Subgroups — C₁₃×#24989 #15711328

Order 3328.

620 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2082	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2049	C₂	1	2	yes	maximal
5	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1905	C₂	1	2	yes	maximal
8	C₁₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1830	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1814	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1757	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₁₃×#519	C₂²	1	2	yes	—
16	C₁₃×#473	—	2	2	no	—
17	C₁₃×#473	—	2	2	no	—
18	C₁₃×#441	—	2	2	no	—
19	C₄×C₁₃×Q₁₆	—	2	2	no	—
20	C₁₃×#430	C₂²	1	2	yes	—
21	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₂²	1	1	yes	characteristic
24	C₁₃×#421	C₂²	1	2	yes	—
25	C₁₃×#419	C₂²	1	2	yes	—
26	C₁₃×#419	C₂²	1	2	yes	—
27	C₁₃×#413	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#101	C₂²	1	2	yes	—
29	C₂×C₁₃×#101	C₂²	1	2	yes	—
30	C₁₃×#410	C₂²	1	1	yes	characteristic
31	C₁₃×#405	C₂²	1	1	yes	characteristic
32	C₁₃×#405	C₂²	1	1	yes	characteristic
33	C₁₃×#344	C₂²	1	1	yes	characteristic
34	C₁₃×#344	C₂²	1	1	yes	characteristic
35	C₁₃×#344	C₂²	1	2	yes	—
36	C₁₃×#344	C₂²	1	2	yes	—
37	C₁₃×#344	C₂²	1	2	yes	—
38	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₁₃×#137	—	2	4	no	—
42	C₁₃×#137	—	4	2	no	—
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	1	no	—
45	C₂×C₁₃×Q₁₆	—	2	1	no	—
46	C₂×C₁₃×Q₁₆	—	2	1	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
49	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₁₃×#131	—	2	1	no	—
52	C₁₃×#131	—	2	1	no	—
53	C₁₃×#131	—	2	1	no	—
54	C₁₃×#131	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₁₃	—	2	4	no	—
64	C₄×Q₈×C₁₃	—	4	2	no	—
65	C₁₃×#117	—	2	4	no	—
66	C₁₃×#117	C₂³	1	1	yes	characteristic
67	C₁₃×#117	C₂³	1	2	yes	—
68	C₁₃×#117	C₂³	1	1	yes	characteristic
69	C₁₃×#108	—	2	1	no	—
70	C₁₃×#108	—	2	1	no	—
71	C₁₃×#108	—	2	1	no	—
72	C₁₃×#108	—	2	1	no	—
73	C₁₃×#108	—	4	2	no	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#106	—	2	1	no	—
76	C₁₃×#104	—	4	2	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₁₃×#101	—	2	4	no	—
80	C₁₃×#101	—	2	1	no	—
81	C₁₃×#101	—	4	2	no	—
82	C₁₃×#100	—	2	1	no	—
83	C₁₃×#99	—	2	2	no	—
84	C₁₃×#97	—	2	1	no	—
85	C₁₃×#97	—	2	1	no	—
86	C₄×C₈×C₁₃	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	#24989	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₁₃×#41	—	2	1	no	—
90	C₁₃×#41	—	2	1	no	—
91	C₁₃×#41	—	2	1	no	—
92	C₁₃×#41	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
99	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₁₃×Q₁₆	—	2	2	no	—
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	—	2	2	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	4	4	no	—
110	C₁₃×SD₁₆	—	4	4	no	—
111	C₁₃×M₁₆	—	2	1	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	—	2	1	no	—
114	C₁₃×M₁₆	—	2	1	no	—
115	C₁₃×M₁₆	—	2	2	no	—
116	C₁₃×M₁₆	—	2	1	no	—
117	C₁₃×M₁₆	—	2	1	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	1	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	—	4	1	no	—
122	C₁₃×M₁₆	—	4	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
133	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
134	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
135	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₁₃×C₂²⋊C₄	#41	1	2	yes	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	4	4	no	—
147	C₂×#473	C₂×C₁₃	1	1	yes	characteristic
148	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2082	C₂×C₁₃	1	2	yes	complemented
150	#2049	C₂×C₁₃	1	2	yes	—
151	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1953	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1905	C₂×C₁₃	1	2	yes	—
154	#1833	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1830	C₂×C₁₃	1	2	yes	complemented
156	#1814	C₂×C₁₃	1	1	yes	characteristic
157	#1757	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	4	no	—
161	Q₈×C₁₃	—	2	4	no	—
162	Q₈×C₁₃	—	2	1	no	—
163	Q₈×C₁₃	—	2	1	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	2	1	no	—
167	D₄×C₁₃	—	2	1	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
185	C₈×C₁₃	—	4	1	no	—
186	C₈×C₁₃	—	4	2	no	—
187	C₈×C₁₃	—	4	1	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₈×C₁₃	—	4	1	no	—
190	C₈×C₁₃	#123	1	1	yes	characteristic
191	C₈×C₁₃	#123	1	1	yes	characteristic
192	C₈×C₁₃	#123	1	1	yes	characteristic
193	C₈×C₁₃	#123	1	1	yes	characteristic
194	C₂×#137	C₂²×C₁₃	1	2	yes	—
195	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
197	#519	C₂²×C₁₃	1	2	yes	—
198	#473	—	2	2	no	—
199	#473	—	2	2	no	—
200	#441	—	2	2	no	—
201	C₄×Q₁₆	—	2	2	no	—
202	#430	C₂²×C₁₃	1	2	yes	—
203	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
205	#427	C₂²×C₁₃	1	1	yes	characteristic
206	#421	C₂²×C₁₃	1	2	yes	—
207	#419	C₂²×C₁₃	1	2	yes	—
208	#419	C₂²×C₁₃	1	2	yes	—
209	#413	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#101	C₂²×C₁₃	1	2	yes	—
211	C₂×#101	C₂²×C₁₃	1	2	yes	—
212	#410	C₂²×C₁₃	1	1	yes	characteristic
213	#405	C₂²×C₁₃	1	1	yes	characteristic
214	#405	C₂²×C₁₃	1	1	yes	characteristic
215	#344	C₂²×C₁₃	1	2	yes	—
216	#344	C₂²×C₁₃	1	2	yes	—
217	#344	C₂²×C₁₃	1	1	yes	characteristic
218	#344	C₂²×C₁₃	1	1	yes	characteristic
219	#344	C₂²×C₁₃	1	2	yes	—
220	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₁₃	—	4	1	no	—
222	C₂²×C₁₃	—	4	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	#529	1	1	yes	characteristic
225	C₂²×C₁₃	#546	1	1	yes	characteristic
226	C₂²×C₁₃	#555	1	1	yes	characteristic
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	—	8	1	no	—
232	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
233	C₄×C₁₃	#540	1	1	yes	characteristic
234	C₄×C₁₃	#546	1	1	yes	characteristic
235	C₄×C₁₃	#553	1	1	yes	characteristic
236	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
238	#137	—	2	4	no	—
239	#137	—	4	2	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
246	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
247	C₂×SD₁₆	—	2	2	no	—
248	#131	—	2	1	no	—
249	#131	—	2	1	no	—
250	#131	—	2	1	no	—
251	#131	—	2	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
255	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
257	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	—	4	2	no	—
262	#117	—	2	4	no	—
263	#117	C₂³×C₁₃	1	2	yes	—
264	#117	C₂³×C₁₃	1	1	yes	characteristic
265	#117	C₂³×C₁₃	1	1	yes	characteristic
266	#108	—	2	1	no	—
267	#108	—	2	1	no	—
268	#108	—	2	1	no	—
269	#108	—	2	1	no	—
270	#108	—	4	2	no	—
271	#107	—	2	1	no	—
272	#106	—	2	1	no	—
273	#104	—	4	2	no	—
274	#103	—	2	4	no	—
275	#103	—	4	2	no	—
276	#101	—	2	4	no	—
277	#101	—	2	1	no	—
278	#101	—	4	2	no	—
279	#100	—	2	1	no	—
280	#99	—	2	2	no	—
281	#97	—	2	1	no	—
282	#97	—	2	1	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₂×C₁₃	—	2	1	no	—
286	C₂×C₁₃	—	2	1	no	—
287	C₂×C₁₃	—	2	1	no	—
288	C₂×C₁₃	—	8	1	no	—
289	C₂×C₁₃	#2420	1	1	yes	characteristic
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
300	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
306	Q₁₆	—	2	2	no	—
307	Q₁₆	—	2	2	no	—
308	Q₁₆	—	2	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	4	4	no	—
311	SD₁₆	—	4	4	no	—
312	M₁₆	—	2	1	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	2	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	1	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	1	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
334	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
335	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
336	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	C₁₃×#41	1	2	yes	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	4	no	—
348	C₁₃	#24989	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	1	no	—
350	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	1	no	—
381	C₈	C₁₃×#123	1	1	yes	characteristic
382	C₈	C₁₃×#123	1	1	yes	characteristic
383	C₈	C₁₃×#123	1	1	yes	characteristic
384	C₈	C₁₃×#123	1	1	yes	characteristic
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₁₃×#529	1	1	yes	characteristic
389	C₂²	C₁₃×#546	1	1	yes	characteristic
390	C₂²	C₁₃×#555	1	1	yes	characteristic
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	4	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
397	C₄	C₁₃×#540	1	1	yes	characteristic
398	C₄	C₁₃×#546	1	1	yes	characteristic
399	C₄	C₁₃×#553	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	C₁₃×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2950	C₂	semidirect
3. C₁₃×#2082	C₂	semidirect
5. C₁₃×#1979	C₂	semidirect
6. C₁₃×#1953	C₂	semidirect
8. C₁₃×#1833	C₂	semidirect
9. C₁₃×#1830	C₂	semidirect
88. #24989	C₁₃	direct (N × H)
148. #2950	C₂×C₁₃	semidirect
149. #2082	C₂×C₁₃	semidirect
151. #1979	C₂×C₁₃	semidirect
152. #1953	C₂×C₁₃	semidirect
154. #1833	C₂×C₁₃	semidirect
155. #1830	C₂×C₁₃	semidirect
348. C₁₃	#24989	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#473	2
C₁₃×#2950	2
C₁₃×#2082	2
C₁₃×#2049	2
C₁₃×#1979	2
C₁₃×#1953	2
C₁₃×#1905	2
C₁₃×#1833	2
C₁₃×#1830	2
C₁₃×#1814	2
C₁₃×#1757	2
#24989	13

Subgroups — C13×#24989 #15711328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24989 #15711328