Subgroups — C₁₃×#33691 #15720030

Order 3328.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3173	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2230	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2212	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2191	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2190	C₂	1	1	yes	maximal, characteristic
9	C₁₃×AGL(1,ℤ/16)	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2180	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#575	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	—	2	1	no	—
14	C₁₃×#542	—	2	1	no	—
15	C₁₃×#510	C₂²	1	2	yes	—
16	C₁₃×#509	C₂²	1	2	yes	—
17	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#489	—	2	1	no	—
20	C₁₃×#470	C₂²	1	1	yes	characteristic
21	C₁₃×#469	C₂²	1	1	yes	characteristic
22	C₁₃×#465	—	2	1	no	—
23	C₁₃×#444	—	2	1	no	—
24	C₁₃×#444	C₂²	1	2	yes	—
25	C₁₃×#443	—	2	1	no	—
26	C₁₃×#443	C₂²	1	2	yes	—
27	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
29	C₄×C₁₃×SD₁₆	—	2	1	no	—
30	C₁₃×#430	C₂²	1	1	yes	characteristic
31	C₁₃×#421	—	2	1	no	—
32	C₁₃×#405	C₂²	1	1	yes	characteristic
33	C₁₃×#365	C₂²	1	2	yes	complemented
34	C₁₃×#365	C₂²	1	2	yes	complemented
35	C₁₃×#364	C₂²	1	2	yes	complemented
36	C₁₃×#362	C₂²	1	2	yes	complemented
37	C₁₃×#361	C₂²	1	2	yes	complemented
38	C₁₃×#360	C₂²	1	2	yes	—
39	C₁₃×#360	C₂²	1	2	yes	—
40	C₁₃×#349	C₂²	1	1	yes	characteristic
41	C₁₃×#349	C₂²	1	1	yes	characteristic
42	C₁₃×#347	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₁₃×#137	—	2	2	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₃×#135	—	2	1	no	—
47	C₁₃×#135	C₂³	1	2	yes	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
51	C₁₃×#131	—	2	2	no	—
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	—	4	1	no	—
54	C₁₃×#131	—	4	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	4	1	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	—	4	1	no	—
59	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×#126	—	4	1	no	—
62	C₁₃×#124	—	2	1	no	—
63	C₁₃×#124	—	4	1	no	—
64	C₁₃×#123	—	4	1	no	—
65	C₁₃×C₂²⋊Q₈	—	2	1	no	—
66	C₁₃×C₂²⋊Q₈	—	4	1	no	—
67	C₁₃×#121	—	2	1	no	—
68	C₄×Q₈×C₁₃	—	2	1	no	—
69	C₄×D₄×C₁₃	—	2	1	no	—
70	C₁₃×#117	D₄	1	1	yes	characteristic
71	C₁₃×Q₃₂	—	2	2	no	—
72	C₁₃×SD₃₂	—	2	2	no	—
73	C₁₃×SD₃₂	—	2	2	no	—
74	C₁₃×D₁₆	—	2	2	no	—
75	C₁₃×M₃₂	C₂³	1	2	yes	—
76	C₁₃×M₃₂	C₂³	1	2	yes	—
77	C₁₃×#108	—	2	1	no	—
78	C₁₃×#108	C₂³	1	2	yes	—
79	C₁₃×#106	—	2	1	no	—
80	C₁₃×#106	C₂³	1	1	yes	characteristic
81	C₁₃×#106	C₂³	1	1	yes	characteristic
82	C₁₃×#104	—	2	2	no	—
83	C₁₃×#104	—	2	2	no	—
84	C₁₃×#103	—	2	1	no	—
85	C₁₃×#103	—	2	1	no	—
86	C₁₃×#102	—	2	1	no	—
87	C₁₃×#102	—	2	1	no	—
88	C₁₃×#97	D₄	1	1	yes	characteristic
89	C₁₃×#97	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	#33691	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	2	2	no	—
95	C₁₃×#41	—	4	1	no	—
96	C₁₃×#41	—	4	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₁₃×Q₁₆	—	2	1	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	#41	1	2	yes	—
110	C₁₃×SD₁₆	—	2	2	no	—
111	C₁₃×SD₁₆	—	2	2	no	—
112	C₁₃×SD₁₆	—	4	1	no	—
113	C₁₃×SD₁₆	—	4	1	no	—
114	C₁₃×D₈	—	2	1	no	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	#41	1	2	yes	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	4	2	no	—
120	C₁₃×M₁₆	—	4	1	no	—
121	C₁₃×M₁₆	—	4	2	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₂×C₈×C₁₃	—	4	2	no	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	1	no	—
136	C₁₃×C₄⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₁₃×C₂²⋊C₄	—	4	1	no	—
140	C₁₃×C₂²⋊C₄	—	4	1	no	—
141	C₁₃×C₂²⋊C₄	—	4	1	no	—
142	C₁₃×C₂²⋊C₄	—	4	1	no	—
143	C₄²×C₁₃	—	4	1	no	—
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×C₁₆	—	2	2	no	—
147	C₁₃×C₁₆	—	2	2	no	—
148	#3173	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2955	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2239	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2238	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2230	C₂×C₁₃	1	2	yes	complemented
153	#2212	C₂×C₁₃	1	2	yes	complemented
154	#2191	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2190	C₂×C₁₃	1	1	yes	characteristic
156	AGL(1,ℤ/16)	C₂×C₁₃	1	2	yes	complemented
157	#2180	C₂×C₁₃	1	2	yes	complemented
158	#2166	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	4	1	no	—
164	Q₈×C₁₃	—	4	1	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	Q₈×C₁₃	—	16	1	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	16	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	16	1	no	—
185	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₁₃	—	2	1	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₈×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₈×C₁₃	C₂×#41	1	2	yes	—
193	#575	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#131	—	2	1	no	—
195	#542	—	2	1	no	—
196	#510	C₂²×C₁₃	1	2	yes	—
197	#509	C₂²×C₁₃	1	2	yes	—
198	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
199	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
200	#489	—	2	1	no	—
201	#470	C₂²×C₁₃	1	1	yes	characteristic
202	#469	C₂²×C₁₃	1	1	yes	characteristic
203	#465	—	2	1	no	—
204	#444	—	2	1	no	—
205	#444	C₂²×C₁₃	1	2	yes	—
206	#443	—	2	1	no	—
207	#443	C₂²×C₁₃	1	2	yes	—
208	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
209	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
210	C₄×SD₁₆	—	2	1	no	—
211	#430	C₂²×C₁₃	1	1	yes	characteristic
212	#421	—	2	1	no	—
213	#405	C₂²×C₁₃	1	1	yes	characteristic
214	#365	C₂²×C₁₃	1	2	yes	complemented
215	#365	C₂²×C₁₃	1	2	yes	complemented
216	#364	C₂²×C₁₃	1	2	yes	complemented
217	#362	C₂²×C₁₃	1	2	yes	complemented
218	#361	C₂²×C₁₃	1	2	yes	complemented
219	#360	C₂²×C₁₃	1	2	yes	—
220	#360	C₂²×C₁₃	1	2	yes	—
221	#349	C₂²×C₁₃	1	1	yes	characteristic
222	#349	C₂²×C₁₃	1	1	yes	characteristic
223	#347	C₂²×C₁₃	1	2	yes	complemented
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	4	1	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	8	1	no	—
231	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	4	1	no	—
234	C₄×C₁₃	—	4	1	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	—	8	1	no	—
239	C₄×C₁₃	#525	1	1	yes	characteristic
240	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×#41	—	2	1	no	—
242	#137	—	2	2	no	—
243	AGL(1,ℤ/8)	—	2	2	no	—
244	#135	—	2	1	no	—
245	#135	C₂³×C₁₃	1	2	yes	—
246	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	1	no	—
248	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
249	#131	—	2	2	no	—
250	#131	—	2	2	no	—
251	#131	—	4	1	no	—
252	#131	—	4	1	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	4	1	no	—
255	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	—	4	1	no	—
257	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	1	no	—
259	#126	—	4	1	no	—
260	#124	—	2	1	no	—
261	#124	—	4	1	no	—
262	#123	—	4	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	4	1	no	—
265	#121	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	#117	D₄×C₁₃	1	1	yes	characteristic
269	Q₃₂	—	2	2	no	—
270	SD₃₂	—	2	2	no	—
271	SD₃₂	—	2	2	no	—
272	D₁₆	—	2	2	no	—
273	M₃₂	C₂³×C₁₃	1	2	yes	—
274	M₃₂	C₂³×C₁₃	1	2	yes	—
275	#108	—	2	1	no	—
276	#108	C₂³×C₁₃	1	2	yes	—
277	#106	—	2	1	no	—
278	#106	C₂³×C₁₃	1	1	yes	characteristic
279	#106	C₂³×C₁₃	1	1	yes	characteristic
280	#104	—	2	2	no	—
281	#104	—	2	2	no	—
282	#103	—	2	1	no	—
283	#103	—	2	1	no	—
284	#102	—	2	1	no	—
285	#102	—	2	1	no	—
286	#97	D₄×C₁₃	1	1	yes	characteristic
287	#97	C₂³×C₁₃	1	1	yes	characteristic
288	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₁₃	—	2	1	no	—
291	C₂×C₁₃	—	4	1	no	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	—	16	1	no	—
294	C₂×C₁₃	#3109	1	1	yes	characteristic
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	Q₁₆	—	2	1	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	C₁₃×#41	1	2	yes	—
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	4	1	no	—
315	SD₁₆	—	4	1	no	—
316	D₈	—	2	1	no	—
317	D₈	—	2	2	no	—
318	D₈	C₁₃×#41	1	2	yes	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	4	2	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₄²	—	4	1	no	—
346	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₁₃	#33691	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	16	1	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	16	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	16	1	no	—
377	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	2	no	—
382	C₈	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₈	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₈	C₂×C₁₃×#41	1	2	yes	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	1	no	—
400	C₄	C₁₃×#525	1	1	yes	characteristic
401	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	16	1	no	—
406	C₂	C₁₃×#3109	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#3109
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#2190	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3173	C₂	semidirect
2. C₁₃×#2955	C₂	semidirect
3. C₁₃×#2239	C₂	semidirect
4. C₁₃×#2238	C₂	semidirect
5. C₁₃×#2230	C₂	semidirect
6. C₁₃×#2212	C₂	semidirect
7. C₁₃×#2191	C₂	semidirect
9. C₁₃×AGL(1,ℤ/16)	C₂	semidirect
10. C₁₃×#2180	C₂	semidirect
11. C₁₃×#2166	C₂	semidirect
17. C₁₃×#498	C₂²	semidirect
18. C₁₃×#495	C₂²	semidirect
27. C₁₃×#442	C₂²	semidirect
28. C₁₃×#441	C₂²	semidirect
33. C₁₃×#365	C₂²	semidirect
34. C₁₃×#365	C₂²	semidirect
35. C₁₃×#364	C₂²	semidirect
36. C₁₃×#362	C₂²	semidirect
37. C₁₃×#361	C₂²	semidirect
42. C₁₃×#347	C₂²	semidirect
92. #33691	C₁₃	direct (N × H)
148. #3173	C₂×C₁₃	semidirect
149. #2955	C₂×C₁₃	semidirect
150. #2239	C₂×C₁₃	semidirect
151. #2238	C₂×C₁₃	semidirect
152. #2230	C₂×C₁₃	semidirect
153. #2212	C₂×C₁₃	semidirect
154. #2191	C₂×C₁₃	semidirect
156. AGL(1,ℤ/16)	C₂×C₁₃	semidirect
157. #2180	C₂×C₁₃	semidirect
158. #2166	C₂×C₁₃	semidirect
198. #498	C₂²×C₁₃	semidirect
199. #495	C₂²×C₁₃	semidirect
208. #442	C₂²×C₁₃	semidirect
209. #441	C₂²×C₁₃	semidirect
214. #365	C₂²×C₁₃	semidirect
215. #365	C₂²×C₁₃	semidirect
216. #364	C₂²×C₁₃	semidirect
217. #362	C₂²×C₁₃	semidirect
218. #361	C₂²×C₁₃	semidirect
223. #347	C₂²×C₁₃	semidirect
350. C₁₃	#33691	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3173	2
C₁₃×#2955	2
C₁₃×#2239	2
C₁₃×#2238	2
C₁₃×#2230	2
C₁₃×#2212	2
C₁₃×#2191	2
C₁₃×#2190	2
C₁₃×AGL(1,ℤ/16)	2
C₁₃×#2180	2
C₁₃×#2166	2
#33691	13

Subgroups — C13×#33691 #15720030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33691 #15720030