Subgroups — C₁₃×#33851 #15720190

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₁₃×#548	—	2	2	no	—
15	C₁₃×#508	—	2	4	no	—
16	C₂×C₁₃×Q₃₂	—	2	4	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	2	yes	—
26	C₁₃×#467	C₂²	1	2	yes	—
27	C₁₃×#466	C₂²	1	2	yes	—
28	C₁₃×#464	—	2	2	no	—
29	C₁₃×#452	—	2	2	no	—
30	C₁₃×#448	—	2	2	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
32	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#366	C₂²	1	1	yes	characteristic
34	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₁₃×#358	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#357	C₂²	1	2	yes	—
38	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₁₃×#135	—	2	4	no	—
44	C₁₃×#135	—	4	2	no	—
45	C₂×C₁₃×Q₁₆	—	2	4	no	—
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	4	2	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×D₈	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#124	—	2	2	no	—
56	C₁₃×#124	—	4	2	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	—	4	2	no	—
59	C₁₃×#121	—	2	2	no	—
60	C₁₃×#121	—	4	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	4	2	no	—
63	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
64	C₁₃×Q₃₂	—	2	4	no	—
65	C₁₃×Q₃₂	—	2	2	no	—
66	C₁₃×Q₃₂	D₄	1	4	yes	complemented
67	C₁₃×SD₃₂	—	2	4	no	—
68	C₁₃×SD₃₂	—	4	2	no	—
69	C₁₃×D₁₆	—	2	2	no	—
70	C₂×C₁₃×C₁₆	—	2	2	no	—
71	C₂×C₁₃×C₁₆	—	2	2	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂³	1	2	yes	—
77	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
82	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	#33851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₁₃×#41	—	4	4	no	—
86	C₁₃×#41	—	8	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	4	2	no	—
91	C₂×Q₈×C₁₃	—	8	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×Q₁₆	—	2	2	no	—
102	C₁₃×Q₁₆	—	2	2	no	—
103	C₁₃×Q₁₆	—	4	4	no	—
104	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
105	C₁₃×SD₁₆	—	4	4	no	—
106	C₁₃×SD₁₆	—	8	2	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	2	no	—
125	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
126	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
127	C₄²×C₁₃	—	4	2	no	—
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₁₆	—	2	1	no	—
130	C₁₃×C₁₆	—	2	1	no	—
131	C₁₃×C₁₆	—	2	1	no	—
132	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
133	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂²×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#3285	C₂×C₁₃	1	2	yes	complemented
136	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2216	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2215	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2211	C₂×C₁₃	1	2	yes	complemented
140	#2189	C₂×C₁₃	1	2	yes	complemented
141	#2185	C₂×C₁₃	1	2	yes	complemented
142	C₄×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
143	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
146	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
147	Q₈×C₁₃	—	2	4	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	4	2	no	—
151	Q₈×C₁₃	—	8	4	no	—
152	D₄×C₁₃	—	2	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	8	4	no	—
156	D₄×C₁₃	—	8	4	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	8	4	no	—
165	C₂×C₄×C₁₃	—	8	4	no	—
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	—	2	1	no	—
174	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×#135	C₂²×C₁₃	1	2	yes	—
177	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
178	#548	—	2	2	no	—
179	#508	—	2	4	no	—
180	C₂×Q₃₂	—	2	4	no	—
181	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
182	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
185	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
186	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
189	#495	C₂²×C₁₃	1	2	yes	—
190	#467	C₂²×C₁₃	1	2	yes	—
191	#466	C₂²×C₁₃	1	2	yes	—
192	#464	—	2	2	no	—
193	#452	—	2	2	no	—
194	#448	—	2	2	no	—
195	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
196	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
197	#366	C₂²×C₁₃	1	1	yes	characteristic
198	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
199	#358	C₂²×C₁₃	1	2	yes	—
200	#358	C₂²×C₁₃	1	2	yes	—
201	#357	C₂²×C₁₃	1	2	yes	—
202	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	#508	1	2	yes	complemented
214	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	8	2	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	D₄²	1	1	yes	characteristic
223	C₄×C₁₃	#576	1	1	yes	characteristic
224	C₂×#41	—	2	2	no	—
225	C₂²×Q₈	—	2	2	no	—
226	#135	—	2	4	no	—
227	#135	—	4	2	no	—
228	C₂×Q₁₆	—	2	4	no	—
229	C₂×Q₁₆	—	2	2	no	—
230	C₂×Q₁₆	—	4	2	no	—
231	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
232	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
233	C₂×SD₁₆	—	2	2	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×D₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	#124	—	2	2	no	—
239	#124	—	4	2	no	—
240	C₂²⋊Q₈	—	2	2	no	—
241	C₂²⋊Q₈	—	4	2	no	—
242	#121	—	2	2	no	—
243	#121	—	4	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×D₄	—	4	2	no	—
246	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
247	Q₃₂	—	2	4	no	—
248	Q₃₂	—	2	2	no	—
249	Q₃₂	D₄×C₁₃	1	4	yes	complemented
250	SD₃₂	—	2	4	no	—
251	SD₃₂	—	4	2	no	—
252	D₁₆	—	2	2	no	—
253	C₂×C₁₆	—	2	2	no	—
254	C₂×C₁₆	—	2	2	no	—
255	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
259	#107	C₂³×C₁₃	1	2	yes	—
260	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
261	#103	—	2	2	no	—
262	#103	—	2	2	no	—
263	#102	—	2	2	no	—
264	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
265	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₁₃	—	2	2	no	—
268	C₂×C₁₃	—	4	1	no	—
269	C₂×C₁₃	—	16	2	no	—
270	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
272	C₂×C₁₃	#3417	1	1	yes	characteristic
273	#41	—	4	4	no	—
274	#41	—	8	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	8	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	2	2	no	—
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	4	4	no	—
292	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
293	SD₁₆	—	4	4	no	—
294	SD₁₆	—	8	2	no	—
295	D₈	—	2	2	no	—
296	D₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
314	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
315	C₄²	—	4	2	no	—
316	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	1	no	—
320	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
321	C₁₃	#33851	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	4	2	no	—
323	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
324	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
325	Q₈	—	2	4	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	8	4	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	—	8	4	no	—
344	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
346	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
347	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
353	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	C₁₃×#508	1	2	yes	complemented
363	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	D₄²×C₁₃	1	1	yes	characteristic
372	C₄	C₁₃×#576	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	16	2	no	—
376	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
377	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
378	C₂	C₁₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#508	C₂	semidirect
2. C₂²×C₁₃×Q₃₂	C₂	semidirect
3. C₁₃×#3285	C₂	semidirect
4. C₁₃×#2249	C₂	semidirect
5. C₁₃×#2216	C₂	semidirect
6. C₁₃×#2215	C₂	semidirect
7. C₁₃×#2211	C₂	semidirect
8. C₁₃×#2189	C₂	semidirect
9. C₁₃×#2185	C₂	semidirect
10. C₄×C₁₃×Q₃₂	C₂	semidirect
11. D₄×C₁₃×C₁₆	C₂	semidirect
66. C₁₃×Q₃₂	D₄	semidirect
84. #33851	C₁₃	direct (N × H)
133. C₂×#508	C₂×C₁₃	semidirect
134. C₂²×Q₃₂	C₂×C₁₃	semidirect
135. #3285	C₂×C₁₃	semidirect
136. #2249	C₂×C₁₃	semidirect
137. #2216	C₂×C₁₃	semidirect
138. #2215	C₂×C₁₃	semidirect
139. #2211	C₂×C₁₃	semidirect
140. #2189	C₂×C₁₃	semidirect
141. #2185	C₂×C₁₃	semidirect
142. C₄×Q₃₂	C₂×C₁₃	semidirect
143. D₄×C₁₆	C₂×C₁₃	semidirect
213. C₂²×C₁₃	#508	semidirect
249. Q₃₂	D₄×C₁₃	semidirect
321. C₁₃	#33851	direct (N × H)
362. C₂²	C₁₃×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#508	2
C₂²×C₁₃×Q₃₂	2
C₁₃×#3285	2
C₁₃×#2249	2
C₁₃×#2216	2
C₁₃×#2215	2
C₁₃×#2211	2
C₁₃×#2189	2
C₁₃×#2185	2
C₄×C₁₃×Q₃₂	2
D₄×C₁₃×C₁₆	2
#33851	13

Subgroups — C13×#33851 #15720190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33851 #15720190