Subgroups — C₈×D₁₃⋊M₁₆ #16792571

Order 3328.

1046 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	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×#6118	C₂	1	4	yes	maximal, complemented
4	C₈×#6122	C₂	1	4	yes	maximal, complemented
5	#13130032	C₂	1	2	yes	maximal, complemented
6	C₈×D₁₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₃⋊M₁₆	C₄	1	2	yes	—
9	C₂²×C₈×D₁₃	C₄	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719125	C₂²	1	2	yes	—
12	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
13	C₄×#6122	C₄	1	2	yes	—
14	C₄×#6122	C₂²	1	2	yes	—
15	#11719119	C₄	1	2	yes	—
16	#11719051	C₂²	1	2	yes	—
17	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
18	#11719049	C₄	1	2	yes	—
19	C₄×#6118	C₄	1	2	yes	—
20	C₄×#6118	C₂²	1	2	yes	—
21	#11719047	C₄	1	2	yes	—
22	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
23	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	C₂×C₄×#1055	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₄	1	2	yes	—
29	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₃	C₂²	1	2	yes	—
33	#1057⋊C₈	C₂²	1	8	yes	complemented
34	C₈×#1057	C₂²	1	8	yes	complemented
35	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×#6122	C₂×C₄	1	4	yes	—
39	D₁₃⋊M₁₆	C₈	1	16	yes	direct product factor
40	C₂×#6118	C₂×C₄	1	4	yes	—
41	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
42	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₁₃	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	C₂²×#1055	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₁₃	—	2	8	no	—
50	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
51	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	C₂²⋊#1057	C₂×C₄	1	4	yes	—
63	#88112	C₂×C₄	1	4	yes	—
64	#88111	C₂×C₄	1	4	yes	—
65	#88110	C₂×C₄	1	4	yes	—
66	#88110	C₂×C₄	1	4	yes	—
67	C₄⋊#1057	C₂×C₄	1	4	yes	—
68	C₄×#1057	C₂×C₄	1	4	yes	—
69	C₄×#1057	C₂×C₄	1	4	yes	—
70	C₄×#1057	C₂³	1	4	yes	—
71	C₄×#1057	C₂³	1	4	yes	—
72	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
76	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
77	C₈×Dic₁₃	C₂³	1	2	yes	—
78	C₈×Dic₁₃	C₂³	1	2	yes	—
79	C₄×#1055	C₂×C₄	1	1	yes	characteristic
80	C₄×#1055	C₂×C₄	1	2	yes	—
81	C₄×#1055	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×M₁₆	—	13	1	no	maximal, Sylow
83	C₂³×D₁₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	—	2	4	no	—
91	C₂×C₄×D₁₃	—	2	4	no	—
92	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
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	C₂×C₈	1	8	yes	—
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	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	#6122	C₂×C₈	1	16	yes	complemented
106	C₂×#1057	C₂²×C₄	1	8	yes	—
107	C₂×#1057	C₂²×C₄	1	8	yes	—
108	#6118	C₂×C₈	1	16	yes	complemented
109	D₁₃⋊C₈	—	2	8	no	—
110	D₁₃⋊C₈	C₂×C₈	1	16	yes	complemented
111	C₂×C₈×C₁₃	—	2	4	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₄²×C₁₃	C₄²	1	1	yes	characteristic
115	C₄²×C₁₃	C₄²	1	1	yes	characteristic
116	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄²	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	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	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
130	C₂×#1055	—	2	4	no	—
131	C₂×#1055	C₂²×C₄	1	2	yes	—
132	C₂×#1055	C₂²×C₄	1	2	yes	—
133	C₈×D₁₃	—	2	4	no	—
134	C₈×D₁₃	—	2	4	no	—
135	C₈×D₁₃	—	2	4	no	—
136	C₈×D₁₃	M₁₆	1	8	yes	complemented
137	C₂×#431	—	13	1	no	—
138	C₂×C₄×M₁₆	—	13	1	no	—
139	C₂²×C₄×C₈	—	13	1	no	—
140	C₈×M₁₆	—	13	4	no	—
141	C₈×M₁₆	—	13	4	no	—
142	C₂×#322	—	13	2	no	—
143	C₂×C₈²	—	13	2	no	—
144	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
145	C₂²×D₁₃	—	2	2	no	—
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	C₄×C₈	1	4	yes	—
148	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
149	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	—	2	2	no	—
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	C₂×C₄²	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
166	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	C₄×C₈	1	4	yes	—
175	C₄×D₁₃	C₄×C₈	1	4	yes	—
176	C₄×D₁₃	C₂²×C₈	1	4	yes	—
177	C₄×D₁₃	C₂²×C₈	1	4	yes	—
178	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
179	C₄×D₁₃	#131	1	4	yes	—
180	#1057	—	2	8	no	—
181	#1057	C₂²×C₈	1	16	yes	complemented
182	C₈×C₁₃	—	2	2	no	—
183	C₈×C₁₃	C₂×M₁₆	1	4	yes	complemented
184	#1055	—	2	2	no	—
185	#1055	C₂×M₁₆	1	4	yes	complemented
186	C₂²×M₁₆	—	13	2	no	—
187	C₂³×C₈	—	13	2	no	—
188	C₂²×C₄²	—	13	1	no	—
189	#431	—	13	2	no	—
190	#431	—	13	2	no	—
191	#431	—	13	2	no	—
192	#431	—	13	2	no	—
193	C₂×C₄⋊C₈	—	13	2	no	—
194	C₂×C₂²⋊C₈	—	13	2	no	—
195	C₄×M₁₆	—	13	2	no	—
196	C₄×M₁₆	—	13	2	no	—
197	C₄×M₁₆	—	13	2	no	—
198	C₄×M₁₆	—	13	2	no	—
199	C₂×#97	—	13	2	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	2	no	—
202	C₂×C₄×C₈	—	13	2	no	—
203	C₂×C₄×C₈	—	13	1	no	—
204	C₂×C₄×C₈	—	13	1	no	—
205	C₂×C₄×C₈	—	13	2	no	—
206	C₂×C₄×C₈	—	13	2	no	—
207	C₂×C₄×C₈	—	13	1	no	—
208	C₂×C₄×C₈	—	13	1	no	—
209	C₂×C₄×C₈	—	13	1	no	—
210	C₂×C₄×C₈	#261	1	1	yes	characteristic
211	#322	—	13	8	no	—
212	C₈²	—	13	8	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
216	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
217	C₂×D₁₃	—	2	1	no	—
218	C₂×D₁₃	—	2	1	no	—
219	C₂×D₁₃	—	2	8	no	—
220	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
221	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
222	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
223	C₂×D₁₃	#405	1	2	yes	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
227	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
228	C₄×C₁₃	#405	1	2	yes	—
229	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
230	Dic₁₃	—	2	1	no	—
231	Dic₁₃	—	2	1	no	—
232	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
233	Dic₁₃	C₄×M₁₆	1	2	yes	—
234	Dic₁₃	C₂³×C₈	1	2	yes	—
235	Dic₁₃	C₂×#131	1	2	yes	—
236	C₂³×C₄	—	13	1	no	—
237	C₂³×C₄	—	13	1	no	—
238	C₂³×C₄	—	13	1	no	—
239	C₂×M₁₆	—	13	4	no	—
240	C₂×M₁₆	—	13	4	no	—
241	C₂×M₁₆	—	13	16	no	—
242	C₂²×C₈	—	13	4	no	—
243	C₂²×C₈	—	13	2	no	—
244	C₂²×C₈	—	13	4	no	—
245	C₂²×C₈	—	13	2	no	—
246	C₂²×C₈	—	13	2	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	—	13	2	no	—
249	C₂²×C₈	—	26	8	no	—
250	C₂²×C₈	C₂×#261	1	2	yes	—
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	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	C₂×#261	1	1	yes	characteristic
263	C₄⋊C₈	—	13	4	no	—
264	C₄⋊C₈	—	13	4	no	—
265	C₂²⋊C₈	—	13	4	no	—
266	C₂²⋊C₈	—	13	4	no	—
267	#97	—	13	4	no	—
268	#97	—	13	4	no	—
269	C₄×C₈	—	13	4	no	—
270	C₄×C₈	—	13	4	no	—
271	C₄×C₈	—	13	4	no	—
272	C₄×C₈	—	13	4	no	—
273	C₄×C₈	—	13	2	no	—
274	C₄×C₈	—	13	2	no	—
275	C₄×C₈	—	13	2	no	—
276	C₄×C₈	—	13	2	no	—
277	C₄×C₈	—	13	2	no	—
278	C₄×C₈	—	13	1	no	—
279	C₄×C₈	—	13	1	no	—
280	C₄×C₈	C₂×#261	1	2	yes	—
281	C₄×C₈	C₂×#261	1	1	yes	characteristic
282	C₄×C₈	C₂×#261	1	1	yes	characteristic
283	C₂×C₁₃	—	2	2	no	—
284	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
285	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
287	D₁₃	—	2	2	no	—
288	D₁₃	C₈×M₁₆	1	4	yes	complemented
289	C₂⁴	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	8	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	4	no	—
308	C₂²×C₄	C₄×#261	1	1	yes	characteristic
309	C₂²×C₄	C₄×#261	1	1	yes	characteristic
310	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
311	M₁₆	—	13	16	no	—
312	M₁₆	—	13	16	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	13	8	no	—
315	C₂×C₈	—	13	16	no	—
316	C₂×C₈	—	13	2	no	—
317	C₂×C₈	—	13	8	no	—
318	C₂×C₈	—	13	8	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	26	4	no	—
321	C₂×C₈	—	26	4	no	—
322	C₂×C₈	—	26	4	no	—
323	C₂×C₈	—	26	8	no	—
324	C₂×C₈	—	26	4	no	—
325	C₂×C₈	C₂²×#261	1	2	yes	—
326	C₂×C₈	C₂²×#261	1	2	yes	—
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	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	C₄×#261	1	1	yes	characteristic
340	C₄²	C₄×#261	1	1	yes	characteristic
341	C₄²	C₂²×#261	1	1	yes	characteristic
342	C₄²	C₂²×#261	1	1	yes	characteristic
343	C₁₃	C₂×C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	13	1	no	—
345	C₂³	—	13	4	no	—
346	C₂³	—	13	1	no	—
347	C₂³	—	26	2	no	—
348	C₂³	—	26	2	no	—
349	C₂³	C₂×C₄×#261	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	13	4	no	—
353	C₂×C₄	—	13	1	no	—
354	C₂×C₄	—	13	1	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	4	no	—
358	C₂×C₄	—	13	4	no	—
359	C₂×C₄	—	13	4	no	—
360	C₂×C₄	—	13	4	no	—
361	C₂×C₄	—	13	4	no	—
362	C₂×C₄	—	13	4	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	2	no	—
368	C₂×C₄	—	26	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	C₈×#261	1	4	yes	—
374	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
376	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
379	C₂×C₄	C₂³×#261	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	13	16	no	—
382	C₈	—	13	4	no	—
383	C₈	—	26	8	no	—
384	C₈	—	26	2	no	—
385	C₈	D₁₃⋊M₁₆	1	4	yes	direct product factor
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	13	2	no	—
389	C₂²	—	13	2	no	—
390	C₂²	—	13	2	no	—
391	C₂²	—	13	2	no	—
392	C₂²	—	26	8	no	—
393	C₂²	—	26	1	no	—
394	C₂²	—	26	1	no	—
395	C₂²	C₂×C₈×#261	1	2	yes	—
396	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	13	2	no	—
400	C₄	—	13	2	no	—
401	C₄	—	13	2	no	—
402	C₄	—	13	2	no	—
403	C₄	—	26	1	no	—
404	C₄	—	26	1	no	—
405	C₄	C₂×C₈×#261	1	2	yes	—
406	C₄	C₂×C₈×#261	1	2	yes	—
407	C₄	#11719089	1	2	yes	—
408	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	13	4	no	—
411	C₂	—	26	2	no	—
412	C₂	C₂²×C₈×#261	1	1	yes	characteristic
413	C₂	C₄×D₁₃⋊M₁₆	1	1	yes	characteristic
414	C₂	C₂×#11719089	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×C₈×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₈×#6118	C₂	semidirect
4. C₈×#6122	C₂	semidirect
5. #13130032	C₂	semidirect
6. C₈×D₁₃⋊C₈	C₂	semidirect
33. #1057⋊C₈	C₂²	semidirect
34. C₈×#1057	C₂²	semidirect
39. D₁₃⋊M₁₆	C₈	direct (N × H)
105. #6122	C₂×C₈	semidirect
108. #6118	C₂×C₈	semidirect
110. D₁₃⋊C₈	C₂×C₈	semidirect
136. C₈×D₁₃	M₁₆	semidirect
181. #1057	C₂²×C₈	semidirect
183. C₈×C₁₃	C₂×M₁₆	semidirect
185. #1055	C₂×M₁₆	semidirect
288. D₁₃	C₈×M₁₆	semidirect
343. C₁₃	C₂×C₈×M₁₆	semidirect
385. C₈	D₁₃⋊M₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₄×D₁₃⋊M₁₆	2
C₈×#6118	2
C₈×#6122	2
#13130032	2
C₈×D₁₃⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂×C₈×M₁₆	13

Subgroups — C8×D13⋊M16 #16792571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₁₃⋊M₁₆ #16792571