Subgroups — #16792604

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130048	C₂	1	4	yes	maximal, complemented
4	#13130047	C₂	1	4	yes	maximal, complemented
5	#13130032	C₂	1	2	yes	maximal, complemented
6	#13130030	C₂	1	2	yes	maximal, complemented
7	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₃⋊M₁₆	C₄	1	2	yes	—
9	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₄×#6122	C₄	1	2	yes	—
12	C₄×#6122	C₂²	1	2	yes	—
13	C₂×C₄×#1057	C₄	1	2	yes	—
14	C₂×C₄×#1057	C₂²	1	2	yes	—
15	C₄×#6118	C₄	1	2	yes	—
16	C₄×#6118	C₂²	1	2	yes	—
17	#11719047	C₄	1	2	yes	—
18	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
19	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
20	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
22	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
24	C₁₃×#431	C₄	1	1	yes	characteristic
25	#11718586	C₄	1	1	yes	characteristic
26	#11718494	C₂²	1	2	yes	—
27	D₁₃×C₄⋊C₈	C₄	1	2	yes	—
28	D₁₃×C₂²⋊C₈	C₄	1	2	yes	—
29	#11718379	C₂²	1	2	yes	—
30	#11718346	C₄	1	2	yes	—
31	C₄×C₈×D₁₃	C₂²	1	2	yes	—
32	#1057⋊C₈	C₂²	1	8	yes	complemented
33	#11718251	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×#6122	C₂×C₄	1	4	yes	—
38	C₂²×#1057	C₂×C₄	1	4	yes	—
39	D₁₃⋊M₁₆	—	2	8	no	—
40	C₂×#6118	C₂×C₄	1	4	yes	—
41	C₂×D₁₃⋊C₈	—	2	8	no	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
44	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
45	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂³	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	#88110	C₂×C₄	1	4	yes	—
60	#88110	C₂×C₄	1	4	yes	—
61	C₄×#1057	C₂×C₄	1	4	yes	—
62	C₄×#1057	C₂×C₄	1	2	yes	—
63	C₄×#1057	C₂×C₄	1	4	yes	—
64	C₄×#1057	C₂×C₄	1	2	yes	—
65	C₄×#1057	C₂×C₄	1	4	yes	—
66	C₄×#1057	C₂³	1	2	yes	—
67	C₄×#1057	C₂³	1	4	yes	—
68	C₄×#1057	C₂³	1	2	yes	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
72	C₂²⋊#1055	C₂×C₄	1	2	yes	—
73	#88060	C₂×C₄	1	4	yes	—
74	#88054	C₂×C₄	1	4	yes	—
75	C₈×Dic₁₃	C₂³	1	4	yes	—
76	C₄⋊#1055	C₂×C₄	1	2	yes	—
77	C₄×#1055	C₂×C₄	1	2	yes	—
78	C₂×#1451	—	13	1	no	maximal, Sylow
79	C₂³×D₁₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
84	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	—	2	4	no	—
87	C₂×C₄×D₁₃	—	2	4	no	—
88	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
95	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	#6122	—	2	8	no	—
102	C₂×#1057	—	2	8	no	—
103	C₂×#1057	C₂²×C₄	1	4	yes	—
104	C₂×#1057	C₂²×C₄	1	8	yes	—
105	C₂×#1057	C₂²×C₄	1	4	yes	—
106	#6118	—	2	8	no	—
107	D₁₃⋊C₈	—	2	4	no	—
108	D₁₃⋊C₈	—	2	8	no	—
109	D₁₃⋊C₈	—	2	8	no	—
110	D₁₃⋊C₈	M₁₆	1	8	yes	complemented
111	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
112	C₄²×C₁₃	C₄²	1	1	yes	characteristic
113	C₄²×C₁₃	C₄²	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂²×C₄	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	C₂⁴	1	1	yes	characteristic
128	C₂×#1055	C₂²×C₄	1	4	yes	—
129	C₈×D₁₃	—	2	8	no	—
130	C₂×#431	—	13	1	no	—
131	C₂×C₄×M₁₆	—	13	1	no	—
132	C₂²×C₄×C₈	—	13	1	no	—
133	#1451	—	13	4	no	—
134	#1451	—	13	4	no	—
135	C₂×#322	—	13	2	no	—
136	C₂×#322	—	13	2	no	—
137	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
138	C₂²×D₁₃	—	2	2	no	—
139	C₂²×D₁₃	—	2	2	no	—
140	C₂²×D₁₃	#97	1	4	yes	—
141	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
142	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	#97	1	4	yes	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×Dic₁₃	—	2	2	no	—
153	C₂×Dic₁₃	—	2	2	no	—
154	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
159	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₄×D₁₃	—	2	2	no	—
162	C₄×D₁₃	—	2	2	no	—
163	C₄×D₁₃	—	2	2	no	—
164	C₄×D₁₃	—	2	2	no	—
165	C₄×D₁₃	—	2	2	no	—
166	C₄×D₁₃	—	2	2	no	—
167	C₄×D₁₃	#97	1	4	yes	—
168	C₄×D₁₃	#97	1	4	yes	—
169	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
170	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
171	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
172	C₄×D₁₃	#131	1	4	yes	—
173	#1057	—	2	4	no	—
174	#1057	—	2	8	no	—
175	#1057	C₂×M₁₆	1	8	yes	complemented
176	C₈×C₁₃	—	2	4	no	—
177	#1055	—	2	4	no	—
178	C₂²×M₁₆	—	13	2	no	—
179	C₂³×C₈	—	13	2	no	—
180	C₂²×C₄²	—	13	1	no	—
181	#431	—	13	1	no	—
182	#431	—	13	2	no	—
183	#431	—	13	2	no	—
184	#431	—	13	2	no	—
185	#431	#261	1	1	yes	characteristic
186	C₂×C₄⋊C₈	—	13	2	no	—
187	C₂×C₂²⋊C₈	—	13	2	no	—
188	C₄×M₁₆	—	13	2	no	—
189	C₄×M₁₆	—	13	2	no	—
190	C₄×M₁₆	—	13	2	no	—
191	C₄×M₁₆	—	13	2	no	—
192	C₂×#97	—	13	2	no	—
193	C₂×C₄×C₈	—	13	2	no	—
194	C₂×C₄×C₈	—	13	2	no	—
195	C₂×C₄×C₈	—	13	1	no	—
196	C₂×C₄×C₈	—	13	1	no	—
197	C₂×C₄×C₈	—	13	2	no	—
198	C₂×C₄×C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	2	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	2	no	—
202	#322	—	13	8	no	—
203	#322	—	13	8	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	C₂×#97	1	2	yes	—
207	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
208	C₂×D₁₃	—	2	1	no	—
209	C₂×D₁₃	—	2	1	no	—
210	C₂×D₁₃	—	2	8	no	—
211	C₂×D₁₃	C₂×#97	1	2	yes	—
212	C₂×D₁₃	C₂×#97	1	2	yes	—
213	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
214	C₂×D₁₃	#405	1	2	yes	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	C₂×#97	1	2	yes	—
218	C₄×C₁₃	C₂×#97	1	2	yes	—
219	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
220	C₄×C₁₃	C₂×#131	1	2	yes	—
221	Dic₁₃	—	2	1	no	—
222	Dic₁₃	—	2	1	no	—
223	Dic₁₃	C₂×#97	1	2	yes	—
224	Dic₁₃	#405	1	2	yes	—
225	Dic₁₃	C₂²×M₁₆	1	2	yes	—
226	Dic₁₃	C₂²×M₁₆	1	2	yes	—
227	C₂³×C₄	—	13	1	no	—
228	C₂³×C₄	—	13	1	no	—
229	C₂³×C₄	—	13	1	no	—
230	C₂×M₁₆	—	13	4	no	—
231	C₂×M₁₆	—	13	4	no	—
232	C₂×M₁₆	—	26	8	no	—
233	C₂²×C₈	—	13	2	no	—
234	C₂²×C₈	—	13	4	no	—
235	C₂²×C₈	—	13	2	no	—
236	C₂²×C₈	—	13	4	no	—
237	C₂²×C₈	—	13	4	no	—
238	C₂²×C₈	—	13	4	no	—
239	C₂²×C₈	—	26	8	no	—
240	C₂×C₄²	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	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	C₂×#261	1	1	yes	characteristic
252	C₄⋊C₈	—	13	4	no	—
253	C₄⋊C₈	—	13	2	no	—
254	C₄⋊C₈	C₂×#261	1	2	yes	—
255	C₂²⋊C₈	—	13	2	no	—
256	C₂²⋊C₈	—	13	4	no	—
257	C₂²⋊C₈	C₂×#261	1	2	yes	—
258	#97	—	13	4	no	—
259	#97	—	13	4	no	—
260	C₄×C₈	—	13	2	no	—
261	C₄×C₈	—	13	4	no	—
262	C₄×C₈	—	13	4	no	—
263	C₄×C₈	—	13	2	no	—
264	C₄×C₈	—	13	4	no	—
265	C₄×C₈	—	13	2	no	—
266	C₄×C₈	—	13	2	no	—
267	C₄×C₈	—	13	4	no	—
268	C₄×C₈	—	13	4	no	—
269	C₄×C₈	—	13	2	no	—
270	C₄×C₈	C₂×#261	1	2	yes	—
271	C₂×C₁₃	—	2	2	no	—
272	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
273	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
274	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
275	D₁₃	—	2	2	no	—
276	D₁₃	#1451	1	4	yes	complemented
277	C₂⁴	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	8	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	26	4	no	—
295	C₂²×C₄	—	26	4	no	—
296	C₂²×C₄	C₄×#261	1	1	yes	characteristic
297	C₂²×C₄	C₄×#261	1	1	yes	characteristic
298	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
299	M₁₆	—	26	8	no	—
300	M₁₆	—	26	8	no	—
301	C₂×C₈	—	13	4	no	—
302	C₂×C₈	—	13	8	no	—
303	C₂×C₈	—	13	4	no	—
304	C₂×C₈	—	13	8	no	—
305	C₂×C₈	—	13	4	no	—
306	C₂×C₈	—	26	8	no	—
307	C₂×C₈	—	26	8	no	—
308	C₂×C₈	—	26	8	no	—
309	C₂×C₈	—	26	4	no	—
310	C₂×C₈	—	26	8	no	—
311	C₂×C₈	C₂²×#261	1	4	yes	—
312	C₄²	—	13	1	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	1	no	—
324	C₄²	C₄×#261	1	1	yes	characteristic
325	C₄²	C₄×#261	1	1	yes	characteristic
326	C₄²	C₂²×#261	1	1	yes	characteristic
327	C₄²	C₂²×#261	1	1	yes	characteristic
328	C₁₃	C₂×#1451	1	1	yes	characteristic, complemented, Sylow
329	C₂³	—	13	1	no	—
330	C₂³	—	13	4	no	—
331	C₂³	—	13	1	no	—
332	C₂³	—	26	2	no	—
333	C₂³	—	26	2	no	—
334	C₂³	C₂×C₄×#261	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	13	4	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	13	1	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	4	no	—
343	C₂×C₄	—	13	4	no	—
344	C₂×C₄	—	13	4	no	—
345	C₂×C₄	—	13	4	no	—
346	C₂×C₄	—	13	4	no	—
347	C₂×C₄	—	13	4	no	—
348	C₂×C₄	—	13	1	no	—
349	C₂×C₄	—	13	1	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	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	#88100	1	4	yes	—
359	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
364	C₂×C₄	C₂³×#261	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	13	8	no	—
367	C₈	—	26	4	no	—
368	C₈	—	26	8	no	—
369	C₈	—	26	4	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	13	2	no	—
373	C₂²	—	13	2	no	—
374	C₂²	—	13	2	no	—
375	C₂²	—	13	2	no	—
376	C₂²	—	26	8	no	—
377	C₂²	—	26	1	no	—
378	C₂²	—	26	1	no	—
379	C₂²	C₂×#88100	1	2	yes	—
380	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	13	2	no	—
384	C₄	—	13	2	no	—
385	C₄	—	13	2	no	—
386	C₄	—	13	2	no	—
387	C₄	—	26	1	no	—
388	C₄	—	26	1	no	—
389	C₄	C₂×#88100	1	2	yes	—
390	C₄	C₂×#88100	1	2	yes	—
391	C₄	M₁₆×#261	1	2	yes	—
392	C₄	D₁₃⋊#131	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	13	4	no	—
395	C₂	—	26	2	no	—
396	C₂	C₂²×#88100	1	1	yes	characteristic
397	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
398	C₂	#13131396	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	C₂×#1451
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130048	C₂	semidirect
4. #13130047	C₂	semidirect
5. #13130032	C₂	semidirect
6. #13130030	C₂	semidirect
32. #1057⋊C₈	C₂²	semidirect
33. #11718251	C₂²	semidirect
110. D₁₃⋊C₈	M₁₆	semidirect
175. #1057	C₂×M₁₆	semidirect
276. D₁₃	#1451	semidirect
328. C₁₃	C₂×#1451	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₃⋊M₁₆	2
C₂×C₄×D₁₃⋊C₈	2
#13130048	2
#13130047	2
#13130032	2
#13130030	2
D₁₃×#431	2
C₂×#1451	13