Subgroups — C₁₃×#33584 #15719923

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 370 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	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2211	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2210	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×SD₁₆	—	2	1	no	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	—	2	1	no	—
15	C₄×C₁₃×#41	—	2	1	no	—
16	C₁₃×#510	—	2	4	no	—
17	C₁₃×#509	—	2	4	no	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
21	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
22	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
24	C₁₃×#495	—	2	2	no	—
25	C₁₃×#495	C₂²	1	4	yes	—
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
27	C₄×C₁₃×SD₁₆	—	2	2	no	—
28	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
29	C₁₃×#427	C₂²	1	1	yes	characteristic
30	C₁₃×#416	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
33	C₁₃×#358	C₂²	1	4	yes	complemented
34	C₁₃×#357	C₂²	1	4	yes	—
35	C₂×C₁₃×#41	—	2	1	no	—
36	C₂²×Q₈×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₁₃×#135	—	2	2	no	—
39	C₁₃×#135	D₄	1	4	yes	—
40	C₂×C₁₃×Q₁₆	—	2	2	no	—
41	C₂×C₁₃×Q₁₆	—	2	1	no	—
42	C₂×C₁₃×Q₁₆	—	2	2	no	—
43	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
44	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×SD₁₆	—	2	4	no	—
47	C₂×C₁₃×SD₁₆	—	4	4	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	C₂³	1	2	yes	—
52	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#124	—	2	4	no	—
56	C₁₃×#124	—	4	1	no	—
57	C₁₃×#124	—	4	1	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	—	4	1	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
64	C₂×C₄²×C₁₃	—	4	1	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₁₃×Q₃₂	—	2	4	no	—
67	C₁₃×SD₃₂	—	2	4	no	—
68	C₁₃×SD₃₂	—	2	4	no	—
69	C₁₃×D₁₆	—	2	4	no	—
70	C₁₃×M₃₂	—	2	2	no	—
71	C₁₃×M₃₂	—	2	2	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₁₃×#107	C₂³	1	2	yes	—
75	C₁₃×#106	—	2	1	no	—
76	C₁₃×#103	—	2	2	no	—
77	C₁₃×#102	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	2	yes	—
79	C₄×C₈×C₁₃	C₂³	1	2	yes	—
80	#33584	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	4	1	no	—
82	C₁₃×#41	—	2	4	no	—
83	C₁₃×#41	—	4	2	no	—
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	4	2	no	—
89	C₂×D₄×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	—	4	1	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	D₈	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×Q₁₆	—	2	1	no	—
102	C₁₃×Q₁₆	—	2	2	no	—
103	C₁₃×Q₁₆	—	4	2	no	—
104	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
105	C₁₃×SD₁₆	—	2	4	no	—
106	C₁₃×SD₁₆	—	4	8	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	2	1	no	—
109	C₁₃×D₈	—	2	2	no	—
110	C₁₃×D₈	—	4	2	no	—
111	C₁₃×D₈	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	#41	1	2	yes	—
117	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₄²×C₁₃	—	4	1	no	—
125	C₄²×C₁₃	—	4	2	no	—
126	C₄²×C₁₃	D₈	1	1	yes	characteristic
127	C₄²×C₁₃	D₈	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	2	yes	—
129	C₁₃×C₁₆	—	2	2	no	—
130	C₁₃×C₁₆	—	2	2	no	—
131	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×#509	C₂×C₁₃	1	1	yes	characteristic
133	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#2211	C₂×C₁₃	1	4	yes	complemented
136	#2210	C₂×C₁₃	1	4	yes	complemented
137	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2141	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	8	4	no	—
143	C₂³×C₁₃	—	8	2	no	—
144	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	2	no	—
146	Q₈×C₁₃	—	4	1	no	—
147	Q₈×C₁₃	—	4	2	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	8	2	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	4	4	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	1	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	8	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	8	4	no	—
162	C₂×C₄×C₁₃	—	8	2	no	—
163	C₂×C₄×C₁₃	#121	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	#121	1	2	yes	—
171	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
174	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×SD₁₆	—	2	1	no	—
176	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
177	C₂×#124	—	2	1	no	—
178	C₄×#41	—	2	1	no	—
179	#510	—	2	4	no	—
180	#509	—	2	4	no	—
181	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
182	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
183	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
184	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
185	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
187	#495	—	2	2	no	—
188	#495	C₂²×C₁₃	1	4	yes	—
189	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
190	C₄×SD₁₆	—	2	2	no	—
191	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
192	#427	C₂²×C₁₃	1	1	yes	characteristic
193	#416	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
196	#358	C₂²×C₁₃	1	4	yes	complemented
197	#357	C₂²×C₁₃	1	4	yes	—
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	—	4	2	no	—
200	C₂²×C₁₃	—	8	2	no	—
201	C₂²×C₁₃	—	8	4	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	16	4	no	—
204	C₂²×C₁₃	#459	1	2	yes	—
205	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
206	C₄×C₁₃	—	2	2	no	—
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	4	2	no	—
209	C₄×C₁₃	—	8	2	no	—
210	C₄×C₁₃	—	8	2	no	—
211	C₄×C₁₃	#459	1	2	yes	—
212	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
213	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×#41	—	2	1	no	—
215	C₂²×Q₈	—	2	1	no	—
216	C₂²×D₄	—	2	1	no	—
217	#135	—	2	2	no	—
218	#135	D₄×C₁₃	1	4	yes	—
219	C₂×Q₁₆	—	2	2	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	—	2	2	no	—
222	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
223	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	4	4	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	C₂³×C₁₃	1	2	yes	—
231	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
232	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
234	#124	—	2	4	no	—
235	#124	—	4	1	no	—
236	#124	—	4	1	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	4	2	no	—
240	#117	—	2	1	no	—
241	#117	—	4	1	no	—
242	C₂×C₂²⋊C₄	—	4	2	no	—
243	C₂×C₄²	—	4	1	no	—
244	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
245	Q₃₂	—	2	4	no	—
246	SD₃₂	—	2	4	no	—
247	SD₃₂	—	2	4	no	—
248	D₁₆	—	2	4	no	—
249	M₃₂	—	2	2	no	—
250	M₃₂	—	2	2	no	—
251	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
252	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
253	#107	C₂³×C₁₃	1	2	yes	—
254	#106	—	2	1	no	—
255	#103	—	2	2	no	—
256	#102	—	2	2	no	—
257	C₄×C₈	D₄×C₁₃	1	2	yes	—
258	C₄×C₈	C₂³×C₁₃	1	2	yes	—
259	C₂×C₁₃	—	2	2	no	—
260	C₂×C₁₃	—	8	2	no	—
261	C₂×C₁₃	—	16	2	no	—
262	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
263	C₂×C₁₃	#3414	1	2	yes	—
264	C₂⁴	—	4	1	no	—
265	#41	—	2	4	no	—
266	#41	—	4	2	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₁₃×D₈	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	2	1	no	—
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	4	2	no	—
287	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
288	SD₁₆	—	2	4	no	—
289	SD₁₆	—	4	8	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	—	4	2	no	—
294	D₈	C₂×D₄×C₁₃	1	2	yes	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
299	C₂×C₈	C₁₃×#41	1	2	yes	—
300	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	2	no	—
309	C₄²	C₁₃×D₈	1	1	yes	characteristic
310	C₄²	C₁₃×D₈	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃	1	2	yes	—
312	C₁₆	—	2	2	no	—
313	C₁₆	—	2	2	no	—
314	C₁₃	#33584	1	1	yes	characteristic, direct product factor, Sylow
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	8	4	no	—
318	C₂³	—	8	2	no	—
319	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
320	Q₈	—	2	2	no	—
321	Q₈	—	4	1	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	C₁₃×#121	1	2	yes	—
339	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
340	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
341	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
342	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	C₁₃×#121	1	2	yes	—
346	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
348	C₂²	—	2	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	4	no	—
353	C₂²	—	16	4	no	—
354	C₂²	C₁₃×#459	1	2	yes	—
355	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	C₁₃×#459	1	2	yes	—
362	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
363	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	—	16	2	no	—
367	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
368	C₂	C₁₃×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#509	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×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. C₂×C₁₃×#495	C₂	semidirect
4. C₄×C₁₃×#135	C₂	semidirect
5. C₁₃×#2211	C₂	semidirect
6. C₁₃×#2210	C₂	semidirect
7. C₁₃×#2150	C₂	semidirect
8. C₁₃×#2141	C₂	semidirect
9. C₁₃×#2140	C₂	semidirect
18. C₂×C₁₃×Q₃₂	C₂²	semidirect
20. C₂×C₁₃×SD₃₂	C₂²	semidirect
26. C₄×C₁₃×Q₁₆	C₂²	semidirect
28. C₄×C₁₃×D₈	C₂²	semidirect
32. C₁₃×C₄⋊C₁₆	C₂²	semidirect
33. C₁₃×#358	C₂²	semidirect
80. #33584	C₁₃	direct (N × H)
131. C₂×#510	C₂×C₁₃	semidirect
133. C₂×#495	C₂×C₁₃	semidirect
134. C₄×#135	C₂×C₁₃	semidirect
135. #2211	C₂×C₁₃	semidirect
136. #2210	C₂×C₁₃	semidirect
137. #2150	C₂×C₁₃	semidirect
138. #2141	C₂×C₁₃	semidirect
139. #2140	C₂×C₁₃	semidirect
181. C₂×Q₃₂	C₂²×C₁₃	semidirect
183. C₂×SD₃₂	C₂²×C₁₃	semidirect
189. C₄×Q₁₆	C₂²×C₁₃	semidirect
191. C₄×D₈	C₂²×C₁₃	semidirect
195. C₄⋊C₁₆	C₂²×C₁₃	semidirect
196. #358	C₂²×C₁₃	semidirect
314. C₁₃	#33584	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×#510	2
C₂×C₁₃×#509	2
C₂×C₁₃×#495	2
C₄×C₁₃×#135	2
C₁₃×#2211	2
C₁₃×#2210	2
C₁₃×#2150	2
C₁₃×#2141	2
C₁₃×#2140	2
#33584	13

Subgroups — C13×#33584 #15719923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33584 #15719923