Subgroups — C₁₃×#33844 #15720183

Order 3328.

674 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×#510	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, 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	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	C₁₃×#550	—	2	1	no	—
15	D₄×Q₈×C₁₃	—	2	1	no	—
16	C₁₃×#510	—	2	8	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
23	C₁₃×#494	C₂²	1	1	yes	characteristic
24	C₁₃×#493	C₂²	1	1	yes	characteristic
25	C₁₃×#467	C₂²	1	2	yes	—
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#462	—	2	1	no	—
28	C₁₃×#460	—	2	1	no	—
29	C₁₃×#451	—	2	2	no	—
30	C₁₃×#449	—	2	2	no	—
31	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#366	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	1	yes	characteristic
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
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	—	4	2	no	—
50	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	4	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#127	—	4	1	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	4	2	no	—
63	C₁₃×#121	—	2	2	no	—
64	C₁₃×#121	—	4	2	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×Q₈×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	4	1	no	—
68	C₄×D₄×C₁₃	—	4	1	no	—
69	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₁₃×Q₃₂	—	2	4	no	—
71	C₁₃×Q₃₂	D₄	1	4	yes	complemented
72	C₁₃×SD₃₂	—	2	4	no	—
73	C₁₃×SD₃₂	—	2	4	no	—
74	C₁₃×SD₃₂	—	4	2	no	—
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	1	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	#33844	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	1	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	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	—	2	1	no	—
108	C₁₃×Q₁₆	—	2	1	no	—
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	4	4	no	—
111	C₁₃×Q₁₆	—	8	1	no	—
112	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
113	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
114	C₁₃×SD₁₆	—	4	4	no	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	8	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₄⋊C₄	—	4	1	no	—
128	C₁₃×C₄⋊C₄	—	4	2	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	D₈	1	2	yes	—
134	C₄²×C₁₃	—	4	1	no	—
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	#3287	C₂×C₁₃	1	1	yes	characteristic
142	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2248	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2220	C₂×C₁₃	1	2	yes	complemented
145	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2189	C₂×C₁₃	1	2	yes	complemented
148	#2185	C₂×C₁₃	1	2	yes	complemented
149	C₄×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	C₂×D₈	1	2	yes	—
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	2	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	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	—	4	2	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	8	4	no	—
164	D₄×C₁₃	—	8	2	no	—
165	D₄×C₁₃	—	16	1	no	—
166	D₄×C₁₃	—	16	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₁₃	—	2	2	no	—
181	C₈×C₁₃	—	2	1	no	—
182	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×#135	C₂²×C₁₃	1	2	yes	—
185	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
186	#550	—	2	1	no	—
187	D₄×Q₈	—	2	1	no	—
188	#510	—	2	8	no	—
189	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
190	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
192	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
193	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
194	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
195	#494	C₂²×C₁₃	1	1	yes	characteristic
196	#493	C₂²×C₁₃	1	1	yes	characteristic
197	#467	C₂²×C₁₃	1	2	yes	—
198	#466	C₂²×C₁₃	1	2	yes	—
199	#462	—	2	1	no	—
200	#460	—	2	1	no	—
201	#451	—	2	2	no	—
202	#449	—	2	2	no	—
203	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
206	#366	C₂²×C₁₃	1	1	yes	characteristic
207	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
208	#358	C₂²×C₁₃	1	1	yes	characteristic
209	#358	C₂²×C₁₃	1	1	yes	characteristic
210	#358	C₂²×C₁₃	1	2	yes	—
211	#357	C₂²×C₁₃	1	2	yes	—
212	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
213	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	8	1	no	—
226	C₄×C₁₃	—	8	1	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	#510	1	2	yes	complemented
229	C₄×C₁₃	D₄²	1	1	yes	characteristic
230	C₄×C₁₃	#576	1	1	yes	characteristic
231	C₂×#41	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	#135	—	2	4	no	—
234	#135	—	4	2	no	—
235	C₂×Q₁₆	—	2	4	no	—
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	4	2	no	—
239	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
240	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	C₂³×C₁₃	1	2	yes	—
245	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	4	1	no	—
248	#127	—	2	1	no	—
249	#127	—	4	1	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	4	2	no	—
252	#121	—	2	2	no	—
253	#121	—	4	2	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×D₄	—	4	1	no	—
257	C₄×D₄	—	4	1	no	—
258	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
259	Q₃₂	—	2	4	no	—
260	Q₃₂	D₄×C₁₃	1	4	yes	complemented
261	SD₃₂	—	2	4	no	—
262	SD₃₂	—	2	4	no	—
263	SD₃₂	—	4	2	no	—
264	M₃₂	—	2	4	no	—
265	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
267	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
268	#107	C₂³×C₁₃	1	1	yes	characteristic
269	#107	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
271	#103	—	2	1	no	—
272	#103	—	2	1	no	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
276	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₁₃	—	4	2	no	—
278	C₂×C₁₃	—	16	2	no	—
279	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
280	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
281	C₂×C₁₃	#3416	1	1	yes	characteristic
282	#41	—	4	4	no	—
283	#41	—	8	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	—	2	1	no	—
301	Q₁₆	—	2	1	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	4	4	no	—
304	Q₁₆	—	8	1	no	—
305	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
306	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
307	SD₁₆	—	4	4	no	—
308	D₈	—	2	2	no	—
309	D₈	—	2	2	no	—
310	D₈	—	8	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₁₆	—	2	2	no	—
331	C₁₆	—	2	1	no	—
332	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
333	C₁₃	#33844	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	4	2	no	—
335	C₂³	C₂×C₁₃×D₈	1	2	yes	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	8	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	8	4	no	—
347	D₄	—	8	2	no	—
348	D₄	—	16	1	no	—
349	D₄	—	16	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
360	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
361	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	1	no	—
365	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₁₃×#510	1	2	yes	complemented
382	C₄	D₄²×C₁₃	1	1	yes	characteristic
383	C₄	C₁₃×#576	1	1	yes	characteristic
384	C₂	—	4	2	no	—
385	C₂	—	16	2	no	—
386	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
387	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
388	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3287	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
3. D₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2248	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2209	C₂	semidirect
7. C₁₃×#2207	C₂	semidirect
8. C₁₃×#2189	C₂	semidirect
9. C₁₃×#2185	C₂	semidirect
10. C₄×C₁₃×Q₃₂	C₂	semidirect
11. C₁₃×#2169	C₂	semidirect
71. C₁₃×Q₃₂	D₄	semidirect
88. #33844	C₁₃	direct (N × H)
140. C₂×#510	C₂×C₁₃	semidirect
142. D₄×Q₁₆	C₂×C₁₃	semidirect
143. #2248	C₂×C₁₃	semidirect
144. #2220	C₂×C₁₃	semidirect
145. #2209	C₂×C₁₃	semidirect
146. #2207	C₂×C₁₃	semidirect
147. #2189	C₂×C₁₃	semidirect
148. #2185	C₂×C₁₃	semidirect
149. C₄×Q₃₂	C₂×C₁₃	semidirect
150. #2169	C₂×C₁₃	semidirect
228. C₄×C₁₃	#510	semidirect
260. Q₃₂	D₄×C₁₃	semidirect
333. C₁₃	#33844	direct (N × H)
381. 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
C₁₃×#3287	2
D₄×C₁₃×Q₁₆	2
C₁₃×#2248	2
C₁₃×#2220	2
C₁₃×#2209	2
C₁₃×#2207	2
C₁₃×#2189	2
C₁₃×#2185	2
C₄×C₁₃×Q₃₂	2
C₁₃×#2169	2
#33844	13

Subgroups — C13×#33844 #15720183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33844 #15720183