Subgroups — C₁₃×#33842 #15720181

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2219	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2188	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	D₄×Q₈×C₁₃	—	2	1	no	—
15	C₁₃×#547	—	2	1	no	—
16	C₁₃×#510	—	2	8	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
23	C₁₃×#494	C₂²	1	1	yes	characteristic
24	C₁₃×#494	C₂²	1	1	yes	characteristic
25	C₁₃×#467	C₂²	1	2	yes	—
26	C₁₃×#467	C₂²	1	2	yes	—
27	C₁₃×#462	—	2	1	no	—
28	C₁₃×#461	—	2	1	no	—
29	C₁₃×#452	—	2	2	no	—
30	C₁₃×#451	—	2	2	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#367	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×#358	C₂²	1	1	yes	characteristic
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	1	yes	characteristic
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂²×Q₈×C₁₃	—	2	2	no	—
44	C₁₃×#135	—	2	4	no	—
45	C₁₃×#135	—	4	2	no	—
46	C₂×C₁₃×Q₁₆	—	2	4	no	—
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	4	1	no	—
60	C₁₃×#123	—	4	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	—	4	2	no	—
64	C₁₃×#121	—	4	1	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	4	1	no	—
68	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
70	C₁₃×Q₃₂	—	2	4	no	—
71	C₁₃×Q₃₂	—	2	4	no	—
72	C₁₃×Q₃₂	—	4	2	no	—
73	C₁₃×SD₃₂	—	2	4	no	—
74	C₁₃×SD₃₂	D₄	1	4	yes	complemented
75	C₁₃×M₃₂	—	2	4	no	—
76	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂³	1	1	yes	characteristic
80	C₁₃×#107	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₃×#103	—	2	1	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#102	—	2	1	no	—
86	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	#33842	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₁₃×#41	—	4	4	no	—
90	C₁₃×#41	—	8	2	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	4	4	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	8	2	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₁₃×Q₁₆	—	2	2	no	—
105	C₁₃×Q₁₆	—	2	2	no	—
106	C₁₃×Q₁₆	—	2	1	no	—
107	C₁₃×Q₁₆	—	2	2	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	4	4	no	—
110	C₁₃×Q₁₆	—	8	1	no	—
111	C₁₃×Q₁₆	—	8	1	no	—
112	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
113	C₁₃×SD₁₆	—	4	4	no	—
114	C₁₃×D₈	—	2	1	no	—
115	C₁₃×D₈	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
135	C₄²×C₁₃	—	4	1	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₁₃×C₁₆	—	2	2	no	—
138	C₁₃×C₁₆	—	2	1	no	—
139	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
140	C₂×#510	C₂×C₁₃	1	2	yes	complemented
141	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#3283	C₂×C₁₃	1	1	yes	characteristic
143	#2247	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2219	C₂×C₁₃	1	2	yes	complemented
145	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2208	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2189	C₂×C₁₃	1	2	yes	complemented
148	#2188	C₂×C₁₃	1	2	yes	complemented
149	C₄×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	C₂×D₈	1	2	yes	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	4	2	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	8	4	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	8	4	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	8	4	no	—
172	C₂×C₄×C₁₃	—	8	4	no	—
173	C₂×C₄×C₁₃	—	8	2	no	—
174	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	—	2	1	no	—
180	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×#135	C₂²×C₁₃	1	2	yes	—
183	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
184	D₄×Q₈	—	2	1	no	—
185	#547	—	2	1	no	—
186	#510	—	2	8	no	—
187	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
188	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
189	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
190	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
191	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
193	#494	C₂²×C₁₃	1	1	yes	characteristic
194	#494	C₂²×C₁₃	1	1	yes	characteristic
195	#467	C₂²×C₁₃	1	2	yes	—
196	#467	C₂²×C₁₃	1	2	yes	—
197	#462	—	2	1	no	—
198	#461	—	2	1	no	—
199	#452	—	2	2	no	—
200	#451	—	2	2	no	—
201	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
204	#367	C₂²×C₁₃	1	1	yes	characteristic
205	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
206	#358	C₂²×C₁₃	1	1	yes	characteristic
207	#358	C₂²×C₁₃	1	2	yes	—
208	#358	C₂²×C₁₃	1	2	yes	—
209	#357	C₂²×C₁₃	1	1	yes	characteristic
210	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
211	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₁₃	—	2	2	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₁₃	—	2	1	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	8	1	no	—
223	C₄×C₁₃	—	8	1	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	#510	1	2	yes	complemented
227	C₄×C₁₃	D₄²	1	1	yes	characteristic
228	C₄×C₁₃	#576	1	1	yes	characteristic
229	C₂×#41	—	2	2	no	—
230	C₂²×Q₈	—	2	2	no	—
231	#135	—	2	4	no	—
232	#135	—	4	2	no	—
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×Q₁₆	—	2	1	no	—
237	C₂×Q₁₆	—	4	2	no	—
238	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
239	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
240	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	4	1	no	—
247	#123	—	4	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	4	2	no	—
251	#121	—	4	1	no	—
252	C₄×Q₈	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	4	1	no	—
255	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	4	1	no	—
257	Q₃₂	—	2	4	no	—
258	Q₃₂	—	2	4	no	—
259	Q₃₂	—	4	2	no	—
260	SD₃₂	—	2	4	no	—
261	SD₃₂	D₄×C₁₃	1	4	yes	complemented
262	M₃₂	—	2	4	no	—
263	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
266	#107	C₂³×C₁₃	1	1	yes	characteristic
267	#107	C₂³×C₁₃	1	1	yes	characteristic
268	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
269	#103	—	2	1	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#102	—	2	1	no	—
273	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
274	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₁₃	—	4	2	no	—
276	C₂×C₁₃	—	8	2	no	—
277	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
279	C₂×C₁₃	#3417	1	1	yes	characteristic
280	#41	—	4	4	no	—
281	#41	—	8	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	8	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	2	1	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	4	4	no	—
301	Q₁₆	—	8	1	no	—
302	Q₁₆	—	8	1	no	—
303	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
304	SD₁₆	—	4	4	no	—
305	D₈	—	2	1	no	—
306	D₈	C₂×D₄×C₁₃	1	2	yes	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
311	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
326	C₄²	—	4	1	no	—
327	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₁₆	—	2	2	no	—
329	C₁₆	—	2	1	no	—
330	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
331	C₁₃	#33842	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	4	1	no	—
333	C₂³	C₂×C₁₃×D₈	1	2	yes	—
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	8	4	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	8	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
357	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	1	no	—
361	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	1	no	—
376	C₄	—	8	1	no	—
377	C₄	C₁₃×#510	1	2	yes	complemented
378	C₄	D₄²×C₁₃	1	1	yes	characteristic
379	C₄	C₁₃×#576	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
383	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
384	C₂	C₁₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3283	C₂
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×#510	C₂	semidirect
2. D₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2247	C₂	semidirect
5. C₁₃×#2219	C₂	semidirect
6. C₁₃×#2209	C₂	semidirect
7. C₁₃×#2208	C₂	semidirect
8. C₁₃×#2189	C₂	semidirect
9. C₁₃×#2188	C₂	semidirect
10. C₄×C₁₃×SD₃₂	C₂	semidirect
11. C₁₃×#2169	C₂	semidirect
74. C₁₃×SD₃₂	D₄	semidirect
88. #33842	C₁₃	direct (N × H)
140. C₂×#510	C₂×C₁₃	semidirect
141. D₄×Q₁₆	C₂×C₁₃	semidirect
143. #2247	C₂×C₁₃	semidirect
144. #2219	C₂×C₁₃	semidirect
145. #2209	C₂×C₁₃	semidirect
146. #2208	C₂×C₁₃	semidirect
147. #2189	C₂×C₁₃	semidirect
148. #2188	C₂×C₁₃	semidirect
149. C₄×SD₃₂	C₂×C₁₃	semidirect
150. #2169	C₂×C₁₃	semidirect
226. C₄×C₁₃	#510	semidirect
261. SD₃₂	D₄×C₁₃	semidirect
331. C₁₃	#33842	direct (N × H)
377. C₄	C₁₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#510	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3283	2
C₁₃×#2247	2
C₁₃×#2219	2
C₁₃×#2209	2
C₁₃×#2208	2
C₁₃×#2189	2
C₁₃×#2188	2
C₄×C₁₃×SD₃₂	2
C₁₃×#2169	2
#33842	13

Subgroups — C13×#33842 #15720181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33842 #15720181