Subgroups — #16792669

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719051	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
3	#13130058	C₂	1	4	yes	maximal, complemented
4	#13130052	C₂	1	2	yes	maximal, complemented
5	#13130043	C₂	1	2	yes	maximal, complemented
6	#13130042	C₂	1	2	yes	maximal, complemented
7	M₁₆×#1057	C₂	1	2	yes	maximal, complemented
8	#13123468	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719125	C₄	1	2	yes	—
11	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
12	C₂×#88111	C₄	1	2	yes	—
13	#11719119	C₂²	1	1	yes	characteristic
14	#11719119	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#1057	C₄	1	2	yes	—
16	C₂×C₄×#1057	C₂²	1	2	yes	—
17	#11719051	C₄	1	2	yes	—
18	#11719051	C₄	1	2	yes	—
19	#11719051	C₄	1	2	yes	—
20	#11719051	C₂²	1	1	yes	characteristic
21	#11719051	C₂²	1	1	yes	characteristic
22	#11719051	C₂²	1	2	yes	—
23	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
24	#11719049	C₂²	1	2	yes	—
25	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
26	C₁₃×#423	C₄	1	1	yes	characteristic
27	#11718787	C₄	1	2	yes	—
28	M₁₆×Dic₁₃	C₂²	1	2	yes	—
29	#11718585	C₄	1	1	yes	characteristic
30	#11718496	C₄	1	2	yes	—
31	#11718496	C₄	1	2	yes	—
32	#11718494	C₂²	1	2	yes	—
33	#11718494	C₂²	1	2	yes	—
34	#1057⋊C₈	C₂²	1	4	yes	complemented
35	#1057⋊C₈	C₂²	1	4	yes	complemented
36	#11718251	C₂²	1	4	yes	complemented
37	C₈×#1057	C₂²	1	4	yes	complemented
38	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×#1057	C₂×C₄	1	4	yes	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
43	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
48	C₂×#6099	C₂×C₄	1	2	yes	—
49	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂³	1	1	yes	characteristic
56	C₄²×D₁₃	C₂³	1	1	yes	characteristic
57	C₂²⋊#1057	C₂×C₄	1	2	yes	—
58	C₂²⋊#1057	C₂×C₄	1	2	yes	—
59	#88112	C₂×C₄	1	4	yes	—
60	#88111	C₂×C₄	1	4	yes	—
61	#88111	C₂×C₄	1	2	yes	—
62	#88111	C₂×C₄	1	2	yes	—
63	#88111	C₂×C₄	1	4	yes	—
64	C₄⋊#1057	C₂×C₄	1	2	yes	—
65	C₄⋊#1057	C₂×C₄	1	2	yes	—
66	C₄⋊#1057	C₂×C₄	1	2	yes	—
67	C₄⋊#1057	C₂×C₄	1	2	yes	—
68	C₄⋊#1057	C₂×C₄	1	4	yes	—
69	C₄×#1057	C₂×C₄	1	4	yes	—
70	C₄×#1057	C₂×C₄	1	4	yes	—
71	C₄×#1057	C₂³	1	2	yes	—
72	C₄×#1057	C₂³	1	2	yes	—
73	C₄×#1057	C₂³	1	2	yes	—
74	C₄×#1057	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
76	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	#88060	C₂×C₄	1	4	yes	—
78	#88060	C₂×C₄	1	4	yes	—
79	#88055	C₂×C₄	1	4	yes	—
80	C₈×Dic₁₃	C₂³	1	4	yes	—
81	C₄⋊#1055	C₂×C₄	1	2	yes	—
82	C₄⋊#1055	C₂×C₄	1	2	yes	—
83	#17326	—	13	1	no	maximal, Sylow
84	C₂³×D₁₃	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	—	2	2	no	—
92	C₂×C₄×D₁₃	—	2	2	no	—
93	C₂×C₄×D₁₃	—	2	4	no	—
94	C₂×C₄×D₁₃	—	4	2	no	—
95	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×#1057	—	4	4	no	—
108	C₂×#1057	C₂²×C₄	1	4	yes	—
109	C₂×#1057	C₂²×C₄	1	4	yes	—
110	C₂×#1057	C₂²×C₄	1	4	yes	—
111	C₂×#1057	C₂²×C₄	1	4	yes	—
112	D₁₃⋊C₈	—	2	8	no	—
113	C₁₃×M₁₆	—	2	4	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₄²	1	1	yes	characteristic
116	C₄²×C₁₃	C₄²	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
123	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
131	#6099	—	2	4	no	—
132	C₂×#1055	C₂²×C₄	1	4	yes	—
133	#2920	—	13	1	no	—
134	C₂×#431	—	13	1	no	—
135	C₂×#431	—	13	1	no	—
136	#1454	—	13	4	no	—
137	#1452	—	13	2	no	—
138	#1451	—	13	2	no	—
139	#1450	—	13	2	no	—
140	C₈×M₁₆	—	13	2	no	—
141	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
142	C₂²×D₁₃	—	2	2	no	—
143	C₂²×D₁₃	—	2	2	no	—
144	C₂²×D₁₃	—	4	1	no	—
145	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#131	1	2	yes	—
155	C₂×C₄×C₁₃	#131	1	2	yes	—
156	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×Dic₁₃	—	2	2	no	—
158	C₂×Dic₁₃	—	2	2	no	—
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	—	2	1	no	—
168	C₄×D₁₃	—	2	1	no	—
169	C₄×D₁₃	—	2	1	no	—
170	C₄×D₁₃	—	2	1	no	—
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	4	1	no	—
178	C₄×D₁₃	—	4	1	no	—
179	C₄×D₁₃	#131	1	4	yes	—
180	#1057	—	2	4	no	—
181	#1057	—	2	4	no	—
182	#1057	—	2	4	no	—
183	#1057	—	2	4	no	—
184	C₈×C₁₃	—	2	4	no	—
185	#1055	—	2	4	no	—
186	C₂²×C₄²	—	13	1	no	—
187	#432	—	13	2	no	—
188	#432	—	13	2	no	—
189	#431	—	13	2	no	—
190	#431	—	13	2	no	—
191	#431	—	13	2	no	—
192	#431	—	13	2	no	—
193	#431	—	13	1	no	—
194	#431	—	13	1	no	—
195	#431	—	13	2	no	—
196	#431	—	13	1	no	—
197	#431	—	13	1	no	—
198	#431	—	13	2	no	—
199	#431	—	13	2	no	—
200	#431	—	13	2	no	—
201	#423	—	13	1	no	—
202	#423	#261	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	13	2	no	—
204	C₂×C₄⋊C₈	—	13	2	no	—
205	#407	—	13	2	no	—
206	C₂×C₂²⋊C₈	—	13	2	no	—
207	C₂×C₂²⋊C₈	—	13	2	no	—
208	C₄×M₁₆	—	13	2	no	—
209	C₂×C₄×C₈	—	13	2	no	—
210	C₂×C₄×C₈	—	13	2	no	—
211	#322	—	13	4	no	—
212	#322	—	13	4	no	—
213	#322	—	13	4	no	—
214	C₈²	—	13	4	no	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	#405	1	2	yes	—
218	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
219	C₂×D₁₃	—	2	1	no	—
220	C₂×D₁₃	—	2	1	no	—
221	C₂×D₁₃	—	2	1	no	—
222	C₂×D₁₃	—	2	1	no	—
223	C₂×D₁₃	—	2	1	no	—
224	C₂×D₁₃	—	4	4	no	—
225	C₂×D₁₃	#405	1	2	yes	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	#405	1	2	yes	—
230	C₄×C₁₃	#405	1	2	yes	—
231	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
232	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
233	Dic₁₃	—	2	1	no	—
234	Dic₁₃	—	2	1	no	—
235	Dic₁₃	—	2	1	no	—
236	Dic₁₃	—	2	1	no	—
237	Dic₁₃	C₂×#131	1	2	yes	—
238	Dic₁₃	#568	1	2	yes	—
239	C₂³×C₄	—	13	1	no	—
240	C₂³×C₄	—	13	1	no	—
241	C₂³×C₄	—	13	1	no	—
242	C₂×M₁₆	—	13	2	no	—
243	C₂×M₁₆	C₂×#261	1	2	yes	—
244	C₂²×C₈	—	13	4	no	—
245	C₂²×C₈	—	13	4	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
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	—	13	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	C₂×#261	1	1	yes	characteristic
258	C₄⋊C₈	—	13	2	no	—
259	C₄⋊C₈	—	13	2	no	—
260	C₄⋊C₈	—	13	2	no	—
261	C₄⋊C₈	—	13	2	no	—
262	C₄⋊C₈	—	13	4	no	—
263	C₄⋊C₈	—	13	4	no	—
264	C₄⋊C₈	—	13	2	no	—
265	C₄⋊C₈	—	13	2	no	—
266	C₄⋊C₈	C₂×#261	1	2	yes	—
267	C₄⋊C₈	C₂×#261	1	2	yes	—
268	C₂²⋊C₈	—	13	4	no	—
269	C₂²⋊C₈	—	13	2	no	—
270	C₂²⋊C₈	—	13	2	no	—
271	C₂²⋊C₈	—	13	4	no	—
272	C₂²⋊C₈	—	13	2	no	—
273	C₂²⋊C₈	—	13	2	no	—
274	C₂²⋊C₈	—	13	4	no	—
275	C₂²⋊C₈	—	13	4	no	—
276	#97	—	13	4	no	—
277	C₄×C₈	—	13	4	no	—
278	C₄×C₈	—	13	4	no	—
279	C₄×C₈	—	13	2	no	—
280	C₄×C₈	—	13	2	no	—
281	C₄×C₈	—	13	2	no	—
282	C₄×C₈	—	13	2	no	—
283	C₄×C₈	—	13	4	no	—
284	C₂×C₁₃	—	2	2	no	—
285	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
287	C₂×C₁₃	#2873	1	1	yes	characteristic
288	D₁₃	—	2	2	no	—
289	D₁₃	—	4	1	no	—
290	C₂⁴	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	26	4	no	—
307	C₂²×C₄	—	26	2	no	—
308	C₂²×C₄	—	26	2	no	—
309	C₂²×C₄	—	52	2	no	—
310	C₂²×C₄	C₄×#261	1	1	yes	characteristic
311	C₂²×C₄	C₄×#261	1	1	yes	characteristic
312	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
313	M₁₆	—	2	4	no	—
314	M₁₆	—	26	4	no	—
315	C₂×C₈	—	13	4	no	—
316	C₂×C₈	—	13	4	no	—
317	C₂×C₈	—	13	4	no	—
318	C₂×C₈	—	13	4	no	—
319	C₂×C₈	—	13	4	no	—
320	C₂×C₈	—	26	8	no	—
321	C₂×C₈	—	52	4	no	—
322	C₂×C₈	C₂²×#261	1	4	yes	—
323	C₄²	—	13	1	no	—
324	C₄²	—	13	1	no	—
325	C₄²	—	13	1	no	—
326	C₄²	—	13	1	no	—
327	C₄²	—	13	1	no	—
328	C₄²	—	13	1	no	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	C₄×#261	1	1	yes	characteristic
336	C₄²	C₄×#261	1	1	yes	characteristic
337	C₄²	C₂²×#261	1	1	yes	characteristic
338	C₄²	C₂²×#261	1	1	yes	characteristic
339	C₁₃	#17326	1	1	yes	characteristic, complemented, Sylow
340	C₂³	—	13	1	no	—
341	C₂³	—	13	1	no	—
342	C₂³	—	26	2	no	—
343	C₂³	—	26	2	no	—
344	C₂³	—	52	1	no	—
345	C₂³	C₂×C₄×#261	1	1	yes	characteristic
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	13	1	no	—
350	C₂×C₄	—	13	4	no	—
351	C₂×C₄	—	13	1	no	—
352	C₂×C₄	—	13	1	no	—
353	C₂×C₄	—	13	1	no	—
354	C₂×C₄	—	13	1	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	2	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	1	no	—
366	C₂×C₄	—	26	1	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	26	1	no	—
369	C₂×C₄	—	52	1	no	—
370	C₂×C₄	—	52	1	no	—
371	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
376	C₂×C₄	#88238	1	2	yes	—
377	C₂×C₄	#88240	1	2	yes	—
378	C₂×C₄	C₂³×#261	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	26	4	no	—
381	C₈	—	26	4	no	—
382	C₈	—	26	4	no	—
383	C₈	—	26	4	no	—
384	C₈	—	26	4	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	13	2	no	—
388	C₂²	—	26	1	no	—
389	C₂²	—	26	1	no	—
390	C₂²	—	26	1	no	—
391	C₂²	—	26	1	no	—
392	C₂²	—	26	1	no	—
393	C₂²	—	52	4	no	—
394	C₂²	#11719072	1	2	yes	—
395	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	13	2	no	—
400	C₄	—	13	2	no	—
401	C₄	—	26	1	no	—
402	C₄	—	26	1	no	—
403	C₄	—	26	1	no	—
404	C₄	—	26	1	no	—
405	C₄	#11719072	1	2	yes	—
406	C₄	#11719099	1	2	yes	—
407	C₄	C₂×#88238	1	1	yes	characteristic
408	C₄	C₂×#88240	1	1	yes	characteristic
409	C₂	—	2	2	no	—
410	C₂	—	26	2	no	—
411	C₂	—	52	1	no	—
412	C₂	C₂×#11719072	1	1	yes	characteristic
413	C₂	C₂×#11719099	1	1	yes	characteristic
414	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#423	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#423	#261
hypocenter	C₁₃	#17326
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
3. #13130058	C₂	semidirect
4. #13130052	C₂	semidirect
5. #13130043	C₂	semidirect
6. #13130042	C₂	semidirect
7. M₁₆×#1057	C₂	semidirect
34. #1057⋊C₈	C₂²	semidirect
35. #1057⋊C₈	C₂²	semidirect
36. #11718251	C₂²	semidirect
37. C₈×#1057	C₂²	semidirect
339. C₁₃	#17326	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719051	2
D₁₃⋊#431	2
#13130058	2
#13130052	2
#13130043	2
#13130042	2
M₁₆×#1057	2
#13123468	2
#17326	13