Subgroups — C₁₃×#33788 #15720127

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2207	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#541	—	2	1	no	—
16	C₁₃×#535	—	2	1	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
21	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#496	—	2	1	no	—
23	C₁₃×#496	—	2	1	no	—
24	C₁₃×#495	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	1	yes	characteristic
26	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#493	C₂²	1	1	yes	characteristic
28	C₁₃×#493	C₂²	1	1	yes	characteristic
29	C₁₃×#491	—	2	1	no	—
30	C₁₃×#470	—	2	1	no	—
31	C₁₃×#467	C₂²	1	2	yes	—
32	C₁₃×#441	—	2	1	no	—
33	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
34	C₁₃×#405	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	1	no	—
52	C₂×C₁₃×SD₁₆	—	2	1	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	4	2	no	—
57	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×#127	—	2	1	no	—
64	C₁₃×#127	—	2	1	no	—
65	C₁₃×#126	—	4	2	no	—
66	C₁₃×#125	—	2	1	no	—
67	C₁₃×#125	—	4	2	no	—
68	C₁₃×#124	—	2	1	no	—
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×C₂²⋊Q₈	—	2	2	no	—
71	C₁₃×#121	—	4	2	no	—
72	C₁₃×#120	—	4	2	no	—
73	C₄×Q₈×C₁₃	—	2	2	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₁₃×Q₃₂	—	4	2	no	—
76	C₁₃×SD₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	—	4	2	no	—
78	C₁₃×SD₃₂	—	4	2	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₁₃×#107	C₂³	1	2	yes	—
82	C₁₃×#106	—	2	1	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#97	D₄	1	1	yes	characteristic
86	C₁₃×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33788	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	—	2	2	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	4	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×SD₁₆	—	4	2	no	—
112	C₁₃×SD₁₆	—	4	2	no	—
113	C₁₃×D₈	—	2	2	no	—
114	C₁₃×D₈	—	2	2	no	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	4	2	no	—
117	C₁₃×D₈	—	4	2	no	—
118	C₁₃×D₈	—	4	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
135	C₄²×C₁₃	—	4	2	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	#3177	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#3155	C₂×C₁₃	1	1	yes	characteristic
142	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2248	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2244	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2242	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2211	C₂×C₁₃	1	2	yes	complemented
147	#2207	C₂×C₁₃	1	2	yes	complemented
148	#2189	C₂×C₁₃	1	2	yes	complemented
149	#2187	C₂×C₁₃	1	2	yes	complemented
150	#2164	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	8	2	no	—
155	C₂³×C₁₃	—	16	2	no	—
156	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
157	Q₈×C₁₃	—	4	1	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	4	1	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	8	2	no	—
168	D₄×C₁₃	—	8	2	no	—
169	D₄×C₁₃	—	16	2	no	—
170	D₄×C₁₃	—	16	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	8	2	no	—
177	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₁₃	—	2	1	no	—
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
185	C₂×AGL(1,ℤ/8)	—	2	1	no	—
186	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
188	#541	—	2	1	no	—
189	#535	—	2	1	no	—
190	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
191	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
192	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
193	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
194	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	#496	—	2	1	no	—
196	#496	—	2	1	no	—
197	#495	C₂²×C₁₃	1	1	yes	characteristic
198	#495	C₂²×C₁₃	1	1	yes	characteristic
199	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
200	#493	C₂²×C₁₃	1	1	yes	characteristic
201	#493	C₂²×C₁₃	1	1	yes	characteristic
202	#491	—	2	1	no	—
203	#470	—	2	1	no	—
204	#467	C₂²×C₁₃	1	2	yes	—
205	#441	—	2	1	no	—
206	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
207	#405	C₂²×C₁₃	1	1	yes	characteristic
208	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
209	#358	C₂²×C₁₃	1	2	yes	complemented
210	#357	C₂²×C₁₃	1	2	yes	—
211	#357	C₂²×C₁₃	1	2	yes	—
212	#357	C₂²×C₁₃	1	2	yes	complemented
213	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
214	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
215	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	1	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	—	16	4	no	—
225	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	#535	1	1	yes	characteristic
233	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×#41	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	AGL(1,ℤ/8)	—	4	4	no	—
237	#135	—	4	2	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	4	2	no	—
248	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₄⋊Q₈	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#126	—	4	2	no	—
257	#125	—	2	1	no	—
258	#125	—	4	2	no	—
259	#124	—	2	1	no	—
260	#124	—	2	1	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	#121	—	4	2	no	—
263	#120	—	4	2	no	—
264	C₄×Q₈	—	2	2	no	—
265	#117	D₄×C₁₃	1	1	yes	characteristic
266	Q₃₂	—	4	2	no	—
267	SD₃₂	—	4	2	no	—
268	SD₃₂	—	4	2	no	—
269	SD₃₂	—	4	2	no	—
270	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
271	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
272	#107	C₂³×C₁₃	1	2	yes	—
273	#106	—	2	1	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#97	D₄×C₁₃	1	1	yes	characteristic
277	#97	D₄×C₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₁₃	—	4	1	no	—
281	C₂×C₁₃	—	16	1	no	—
282	C₂×C₁₃	—	16	1	no	—
283	C₂×C₁₃	—	16	1	no	—
284	C₂×C₁₃	#3205	1	1	yes	characteristic
285	C₂×C₁₃	#3416	1	2	yes	—
286	C₂⁴	—	4	1	no	—
287	#41	—	4	2	no	—
288	#41	—	4	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	4	2	no	—
306	SD₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	2	no	—
313	D₈	—	4	2	no	—
314	D₈	—	4	2	no	—
315	M₁₆	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
331	C₄²	—	4	2	no	—
332	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₁₃	#33788	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	16	2	no	—
342	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
343	Q₈	—	4	1	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	16	2	no	—
356	D₄	—	16	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
364	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
365	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
370	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	C₁₃×#535	1	1	yes	characteristic
388	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂	—	4	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	1	no	—
393	C₂	C₁₃×#3205	1	1	yes	characteristic
394	C₂	C₁₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3177	C₂	semidirect
3. C₁₃×#2251	C₂	semidirect
4. C₁₃×#2248	C₂	semidirect
5. C₁₃×#2244	C₂	semidirect
6. C₁₃×#2242	C₂	semidirect
7. C₁₃×#2211	C₂	semidirect
8. C₁₃×#2207	C₂	semidirect
9. C₁₃×#2189	C₂	semidirect
10. C₁₃×#2187	C₂	semidirect
11. C₁₃×#2164	C₂	semidirect
17. C₂×C₁₃×Q₃₂	C₂²	semidirect
20. C₂×C₁₃×SD₃₂	C₂²	semidirect
21. C₁₃×#499	C₂²	semidirect
26. C₁₃×#494	C₂²	semidirect
33. C₄×C₁₃×Q₁₆	C₂²	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
41. C₁₃×#346	C₂²	semidirect
42. C₄×C₁₃×C₁₆	C₂²	semidirect
89. #33788	C₁₃	direct (N × H)
140. #3177	C₂×C₁₃	semidirect
142. #2251	C₂×C₁₃	semidirect
143. #2248	C₂×C₁₃	semidirect
144. #2244	C₂×C₁₃	semidirect
145. #2242	C₂×C₁₃	semidirect
146. #2211	C₂×C₁₃	semidirect
147. #2207	C₂×C₁₃	semidirect
148. #2189	C₂×C₁₃	semidirect
149. #2187	C₂×C₁₃	semidirect
150. #2164	C₂×C₁₃	semidirect
190. C₂×Q₃₂	C₂²×C₁₃	semidirect
193. C₂×SD₃₂	C₂²×C₁₃	semidirect
194. #499	C₂²×C₁₃	semidirect
199. #494	C₂²×C₁₃	semidirect
206. C₄×Q₁₆	C₂²×C₁₃	semidirect
208. C₄⋊C₁₆	C₂²×C₁₃	semidirect
209. #358	C₂²×C₁₃	semidirect
212. #357	C₂²×C₁₃	semidirect
214. #346	C₂²×C₁₃	semidirect
215. C₄×C₁₆	C₂²×C₁₃	semidirect
336. C₁₃	#33788	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3177	2
C₁₃×#3155	2
C₁₃×#2251	2
C₁₃×#2248	2
C₁₃×#2244	2
C₁₃×#2242	2
C₁₃×#2211	2
C₁₃×#2207	2
C₁₃×#2189	2
C₁₃×#2187	2
C₁₃×#2164	2
#33788	13

Subgroups — C13×#33788 #15720127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33788 #15720127