Subgroups — C₁₃×#25987 #15712326

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2898	C₂	1	2	yes	maximal
3	C₁₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1866	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1859	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1816	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#131	C₂²	1	2	yes	—
12	C₁₃×#544	C₂²	1	1	yes	characteristic
13	C₁₃×#520	C₂²	1	2	yes	—
14	C₁₃×#479	—	2	2	no	—
15	C₁₃×#478	—	2	2	no	—
16	C₁₃×#477	—	2	2	no	—
17	C₁₃×#474	—	2	2	no	—
18	C₂×C₁₃×#108	C₂²	1	2	yes	—
19	C₁₃×#428	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₁₃×#424	C₂²	1	2	yes	—
22	C₂×C₁₃×#104	C₂²	1	2	yes	—
23	C₁₃×#419	—	2	2	no	—
24	C₁₃×#419	C₂²	1	2	yes	—
25	C₁₃×#417	—	2	2	no	—
26	C₁₃×#417	C₂²	1	2	yes	—
27	C₁₃×#417	C₂²	1	2	yes	—
28	C₁₃×#416	—	2	2	no	—
29	C₁₃×#416	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	—	2	2	no	—
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#343	C₂²	1	1	yes	characteristic
36	C₁₃×#343	C₂²	1	2	yes	—
37	C₁₃×#339	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×2₋¹⁺⁴	—	2	4	no	—
40	C₁₃×2₋¹⁺⁴	—	4	1	no	—
41	C₁₃×2₋¹⁺⁴	Q₈	1	4	yes	complemented
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	4	1	no	—
44	C₂×C₁₃×#41	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×#131	—	2	4	no	—
48	C₁₃×#131	—	4	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	1	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	4	2	no	—
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#108	—	4	2	no	—
68	C₁₃×#107	—	2	2	no	—
69	C₁₃×#107	—	2	2	no	—
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#106	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×#104	—	2	4	no	—
75	C₁₃×#103	—	2	2	no	—
76	C₁₃×#103	—	2	2	no	—
77	C₁₃×#103	—	2	2	no	—
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	D₄	1	2	yes	—
82	C₁₃×#103	D₄	1	2	yes	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	D₄	1	2	yes	—
86	C₁₃×#102	D₄	1	2	yes	—
87	C₁₃×#101	—	4	1	no	—
88	C₁₃×#95	—	4	1	no	—
89	#25987	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	2	2	no	—
91	C₁₃×#41	—	2	2	no	—
92	C₁₃×#41	—	2	8	no	—
93	C₁₃×#41	—	4	4	no	—
94	C₁₃×#41	—	4	4	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₁₃×#41	C₂×Q₈	1	4	yes	—
97	C₁₃×#41	#41	1	4	yes	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	4	1	no	—
103	C₂×Q₈×C₁₃	—	4	1	no	—
104	C₂×Q₈×C₁₃	—	4	4	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	4	4	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	8	2	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	#3083	C₂×C₁₃	1	2	yes	complemented
145	#2898	C₂×C₁₃	1	2	yes	—
146	#2095	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2064	C₂×C₁₃	1	2	yes	complemented
148	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1866	C₂×C₁₃	1	2	yes	complemented
150	#1859	C₂×C₁₃	1	2	yes	complemented
151	#1816	C₂×C₁₃	1	2	yes	complemented
152	#1793	C₂×C₁₃	1	1	yes	characteristic
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
155	Q₈×C₁₃	—	2	2	no	—
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	16	1	no	—
160	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	4	4	no	—
165	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	8	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	—	8	1	no	—
182	C₂×C₄×C₁₃	—	16	2	no	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
186	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	—	4	2	no	—
190	C₈×C₁₃	—	4	2	no	—
191	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#131	C₂²×C₁₃	1	2	yes	—
193	#544	C₂²×C₁₃	1	1	yes	characteristic
194	#520	C₂²×C₁₃	1	2	yes	—
195	#479	—	2	2	no	—
196	#478	—	2	2	no	—
197	#477	—	2	2	no	—
198	#474	—	2	2	no	—
199	C₂×#108	C₂²×C₁₃	1	2	yes	—
200	#428	C₂²×C₁₃	1	2	yes	—
201	C₂×#107	C₂²×C₁₃	1	2	yes	—
202	#424	C₂²×C₁₃	1	2	yes	—
203	C₂×#104	C₂²×C₁₃	1	2	yes	—
204	#419	—	2	2	no	—
205	#419	C₂²×C₁₃	1	2	yes	—
206	#417	—	2	2	no	—
207	#417	C₂²×C₁₃	1	2	yes	—
208	#417	C₂²×C₁₃	1	2	yes	—
209	#416	—	2	2	no	—
210	#416	C₂²×C₁₃	1	2	yes	—
211	C₂×#103	—	2	2	no	—
212	C₂×#103	C₂²×C₁₃	1	2	yes	—
213	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
214	#391	C₂²×C₁₃	1	1	yes	characteristic
215	#384	C₂²×C₁₃	1	1	yes	characteristic
216	#343	C₂²×C₁₃	1	2	yes	—
217	#343	C₂²×C₁₃	1	1	yes	characteristic
218	#339	C₂²×C₁₃	1	2	yes	—
219	#336	C₂²×C₁₃	1	1	yes	characteristic
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	4	2	no	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	#543	1	1	yes	characteristic
226	C₂²×C₁₃	D₄²	1	1	yes	characteristic
227	C₂²×C₁₃	#551	1	1	yes	characteristic
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	2	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
236	C₄×C₁₃	#546	1	2	yes	—
237	2₋¹⁺⁴	—	2	4	no	—
238	2₋¹⁺⁴	—	4	1	no	—
239	2₋¹⁺⁴	Q₈×C₁₃	1	4	yes	complemented
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	4	1	no	—
242	C₂×#41	C₂³×C₁₃	1	2	yes	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
245	#131	—	2	4	no	—
246	#131	—	4	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
249	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
252	C₄⋊Q₈	—	2	2	no	—
253	#125	—	2	2	no	—
254	C₂²⋊Q₈	—	4	1	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	4	2	no	—
258	#117	—	2	2	no	—
259	#117	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	4	1	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
265	#108	—	4	2	no	—
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#107	—	2	2	no	—
269	#106	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#104	—	2	4	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	D₄×C₁₃	1	2	yes	—
280	#103	D₄×C₁₃	1	2	yes	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	D₄×C₁₃	1	2	yes	—
284	#102	D₄×C₁₃	1	2	yes	—
285	#101	—	4	1	no	—
286	#95	—	4	1	no	—
287	C₂×C₁₃	—	2	1	no	—
288	C₂×C₁₃	—	2	1	no	—
289	C₂×C₁₃	—	4	4	no	—
290	C₂×C₁₃	#2437	1	1	yes	characteristic
291	C₂×C₁₃	#3288	1	1	yes	characteristic
292	C₂×C₁₃	#3293	1	1	yes	characteristic
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	—	2	8	no	—
296	#41	—	4	4	no	—
297	#41	—	4	4	no	—
298	#41	—	4	4	no	—
299	#41	C₂×Q₈×C₁₃	1	4	yes	—
300	#41	C₁₃×#41	1	4	yes	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
309	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	4	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	4	no	—
331	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	4	2	no	—
347	C₁₃	#25987	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	2	2	no	—
349	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	4	no	—
352	Q₈	—	4	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	16	1	no	—
355	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	4	no	—
360	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	—	16	2	no	—
378	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
379	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
381	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	C₁₃×#543	1	1	yes	characteristic
392	C₂²	D₄²×C₁₃	1	1	yes	characteristic
393	C₂²	C₁₃×#551	1	1	yes	characteristic
394	C₄	—	2	4	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	1	no	—
401	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
402	C₄	C₁₃×#546	1	2	yes	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	4	4	no	—
406	C₂	C₁₃×#2437	1	1	yes	characteristic
407	C₂	C₁₃×#3288	1	1	yes	characteristic
408	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3083	C₂	semidirect
3. C₁₃×#2095	C₂	semidirect
4. C₁₃×#2064	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#1866	C₂	semidirect
7. C₁₃×#1859	C₂	semidirect
8. C₁₃×#1816	C₂	semidirect
41. C₁₃×2₋¹⁺⁴	Q₈	semidirect
89. #25987	C₁₃	direct (N × H)
144. #3083	C₂×C₁₃	semidirect
146. #2095	C₂×C₁₃	semidirect
147. #2064	C₂×C₁₃	semidirect
148. #2028	C₂×C₁₃	semidirect
149. #1866	C₂×C₁₃	semidirect
150. #1859	C₂×C₁₃	semidirect
151. #1816	C₂×C₁₃	semidirect
239. 2₋¹⁺⁴	Q₈×C₁₃	semidirect
347. C₁₃	#25987	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×#3083	2
C₁₃×#2898	2
C₁₃×#2095	2
C₁₃×#2064	2
C₁₃×#2028	2
C₁₃×#1866	2
C₁₃×#1859	2
C₁₃×#1816	2
C₁₃×#1793	2
#25987	13

Subgroups — C13×#25987 #15712326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25987 #15712326