Subgroups — C₁₃×#10853 #15697192

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#341	C₂	1	4	yes	maximal
5	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
6	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#423	—	2	2	no	—
10	C₁₃×#423	C₄	1	4	yes	—
11	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
12	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
13	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
17	C₄×C₁₃×M₁₆	—	2	2	no	—
18	C₄×C₁₃×M₁₆	C₄	1	4	yes	—
19	C₂×C₁₃×#97	—	2	1	no	—
20	C₂×C₄×C₈×C₁₃	—	2	1	no	—
21	C₁₃×#341	—	2	8	no	—
22	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₁₃×M₁₆	—	2	2	no	—
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	—	2	4	no	—
30	C₂×C₁₃×M₁₆	—	2	4	no	—
31	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
34	C₂×C₁₃×M₁₆	Q₈	1	4	yes	—
35	C₂²×C₈×C₁₃	—	2	2	no	—
36	C₂²×C₈×C₁₃	—	2	4	no	—
37	C₂²×C₈×C₁₃	—	2	2	no	—
38	C₂²×C₈×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	—	2	2	no	—
40	C₂²×C₈×C₁₃	—	2	4	no	—
41	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃	D₄	1	2	yes	—
47	C₂×C₄²×C₁₃	D₄	1	2	yes	—
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₁₃×C₄⋊C₈	—	2	4	no	—
51	C₁₃×C₄⋊C₈	—	2	4	no	—
52	C₁₃×C₄⋊C₈	—	2	4	no	—
53	C₁₃×C₄⋊C₈	—	2	4	no	—
54	C₁₃×#97	—	2	4	no	—
55	C₄×C₈×C₁₃	—	2	4	no	—
56	#10853	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₃	—	4	2	no	—
60	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₁₃	#41	1	2	yes	—
77	C₂²×C₄×C₁₃	#41	1	2	yes	—
78	C₁₃×M₁₆	—	2	4	no	—
79	C₁₃×M₁₆	—	2	4	no	—
80	C₁₃×M₁₆	—	2	4	no	—
81	C₁₃×M₁₆	—	2	8	no	—
82	C₁₃×M₁₆	—	4	2	no	—
83	C₁₃×M₁₆	—	4	2	no	—
84	C₁₃×M₁₆	C₄⋊C₄	1	8	yes	—
85	C₂×C₈×C₁₃	—	2	4	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	4	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	8	no	—
91	C₂×C₈×C₁₃	—	4	4	no	—
92	C₂×C₈×C₁₃	—	4	4	no	—
93	C₂×C₈×C₁₃	—	4	2	no	—
94	C₂×C₈×C₁₃	—	4	2	no	—
95	C₄²×C₁₃	C₄²	1	2	yes	—
96	C₄²×C₁₃	C₄²	1	2	yes	—
97	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
99	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
100	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
101	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
102	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
103	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
104	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
105	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
106	C₂×#341	C₂×C₁₃	1	4	yes	—
107	C₂³×C₁₃	—	2	2	no	—
108	C₂³×C₁₃	—	2	2	no	—
109	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂³×C₁₃	#125	1	2	yes	—
113	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
114	C₂×C₄×C₁₃	—	2	2	no	—
115	C₂×C₄×C₁₃	—	2	2	no	—
116	C₂×C₄×C₁₃	—	2	2	no	—
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	—	2	4	no	—
119	C₂×C₄×C₁₃	—	4	2	no	—
120	C₂×C₄×C₁₃	—	4	2	no	—
121	C₂×C₄×C₁₃	#95	1	2	yes	—
122	C₂×C₄×C₁₃	#95	1	2	yes	—
123	C₂×C₄×C₁₃	#95	1	2	yes	—
124	C₂×C₄×C₁₃	#95	1	2	yes	—
125	C₂×C₄×C₁₃	#108	1	4	yes	—
126	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₁₃	#117	1	2	yes	—
132	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
133	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
134	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
135	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
136	C₂×C₄×C₁₃	#121	1	2	yes	—
137	C₂×C₄×C₁₃	#121	1	2	yes	—
138	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
141	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
142	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
144	C₈×C₁₃	—	2	8	no	—
145	C₈×C₁₃	—	4	4	no	—
146	C₈×C₁₃	—	4	4	no	—
147	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
148	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
149	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
150	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
151	#423	—	2	2	no	—
152	#423	C₄×C₁₃	1	4	yes	—
153	C₂×C₄⋊C₈	—	2	2	no	—
154	C₂×C₄⋊C₈	—	2	2	no	—
155	C₂×C₄⋊C₈	—	2	1	no	—
156	C₂×C₄⋊C₈	—	2	1	no	—
157	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
158	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
159	C₄×M₁₆	—	2	2	no	—
160	C₄×M₁₆	C₄×C₁₃	1	4	yes	—
161	C₂×#97	—	2	1	no	—
162	C₂×C₄×C₈	—	2	1	no	—
163	#341	—	2	8	no	—
164	C₂²×C₁₃	—	2	4	no	—
165	C₂²×C₁₃	—	2	4	no	—
166	C₂²×C₁₃	—	2	1	no	—
167	C₂²×C₁₃	—	2	1	no	—
168	C₂²×C₁₃	—	2	1	no	—
169	C₂²×C₁₃	—	2	1	no	—
170	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
171	C₂²×C₁₃	#382	1	1	yes	characteristic
172	C₂²×C₁₃	#384	1	1	yes	characteristic
173	C₂²×C₁₃	#389	1	2	yes	—
174	C₂²×C₁₃	#389	1	2	yes	—
175	C₂²×C₁₃	C₂×#108	1	2	yes	—
176	C₂²×C₁₃	#430	1	2	yes	—
177	C₄×C₁₃	—	2	2	no	—
178	C₄×C₁₃	—	2	2	no	—
179	C₄×C₁₃	—	2	2	no	—
180	C₄×C₁₃	#341	1	4	yes	complemented
181	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
182	C₄×C₁₃	#380	1	2	yes	—
183	C₄×C₁₃	#390	1	1	yes	characteristic
184	C₄×C₁₃	#390	1	1	yes	characteristic
185	C₄×C₁₃	#391	1	1	yes	characteristic
186	C₄×C₁₃	#391	1	1	yes	characteristic
187	C₂³×C₄	Q₈×C₁₃	1	1	yes	characteristic
188	C₂³×C₄	Q₈×C₁₃	1	1	yes	characteristic
189	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	4	no	—
195	C₂×M₁₆	—	2	4	no	—
196	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
197	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
198	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
199	C₂×M₁₆	Q₈×C₁₃	1	4	yes	—
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
207	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
208	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
211	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
212	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
213	C₂×C₄²	D₄×C₁₃	1	2	yes	—
214	C₂×C₄²	D₄×C₁₃	1	2	yes	—
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	2	4	no	—
217	C₄⋊C₈	—	2	4	no	—
218	C₄⋊C₈	—	2	4	no	—
219	#97	—	2	4	no	—
220	C₄×C₈	—	2	4	no	—
221	C₂×C₁₃	—	2	1	no	—
222	C₂×C₁₃	—	2	1	no	—
223	C₂×C₁₃	—	2	2	no	—
224	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
225	C₂×C₁₃	C₂×#341	1	1	yes	characteristic
226	C₂×C₁₃	#1738	1	1	yes	characteristic
227	C₂×C₁₃	#1950	1	4	yes	—
228	C₂⁴	C₂×Q₈×C₁₃	1	1	yes	characteristic
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	4	2	no	—
231	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
235	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
236	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
237	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
238	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
247	C₂²×C₄	C₁₃×#41	1	2	yes	—
248	C₂²×C₄	C₁₃×#41	1	2	yes	—
249	M₁₆	—	2	4	no	—
250	M₁₆	—	2	4	no	—
251	M₁₆	—	2	4	no	—
252	M₁₆	—	2	8	no	—
253	M₁₆	—	4	2	no	—
254	M₁₆	—	4	2	no	—
255	M₁₆	C₁₃×C₄⋊C₄	1	8	yes	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	8	no	—
262	C₂×C₈	—	4	4	no	—
263	C₂×C₈	—	4	4	no	—
264	C₂×C₈	—	4	2	no	—
265	C₂×C₈	—	4	2	no	—
266	C₄²	C₄²×C₁₃	1	2	yes	—
267	C₄²	C₄²×C₁₃	1	2	yes	—
268	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
269	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
270	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
271	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
272	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
273	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
274	C₁₃	#10853	1	1	yes	characteristic, direct product factor, Sylow
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
278	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
279	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
280	C₂³	C₁₃×#125	1	2	yes	—
281	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	C₁₃×#95	1	2	yes	—
290	C₂×C₄	C₁₃×#95	1	2	yes	—
291	C₂×C₄	C₁₃×#95	1	2	yes	—
292	C₂×C₄	C₁₃×#95	1	2	yes	—
293	C₂×C₄	C₁₃×#108	1	4	yes	—
294	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
295	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
299	C₂×C₄	C₁₃×#117	1	2	yes	—
300	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
301	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
302	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
304	C₂×C₄	C₁₃×#121	1	2	yes	—
305	C₂×C₄	C₁₃×#121	1	2	yes	—
306	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
307	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
308	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
309	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
310	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
311	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
312	C₈	—	2	8	no	—
313	C₈	—	4	4	no	—
314	C₈	—	4	4	no	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
322	C₂²	C₁₃×#382	1	1	yes	characteristic
323	C₂²	C₁₃×#384	1	1	yes	characteristic
324	C₂²	C₁₃×#389	1	2	yes	—
325	C₂²	C₁₃×#389	1	2	yes	—
326	C₂²	C₂×C₁₃×#108	1	2	yes	—
327	C₂²	C₁₃×#430	1	2	yes	—
328	C₄	—	2	2	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	C₁₃×#341	1	4	yes	complemented
332	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
333	C₄	C₁₃×#380	1	2	yes	—
334	C₄	C₁₃×#390	1	1	yes	characteristic
335	C₄	C₁₃×#390	1	1	yes	characteristic
336	C₄	C₁₃×#391	1	1	yes	characteristic
337	C₄	C₁₃×#391	1	1	yes	characteristic
338	C₂	—	2	1	no	—
339	C₂	—	2	1	no	—
340	C₂	—	2	2	no	—
341	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
342	C₂	C₂×C₁₃×#341	1	1	yes	characteristic
343	C₂	C₁₃×#1738	1	1	yes	characteristic
344	C₂	C₁₃×#1950	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
56. #10853	C₁₃	direct (N × H)
180. C₄×C₁₃	#341	semidirect
274. C₁₃	#10853	direct (N × H)
331. C₄	C₁₃×#341	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#423	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×C₄×C₁₃×M₁₆	2
C₂×C₁₃×#341	2
#10853	13

Subgroups — C13×#10853 #15697192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10853 #15697192