Subgroups — #15831961

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123954	C₂	1	1	yes	maximal, characteristic
2	#13123949	C₂	1	1	yes	maximal, characteristic
3	C₄×#88161	C₂	1	1	yes	maximal, characteristic
4	#13113602	C₂	1	2	yes	maximal, complemented
5	#13113600	C₂	1	2	yes	maximal, complemented
6	#13113598	C₂	1	2	yes	maximal, complemented
7	#13113590	C₂	1	2	yes	maximal, complemented
8	#13113588	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88161	C₄	1	1	yes	characteristic
13	C₂×#88161	C₄	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	#11718783	C₄	1	1	yes	characteristic
19	#11718783	C₄	1	1	yes	characteristic
20	#11718772	—	2	2	no	—
21	#11718586	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
24	#11718499	—	2	1	no	—
25	#11718498	C₂²	1	2	yes	—
26	#11718498	C₂²	1	2	yes	—
27	#11718496	C₂²	1	2	yes	—
28	#11718496	C₂²	1	2	yes	—
29	#11718492	—	2	1	no	—
30	#11718391	—	2	2	no	—
31	#11718369	C₄	1	2	yes	—
32	#11718369	C₄	1	2	yes	—
33	#11718349	—	2	1	no	—
34	C₄×#6094	C₂²	1	2	yes	—
35	C₄×C₈×D₁₃	C₂²	1	2	yes	—
36	#11718340	—	2	1	no	—
37	C₁₃×#335	C₂²	1	2	yes	—
38	C₁₃×#334	C₂²	1	2	yes	—
39	#11718072	C₂²	1	2	yes	—
40	#11718072	C₂²	1	2	yes	—
41	#11718072	C₂²	1	1	yes	characteristic
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718071	C₂²	1	1	yes	characteristic
44	#11718071	C₂²	1	1	yes	characteristic
45	#11718050	C₂²	1	2	yes	—
46	#11718049	C₂²	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	D₄	1	2	yes	—
53	C₄×C₂²⋊D₁₃	Q₈	1	2	yes	—
54	#88180	C₂×C₄	1	1	yes	characteristic
55	C₂²×#1055	—	2	1	no	—
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	#88161	—	2	4	no	—
59	#88161	—	2	4	no	—
60	C₂×#6094	—	2	2	no	—
61	C₂×#6094	—	2	2	no	—
62	C₂×#6094	C₂×C₄	1	2	yes	—
63	C₂×#6094	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
66	C₄×D₅₂	D₄	1	1	yes	characteristic
67	C₄×D₅₂	Q₈	1	1	yes	characteristic
68	#88126	C₂×C₄	1	2	yes	—
69	C₄²×D₁₃	C₂³	1	2	yes	—
70	C₄×Dic₂₆	D₄	1	1	yes	characteristic
71	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₂²⋊C₈	—	2	1	no	—
77	C₁₃×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	—	2	1	no	—
79	C₄×C₈×C₁₃	C₂³	1	2	yes	—
80	C₂²⋊#1055	—	2	1	no	—
81	#88060	—	2	2	no	—
82	#88060	—	2	2	no	—
83	#88055	—	2	2	no	—
84	#88055	—	2	2	no	—
85	#88055	C₂×C₄	1	2	yes	—
86	#88055	C₂×C₄	1	2	yes	—
87	#88054	—	2	2	no	—
88	#88054	—	2	2	no	—
89	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
90	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
91	C₄⋊#1055	—	2	1	no	—
92	C₄⋊#1055	C₂³	1	1	yes	characteristic
93	C₄⋊#1055	C₂³	1	2	yes	—
94	C₄⋊#1055	C₂³	1	1	yes	characteristic
95	C₄×#1055	—	2	1	no	—
96	C₄×#1055	C₂×C₄	1	1	yes	characteristic
97	C₄×#1055	C₂×C₄	1	1	yes	characteristic
98	C₄×#1055	C₂³	1	1	yes	characteristic
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	#17798	—	13	1	no	maximal, Sylow
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	2	yes	—
105	#6127	—	2	2	no	—
106	#6127	—	2	2	no	—
107	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
111	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	M₁₆	1	4	yes	complemented
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	8	1	no	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
123	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
125	#6103	C₄⋊C₄	1	2	yes	—
126	#6103	C₄⋊C₄	1	2	yes	—
127	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	#6101	C₄⋊C₄	1	2	yes	—
130	#6101	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
132	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
133	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	8	1	no	—
139	C₂×#1055	M₁₆	1	4	yes	complemented
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	#6094	—	2	4	no	—
145	#6094	—	2	4	no	—
146	#6094	—	8	2	no	—
147	#6094	—	8	2	no	—
148	C₈×D₁₃	—	2	4	no	—
149	C₈×D₁₃	—	2	4	no	—
150	#2989	—	13	1	no	—
151	#2989	—	13	1	no	—
152	C₄×#131	—	13	1	no	—
153	#1569	—	13	2	no	—
154	#1569	—	13	2	no	—
155	#1568	—	13	2	no	—
156	#1566	—	13	2	no	—
157	#1565	—	13	1	no	—
158	#1565	D₁₃	1	1	yes	characteristic, complemented
159	#1564	—	13	1	no	—
160	C₂×#334	—	13	1	no	—
161	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂²⋊D₁₃	—	2	4	no	—
175	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
178	D₅₂	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	4	2	no	—
184	Dic₂₆	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	4	1	no	—
187	C₈×C₁₃	—	4	2	no	—
188	C₈×C₁₃	—	4	1	no	—
189	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
190	#1055	—	2	1	no	—
191	#1055	—	2	1	no	—
192	#1055	—	4	1	no	—
193	#1055	—	4	2	no	—
194	#1055	—	4	1	no	—
195	#1055	C₂×M₁₆	1	2	yes	—
196	#1055	C₂×M₁₆	1	2	yes	—
197	C₂×#131	—	13	1	no	—
198	C₂×#131	—	13	1	no	—
199	C₄×#41	—	13	1	no	—
200	#446	—	26	1	no	—
201	#446	—	26	1	no	—
202	#436	—	26	1	no	—
203	#436	—	26	1	no	—
204	#435	—	26	2	no	—
205	#435	—	26	2	no	—
206	#432	—	13	2	no	—
207	#432	—	13	2	no	—
208	#431	—	13	1	no	—
209	#431	C₂×D₁₃	1	1	yes	characteristic
210	#423	—	13	2	no	—
211	#423	—	13	2	no	—
212	C₂×C₄⋊C₈	—	13	1	no	—
213	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	2	no	—
217	#405	—	13	2	no	—
218	C₄×M₁₆	—	13	2	no	—
219	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	#335	—	13	1	no	—
223	#335	—	13	1	no	—
224	#335	—	13	2	no	—
225	#335	C₂×D₁₃	1	2	yes	—
226	#334	—	13	2	no	—
227	#334	—	13	2	no	—
228	#334	—	13	1	no	—
229	#334	—	13	1	no	—
230	#334	—	13	2	no	—
231	#334	C₂×D₁₃	1	2	yes	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	#423	1	2	yes	—
235	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₃	—	2	2	no	—
237	C₂×D₁₃	—	2	2	no	—
238	C₂×D₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	#423	1	2	yes	—
243	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
244	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
245	C₄×C₁₃	#577	1	1	yes	characteristic
246	C₄×C₁₃	#577	1	1	yes	characteristic
247	Dic₁₃	—	2	2	no	—
248	Dic₁₃	—	2	2	no	—
249	Dic₁₃	—	2	2	no	—
250	C₂×#41	—	13	1	no	—
251	#131	—	26	4	no	—
252	#131	—	26	4	no	—
253	C₂×M₁₆	—	13	2	no	—
254	C₂×M₁₆	—	13	2	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	26	2	no	—
257	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
258	C₂×M₁₆	C₄×D₁₃	1	1	yes	characteristic
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	2	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	26	1	no	—
265	C₄×Q₈	—	13	1	no	—
266	C₄×Q₈	—	13	1	no	—
267	C₄×D₄	—	13	2	no	—
268	C₄×D₄	—	13	2	no	—
269	C₄×D₄	—	13	1	no	—
270	C₄×D₄	—	13	1	no	—
271	#117	—	13	1	no	—
272	#117	—	13	2	no	—
273	C₂×C₄²	—	13	2	no	—
274	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	13	2	no	—
277	C₄⋊C₈	—	13	1	no	—
278	C₄⋊C₈	—	13	1	no	—
279	C₄⋊C₈	—	26	2	no	—
280	C₄⋊C₈	—	26	2	no	—
281	C₄⋊C₈	—	26	1	no	—
282	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
283	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²⋊C₈	—	2	1	no	—
286	C₂²⋊C₈	—	26	2	no	—
287	C₂²⋊C₈	—	26	2	no	—
288	C₂²⋊C₈	—	26	1	no	—
289	#97	—	13	2	no	—
290	#97	—	13	2	no	—
291	#97	—	26	2	no	—
292	#97	—	26	2	no	—
293	#97	C₄×D₁₃	1	2	yes	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	13	2	no	—
296	C₄×C₈	—	13	2	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	26	1	no	—
302	C₄×C₈	C₂²×D₁₃	1	2	yes	—
303	C₂×C₁₃	—	2	2	no	—
304	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
305	C₂×C₁₃	#2912	1	1	yes	characteristic
306	C₂×C₁₃	#2916	1	1	yes	characteristic
307	D₁₃	—	4	2	no	—
308	#41	—	26	2	no	—
309	#41	—	26	2	no	—
310	C₂×Q₈	—	13	1	no	—
311	C₂×D₄	—	13	2	no	—
312	C₂×D₄	—	13	1	no	—
313	C₂²×C₄	—	13	2	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	—	13	2	no	—
316	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
318	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
319	M₁₆	—	2	2	no	—
320	M₁₆	—	26	4	no	—
321	M₁₆	—	26	4	no	—
322	M₁₆	—	104	2	no	—
323	M₁₆	—	104	2	no	—
324	M₁₆	#6094	1	4	yes	complemented
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	8	1	no	—
329	C₂×C₈	—	13	4	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	1	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	2	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	—	104	1	no	—
341	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
343	C₄⋊C₄	—	13	2	no	—
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	—	13	1	no	—
346	C₄⋊C₄	—	13	1	no	—
347	C₂²⋊C₄	—	13	2	no	—
348	C₂²⋊C₄	—	13	2	no	—
349	C₂²⋊C₄	—	13	2	no	—
350	C₄²	—	13	2	no	—
351	C₄²	—	13	2	no	—
352	C₄²	—	13	2	no	—
353	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
354	C₄²	D₄×D₁₃	1	1	yes	characteristic
355	C₄²	Q₈×D₁₃	1	1	yes	characteristic
356	C₄²	C₂³×D₁₃	1	1	yes	characteristic
357	C₁₃	#17798	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	13	2	no	—
359	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
360	Q₈	—	26	2	no	—
361	D₄	—	26	4	no	—
362	D₄	—	26	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	13	2	no	—
367	C₂×C₄	—	13	2	no	—
368	C₂×C₄	—	13	2	no	—
369	C₂×C₄	—	26	2	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	52	2	no	—
374	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
375	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#6094	1	2	yes	—
378	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	13	2	no	—
387	C₈	—	13	2	no	—
388	C₈	—	26	1	no	—
389	C₈	—	26	1	no	—
390	C₈	—	52	1	no	—
391	C₈	—	52	1	no	—
392	C₈	—	52	2	no	—
393	C₈	C₂×#6094	1	4	yes	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	26	2	no	—
397	C₂²	—	26	2	no	—
398	C₂²	—	26	2	no	—
399	C₂²	#11718498	1	2	yes	—
400	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	26	2	no	—
405	C₄	—	26	2	no	—
406	C₄	—	26	2	no	—
407	C₄	#11718498	1	2	yes	—
408	C₄	C₂²×#6094	1	1	yes	characteristic
409	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
410	C₄	#11719480	1	1	yes	characteristic
411	C₄	#11719483	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	52	2	no	—
414	C₂	C₂×#11718498	1	1	yes	characteristic
415	C₂	#13123430	1	1	yes	characteristic
416	C₂	#13123446	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1565	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1565	D₁₃
hypocenter	C₁₃	#17798
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #13113602	C₂	semidirect
5. #13113600	C₂	semidirect
6. #13113598	C₂	semidirect
7. #13113590	C₂	semidirect
8. #13113588	C₂	semidirect
9. #13113582	C₂	semidirect
10. C₂×#11718072	C₂	semidirect
11. C₁₃×#1565	C₂	semidirect
113. C₁₃×M₁₆	M₁₆	semidirect
139. C₂×#1055	M₁₆	semidirect
158. #1565	D₁₃	semidirect
324. M₁₆	#6094	semidirect
357. C₁₃	#17798	semidirect

Maximal subgroups

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

subgroup	index
#13123954	2
#13123949	2
C₄×#88161	2
#13113602	2
#13113600	2
#13113598	2
#13113590	2
#13113588	2
#13113582	2
C₂×#11718072	2
C₁₃×#1565	2
#17798	13