Subgroups — C₁₃×#33702 #15720041

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2244	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2243	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2242	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2240	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2108	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×#544	—	2	1	no	—
16	C₁₃×#535	—	2	1	no	—
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₁₃×#501	—	2	2	no	—
20	C₁₃×#500	C₂²	1	2	yes	complemented
21	C₁₃×#499	C₂²	1	2	yes	complemented
22	C₁₃×#496	—	2	2	no	—
23	C₁₃×#495	C₂²	1	2	yes	—
24	C₁₃×#493	C₂²	1	2	yes	—
25	C₁₃×#428	—	2	1	no	—
26	C₁₃×#427	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₁₃×#405	C₂²	1	1	yes	characteristic
29	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#358	C₂²	1	2	yes	complemented
31	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#357	C₂²	1	2	yes	—
33	C₁₃×#357	C₂²	1	2	yes	—
34	C₁₃×#357	C₂²	1	2	yes	—
35	C₁₃×#357	C₂²	1	2	yes	—
36	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#357	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#346	C₂²	1	2	yes	complemented
40	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
44	C₁₃×#135	—	2	2	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	1	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	C₂³	1	2	yes	—
54	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	4	1	no	—
59	C₁₃×#127	—	2	2	no	—
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	4	1	no	—
62	C₁₃×#124	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	—	4	2	no	—
64	C₁₃×#121	—	4	1	no	—
65	C₁₃×#121	—	4	1	no	—
66	C₁₃×#120	—	4	2	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₁₃×M₃₂	—	2	2	no	—
71	C₂×C₁₃×C₁₆	—	2	2	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	1	no	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#107	C₂³	1	2	yes	—
78	C₁₃×#107	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂³	1	1	yes	characteristic
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#97	D₄	1	2	yes	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	#33702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	4	1	no	—
86	C₁₃×#41	—	4	2	no	—
87	C₁₃×#41	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₁₃×Q₁₆	—	2	1	no	—
102	C₁₃×Q₁₆	—	2	1	no	—
103	C₁₃×SD₁₆	—	4	2	no	—
104	C₁₃×SD₁₆	—	4	4	no	—
105	C₁₃×D₈	—	2	2	no	—
106	C₁₃×D₈	—	2	2	no	—
107	C₁₃×D₈	—	2	1	no	—
108	C₁₃×D₈	—	2	1	no	—
109	C₁₃×D₈	—	4	2	no	—
110	C₁₃×D₈	—	4	4	no	—
111	C₁₃×M₁₆	SD₁₆	1	4	yes	—
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃	#41	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	2	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₄⋊C₄	—	4	2	no	—
124	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
125	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
130	C₄²×C₁₃	—	4	1	no	—
131	C₄²×C₁₃	C₂×D₄	1	2	yes	—
132	C₁₃×C₁₆	—	2	1	no	—
133	C₁₃×C₁₆	—	2	1	no	—
134	C₁₃×C₁₆	—	2	2	no	—
135	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#3155	C₂×C₁₃	1	1	yes	characteristic
137	#2244	C₂×C₁₃	1	2	yes	complemented
138	#2243	C₂×C₁₃	1	2	yes	complemented
139	#2242	C₂×C₁₃	1	2	yes	complemented
140	#2240	C₂×C₁₃	1	2	yes	complemented
141	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2108	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	1	no	—
148	C₂³×C₁₃	—	8	2	no	—
149	C₂³×C₁₃	—	16	1	no	—
150	C₂³×C₁₃	—	16	1	no	—
151	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	1	no	—
153	Q₈×C₁₃	—	4	1	no	—
154	Q₈×C₁₃	—	16	2	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	4	1	no	—
157	D₄×C₁₃	—	4	1	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	8	2	no	—
160	D₄×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	16	2	no	—
162	D₄×C₁₃	—	16	2	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	—	16	1	no	—
169	C₂×C₄×C₁₃	#124	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₁₃	#124	1	2	yes	—
176	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
177	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×AGL(1,ℤ/8)	—	2	1	no	—
180	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
181	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
182	#544	—	2	1	no	—
183	#535	—	2	1	no	—
184	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
186	#501	—	2	2	no	—
187	#500	C₂²×C₁₃	1	2	yes	complemented
188	#499	C₂²×C₁₃	1	2	yes	complemented
189	#496	—	2	2	no	—
190	#495	C₂²×C₁₃	1	2	yes	—
191	#493	C₂²×C₁₃	1	2	yes	—
192	#428	—	2	1	no	—
193	#427	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
195	#405	C₂²×C₁₃	1	1	yes	characteristic
196	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
197	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
198	#358	C₂²×C₁₃	1	2	yes	complemented
199	#357	C₂²×C₁₃	1	2	yes	—
200	#357	C₂²×C₁₃	1	2	yes	—
201	#357	C₂²×C₁₃	1	2	yes	—
202	#357	C₂²×C₁₃	1	2	yes	—
203	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
204	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	#357	C₂²×C₁₃	1	2	yes	complemented
206	#346	C₂²×C₁₃	1	2	yes	complemented
207	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	1	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	1	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	16	4	no	—
217	C₂²×C₁₃	#486	1	2	yes	—
218	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	8	1	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	—	8	1	no	—
224	C₄×C₁₃	—	8	1	no	—
225	C₄×C₁₃	#486	1	2	yes	—
226	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
227	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
228	C₂×#41	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	AGL(1,ℤ/8)	—	4	4	no	—
231	#135	—	2	2	no	—
232	#135	—	2	2	no	—
233	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×SD₁₆	—	2	1	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	C₂³×C₁₃	1	2	yes	—
241	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	4	1	no	—
246	#127	—	2	2	no	—
247	#125	—	2	2	no	—
248	#125	—	4	1	no	—
249	#124	—	2	2	no	—
250	C₂²⋊Q₈	—	4	2	no	—
251	#121	—	4	1	no	—
252	#121	—	4	1	no	—
253	#120	—	4	2	no	—
254	#117	—	2	1	no	—
255	#117	D₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	2	1	no	—
257	M₃₂	—	2	2	no	—
258	C₂×C₁₆	—	2	2	no	—
259	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
261	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
262	#107	—	2	1	no	—
263	#107	—	2	2	no	—
264	#107	C₂³×C₁₃	1	2	yes	—
265	#107	C₂³×C₁₃	1	1	yes	characteristic
266	#107	C₂³×C₁₃	1	1	yes	characteristic
267	#106	—	2	1	no	—
268	#106	—	2	2	no	—
269	#97	D₄×C₁₃	1	2	yes	—
270	C₄×C₈	C₂³×C₁₃	1	2	yes	—
271	C₂×C₁₃	—	2	2	no	—
272	C₂×C₁₃	—	16	1	no	—
273	C₂×C₁₃	—	16	2	no	—
274	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
275	C₂×C₁₃	#3415	1	1	yes	characteristic
276	C₂×C₁₃	#3416	1	1	yes	characteristic
277	C₂⁴	—	4	1	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
293	Q₁₆	—	2	1	no	—
294	Q₁₆	—	2	1	no	—
295	SD₁₆	—	4	2	no	—
296	SD₁₆	—	4	4	no	—
297	D₈	—	2	2	no	—
298	D₈	—	2	2	no	—
299	D₈	—	2	1	no	—
300	D₈	—	2	1	no	—
301	D₈	—	4	2	no	—
302	D₈	—	4	4	no	—
303	M₁₆	C₁₃×SD₁₆	1	4	yes	—
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
306	C₂×C₈	C₁₃×#41	1	2	yes	—
307	C₂×C₈	C₁₃×#41	1	2	yes	—
308	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
317	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
322	C₄²	—	4	1	no	—
323	C₄²	C₂×D₄×C₁₃	1	2	yes	—
324	C₁₆	—	2	1	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	2	no	—
327	C₁₃	#33702	1	1	yes	characteristic, direct product factor, Sylow
328	C₂³	—	4	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	8	2	no	—
331	C₂³	—	16	1	no	—
332	C₂³	—	16	1	no	—
333	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
334	Q₈	—	4	1	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	16	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	D₄	—	16	2	no	—
344	D₄	—	16	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	16	1	no	—
351	C₂×C₄	C₁₃×#124	1	2	yes	—
352	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	C₈	C₁₃×#124	1	2	yes	—
358	C₈	C₂×C₁₃×SD₁₆	1	4	yes	—
359	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
360	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	C₁₃×#486	1	2	yes	—
371	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	C₁₃×#486	1	2	yes	—
379	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
380	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	16	2	no	—
383	C₂	—	16	1	no	—
384	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
385	C₂	C₁₃×#3415	1	1	yes	characteristic
386	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×#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×#3164	C₂	semidirect
3. C₁₃×#2244	C₂	semidirect
4. C₁₃×#2243	C₂	semidirect
5. C₁₃×#2242	C₂	semidirect
6. C₁₃×#2240	C₂	semidirect
7. C₁₃×#2140	C₂	semidirect
8. C₁₃×#2139	C₂	semidirect
9. C₁₃×#2138	C₂	semidirect
10. C₂×C₁₃×#357	C₂	semidirect
11. C₁₃×#2108	C₂	semidirect
20. C₁₃×#500	C₂²	semidirect
21. C₁₃×#499	C₂²	semidirect
29. C₁₃×#358	C₂²	semidirect
30. C₁₃×#358	C₂²	semidirect
31. C₁₃×#358	C₂²	semidirect
36. C₁₃×#357	C₂²	semidirect
37. C₁₃×#357	C₂²	semidirect
38. C₁₃×#357	C₂²	semidirect
39. C₁₃×#346	C₂²	semidirect
40. C₄×C₁₃×C₁₆	C₂²	semidirect
84. #33702	C₁₃	direct (N × H)
135. #3164	C₂×C₁₃	semidirect
137. #2244	C₂×C₁₃	semidirect
138. #2243	C₂×C₁₃	semidirect
139. #2242	C₂×C₁₃	semidirect
140. #2240	C₂×C₁₃	semidirect
141. #2140	C₂×C₁₃	semidirect
142. #2139	C₂×C₁₃	semidirect
143. #2138	C₂×C₁₃	semidirect
144. C₂×#357	C₂×C₁₃	semidirect
145. #2108	C₂×C₁₃	semidirect
187. #500	C₂²×C₁₃	semidirect
188. #499	C₂²×C₁₃	semidirect
196. #358	C₂²×C₁₃	semidirect
197. #358	C₂²×C₁₃	semidirect
198. #358	C₂²×C₁₃	semidirect
203. #357	C₂²×C₁₃	semidirect
204. #357	C₂²×C₁₃	semidirect
205. #357	C₂²×C₁₃	semidirect
206. #346	C₂²×C₁₃	semidirect
207. C₄×C₁₆	C₂²×C₁₃	semidirect
327. C₁₃	#33702	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×#3164	2
C₁₃×#3155	2
C₁₃×#2244	2
C₁₃×#2243	2
C₁₃×#2242	2
C₁₃×#2240	2
C₁₃×#2140	2
C₁₃×#2139	2
C₁₃×#2138	2
C₂×C₁₃×#357	2
C₁₃×#2108	2
#33702	13

Subgroups — C13×#33702 #15720041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33702 #15720041