
#11719539	2
#11719536	2
#11719422	2
#11719420	2
#11719317	2
#11719314	2
#11719313	2
D₁₃×#121	2
#11719281	2
#11719279	2
#11719255	2
#11719252	2
#3488	13