Subgroups — C₁₃×#33753 #15720092

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2235	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2233	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2217	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×#121	—	2	1	no	—
14	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
16	C₁₃×#467	—	2	1	no	—
17	C₁₃×#467	—	2	1	no	—
18	C₁₃×#467	C₂²	1	2	yes	—
19	C₁₃×#467	C₂²	1	2	yes	complemented
20	C₁₃×#466	—	2	1	no	—
21	C₁₃×#466	—	2	1	no	—
22	C₁₃×#466	C₂²	1	2	yes	—
23	C₁₃×#466	C₂²	1	2	yes	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#103	—	2	1	no	—
27	C₂×C₁₃×#102	—	2	1	no	—
28	C₁₃×#367	C₂²	1	4	yes	complemented
29	C₁₃×#358	C₂²	1	4	yes	complemented
30	C₁₃×#357	C₂²	1	4	yes	complemented
31	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	—	4	1	no	—
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₁₃×Q₁₆	—	2	1	no	—
38	C₂×C₁₃×Q₁₆	—	4	2	no	—
39	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
40	C₂×C₁₃×D₈	—	2	1	no	—
41	C₂×C₁₃×D₈	—	4	2	no	—
42	C₂×C₁₃×D₈	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	—	4	2	no	—
44	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×C₂²⋊Q₈	—	2	2	no	—
51	C₁₃×C₂²⋊Q₈	—	2	2	no	—
52	C₁₃×C₂²⋊Q₈	—	4	1	no	—
53	C₁₃×C₂²⋊Q₈	—	4	1	no	—
54	C₁₃×#121	—	2	2	no	—
55	C₁₃×#121	—	2	2	no	—
56	C₁₃×#121	—	4	1	no	—
57	C₁₃×#121	—	4	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
63	C₁₃×SD₃₂	—	4	4	no	—
64	C₂×C₁₃×C₁₆	—	4	2	no	—
65	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
66	C₁₃×#107	—	2	1	no	—
67	C₁₃×#107	—	2	1	no	—
68	C₁₃×#107	C₂³	1	2	yes	—
69	C₁₃×#107	C₂³	1	2	yes	—
70	C₁₃×#103	—	2	2	no	—
71	C₁₃×#103	—	2	2	no	—
72	C₁₃×#102	—	2	2	no	—
73	C₁₃×#102	—	2	2	no	—
74	#33753	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	4	1	no	—
76	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	4	1	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	1	no	—
87	C₂×D₄×C₁₃	—	8	4	no	—
88	C₂²×C₄×C₁₃	—	4	1	no	—
89	C₂²×C₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₁₃×Q₁₆	—	2	4	no	—
100	C₁₃×Q₁₆	—	4	2	no	—
101	C₁₃×D₈	—	2	4	no	—
102	C₁₃×D₈	—	4	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	4	1	no	—
107	C₂×C₈×C₁₃	—	4	1	no	—
108	C₂×C₈×C₁₃	—	4	1	no	—
109	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	2	no	—
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₁₆	—	2	4	no	—
124	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
126	#2235	C₂×C₁₃	1	2	yes	complemented
127	#2233	C₂×C₁₃	1	2	yes	complemented
128	#2217	C₂×C₁₃	1	4	yes	complemented
129	#2187	C₂×C₁₃	1	2	yes	complemented
130	#2185	C₂×C₁₃	1	2	yes	complemented
131	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	—	4	1	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	8	2	no	—
136	C₂³×C₁₃	—	8	2	no	—
137	C₂³×C₁₃	—	8	2	no	—
138	C₂³×C₁₃	SD₃₂	1	4	yes	complemented
139	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
140	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
141	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
142	Q₈×C₁₃	—	4	2	no	—
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	8	2	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	8	2	no	—
148	D₄×C₁₃	—	8	4	no	—
149	D₄×C₁₃	—	8	4	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	8	2	no	—
163	C₂×C₄×C₁₃	—	8	2	no	—
164	C₂×C₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₁₃	—	2	1	no	—
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
174	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×C₂²⋊Q₈	—	2	1	no	—
177	C₂×#121	—	2	1	no	—
178	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
179	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
180	#467	—	2	1	no	—
181	#467	—	2	1	no	—
182	#467	C₂²×C₁₃	1	2	yes	—
183	#467	C₂²×C₁₃	1	2	yes	complemented
184	#466	—	2	1	no	—
185	#466	—	2	1	no	—
186	#466	C₂²×C₁₃	1	2	yes	—
187	#466	C₂²×C₁₃	1	2	yes	—
188	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
190	C₂×#103	—	2	1	no	—
191	C₂×#102	—	2	1	no	—
192	#367	C₂²×C₁₃	1	4	yes	complemented
193	#358	C₂²×C₁₃	1	4	yes	complemented
194	#357	C₂²×C₁₃	1	4	yes	complemented
195	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
196	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	4	4	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	16	4	no	—
208	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
209	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
210	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
211	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	—	8	2	no	—
217	C₄×C₁₃	—	8	2	no	—
218	C₄×C₁₃	#534	1	1	yes	characteristic
219	C₄×C₁₃	#575	1	1	yes	characteristic
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	4	1	no	—
223	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×Q₁₆	—	4	2	no	—
226	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
227	C₂×D₈	—	2	1	no	—
228	C₂×D₈	—	4	2	no	—
229	C₂×D₈	C₂³×C₁₃	1	2	yes	—
230	C₂²×C₈	—	4	2	no	—
231	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
232	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
233	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²⋊Q₈	—	2	2	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₂²⋊Q₈	—	4	1	no	—
240	C₂²⋊Q₈	—	4	1	no	—
241	#121	—	2	2	no	—
242	#121	—	2	2	no	—
243	#121	—	4	1	no	—
244	#121	—	4	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	4	1	no	—
248	C₂×C₂²⋊C₄	—	4	1	no	—
249	C₂×C₂²⋊C₄	—	4	1	no	—
250	SD₃₂	—	4	4	no	—
251	C₂×C₁₆	—	4	2	no	—
252	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
253	#107	—	2	1	no	—
254	#107	—	2	1	no	—
255	#107	C₂³×C₁₃	1	2	yes	—
256	#107	C₂³×C₁₃	1	2	yes	—
257	#103	—	2	2	no	—
258	#103	—	2	2	no	—
259	#102	—	2	2	no	—
260	#102	—	2	2	no	—
261	C₂×C₁₃	—	2	2	no	—
262	C₂×C₁₃	—	2	2	no	—
263	C₂×C₁₃	—	2	2	no	—
264	C₂×C₁₃	—	16	2	no	—
265	C₂×C₁₃	#3186	1	1	yes	characteristic
266	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
267	C₂×C₁₃	#3414	1	1	yes	characteristic
268	C₂⁴	—	4	1	no	—
269	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	8	4	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
287	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
288	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	Q₁₆	—	2	4	no	—
293	Q₁₆	—	4	2	no	—
294	D₈	—	2	4	no	—
295	D₈	—	4	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₁₆	—	2	4	no	—
317	C₁₃	#33753	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	—	8	2	no	—
323	C₂³	—	8	2	no	—
324	C₂³	C₁₃×SD₃₂	1	4	yes	complemented
325	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
326	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
327	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	4	no	—
335	D₄	—	8	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
352	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₂×C₁₃×SD₃₂	1	2	yes	—
371	C₂²	C₂×C₁₃×SD₃₂	1	2	yes	—
372	C₂²	C₂×C₁₃×SD₃₂	1	2	yes	—
373	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₁₃×#534	1	1	yes	characteristic
381	C₄	C₁₃×#575	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	2	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₁₃×#3186	1	1	yes	characteristic
387	C₂	C₂²×C₁₃×SD₃₂	1	1	yes	characteristic
388	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#467	C₂	semidirect
3. C₁₃×#2235	C₂	semidirect
4. C₁₃×#2233	C₂	semidirect
5. C₁₃×#2217	C₂	semidirect
6. C₁₃×#2187	C₂	semidirect
7. C₁₃×#2185	C₂	semidirect
8. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
9. C₂²×C₁₃×Q₁₆	C₂²	semidirect
14. C₂×C₁₃×SD₃₂	C₂²	semidirect
15. C₂²×C₁₃×C₁₆	C₂²	semidirect
19. C₁₃×#467	C₂²	semidirect
25. C₂×C₁₃×#107	C₂²	semidirect
28. C₁₃×#367	C₂²	semidirect
29. C₁₃×#358	C₂²	semidirect
30. C₁₃×#357	C₂²	semidirect
32. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
74. #33753	C₁₃	direct (N × H)
124. C₂×#467	C₂×C₁₃	semidirect
126. #2235	C₂×C₁₃	semidirect
127. #2233	C₂×C₁₃	semidirect
128. #2217	C₂×C₁₃	semidirect
129. #2187	C₂×C₁₃	semidirect
130. #2185	C₂×C₁₃	semidirect
131. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
138. C₂³×C₁₃	SD₃₂	semidirect
173. C₂²×Q₁₆	C₂²×C₁₃	semidirect
178. C₂×SD₃₂	C₂²×C₁₃	semidirect
179. C₂²×C₁₆	C₂²×C₁₃	semidirect
183. #467	C₂²×C₁₃	semidirect
189. C₂×#107	C₂²×C₁₃	semidirect
192. #367	C₂²×C₁₃	semidirect
193. #358	C₂²×C₁₃	semidirect
194. #357	C₂²×C₁₃	semidirect
196. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
317. C₁₃	#33753	direct (N × H)
324. C₂³	C₁₃×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₁₃×#2235	2
C₁₃×#2233	2
C₁₃×#2217	2
C₁₃×#2187	2
C₁₃×#2185	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33753	13

Subgroups — C13×#33753 #15720092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33753 #15720092