Subgroups — C₁₃×#33892 #15720231

Order 3328.

620 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	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2140	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₁₃×#555	—	2	1	no	—
14	D₄²×C₁₃	—	2	1	no	—
15	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
17	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
18	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#493	C₂²	1	1	yes	characteristic
20	C₁₃×#482	—	2	2	no	—
21	C₁₃×#476	—	2	1	no	—
22	C₁₃×#466	C₂²	1	2	yes	—
23	C₁₃×#466	C₂²	1	2	yes	complemented
24	C₁₃×#459	—	2	1	no	—
25	C₁₃×#447	—	2	2	no	—
26	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
28	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#427	C₂²	1	2	yes	complemented
30	C₁₃×#367	C₂²	1	2	yes	complemented
31	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#357	C₂²	1	1	yes	characteristic
34	C₁₃×#357	C₂²	1	2	yes	—
35	C₁₃×#357	C₂²	1	2	yes	complemented
36	C₁₃×#357	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	4	1	no	—
43	C₂×C₁₃×D₈	—	2	4	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	1	no	—
46	C₂×C₁₃×D₈	—	4	2	no	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×#127	—	2	1	no	—
53	C₁₃×#124	—	4	2	no	—
54	C₁₃×#121	—	2	2	no	—
55	C₁₃×#121	—	2	2	no	—
56	C₁₃×#121	—	4	1	no	—
57	C₁₃×#121	—	4	1	no	—
58	C₁₃×#120	—	4	2	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
62	C₁₃×#117	—	2	2	no	—
63	C₁₃×#117	—	4	1	no	—
64	C₁₃×D₁₆	—	2	2	no	—
65	C₁₃×D₁₆	—	4	2	no	—
66	C₁₃×M₃₂	—	4	2	no	—
67	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
70	C₁₃×#107	—	2	1	no	—
71	C₁₃×#107	C₂³	1	1	yes	characteristic
72	C₁₃×#107	C₂³	1	2	yes	—
73	C₁₃×#107	C₂³	1	1	yes	characteristic
74	C₁₃×#106	—	2	2	no	—
75	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₁₃×#102	—	2	1	no	—
77	C₁₃×#102	—	2	1	no	—
78	C₁₃×#102	—	2	2	no	—
79	C₁₃×#102	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#33892	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	4	2	no	—
84	C₂×Q₈×C₁₃	—	4	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	4	4	no	—
89	C₂×D₄×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	8	2	no	—
95	C₂×D₄×C₁₃	—	8	4	no	—
96	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₁₃×D₈	—	2	1	no	—
101	C₁₃×D₈	—	2	2	no	—
102	C₁₃×D₈	—	2	1	no	—
103	C₁₃×D₈	—	2	1	no	—
104	C₁₃×D₈	—	2	2	no	—
105	C₁₃×D₈	—	4	4	no	—
106	C₁₃×D₈	—	8	1	no	—
107	C₁₃×D₈	#41	1	2	yes	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
118	C₁₃×C₂²⋊C₄	—	4	2	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
124	C₄²×C₁₃	—	4	2	no	—
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×C₁₆	—	2	1	no	—
127	C₁₃×C₁₆	—	2	1	no	—
128	C₁₃×C₁₆	—	2	2	no	—
129	#3341	C₂×C₁₃	1	1	yes	characteristic, complemented
130	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#2240	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2234	C₂×C₁₃	1	2	yes	complemented
133	#2226	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2218	C₂×C₁₃	1	2	yes	complemented
135	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2184	C₂×C₁₃	1	2	yes	complemented
137	C₄×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2140	C₂×C₁₃	1	2	yes	complemented
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	1	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	8	4	no	—
144	C₂³×C₁₃	—	8	4	no	—
145	C₂³×C₁₃	—	16	2	no	—
146	C₂³×C₁₃	C₂×D₈	1	2	yes	—
147	Q₈×C₁₃	—	16	1	no	—
148	D₄×C₁₃	—	2	2	no	—
149	D₄×C₁₃	—	2	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	1	no	—
155	D₄×C₁₃	—	8	4	no	—
156	D₄×C₁₃	—	8	4	no	—
157	D₄×C₁₃	—	8	2	no	—
158	D₄×C₁₃	—	16	1	no	—
159	D₄×C₁₃	—	16	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	8	2	no	—
166	C₂×C₄×C₁₃	—	8	2	no	—
167	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₃	—	2	2	no	—
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
176	#555	—	2	1	no	—
177	D₄²	—	2	1	no	—
178	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
180	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
181	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
182	#493	C₂²×C₁₃	1	1	yes	characteristic
183	#482	—	2	2	no	—
184	#476	—	2	1	no	—
185	#466	C₂²×C₁₃	1	2	yes	—
186	#466	C₂²×C₁₃	1	2	yes	complemented
187	#459	—	2	1	no	—
188	#447	—	2	2	no	—
189	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
191	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
192	#427	C₂²×C₁₃	1	2	yes	complemented
193	#367	C₂²×C₁₃	1	2	yes	complemented
194	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
196	#357	C₂²×C₁₃	1	1	yes	characteristic
197	#357	C₂²×C₁₃	1	2	yes	—
198	#357	C₂²×C₁₃	1	2	yes	complemented
199	#357	C₂²×C₁₃	1	2	yes	complemented
200	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
201	#357	C₂²×C₁₃	1	2	yes	complemented
202	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
203	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	4	2	no	—
208	C₂²×C₁₃	—	8	1	no	—
209	C₂²×C₁₃	—	8	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	2	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	16	8	no	—
217	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	—	8	1	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	#509	1	2	yes	—
224	C₄×C₁₃	#546	1	1	yes	characteristic
225	C₄×C₁₃	#577	1	1	yes	characteristic
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	4	1	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	4	2	no	—
232	C₂×D₈	C₂³×C₁₃	1	2	yes	—
233	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	C₄⋊Q₈	—	2	1	no	—
237	#127	—	2	1	no	—
238	#124	—	4	2	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	#121	—	4	1	no	—
242	#121	—	4	1	no	—
243	#120	—	4	2	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
247	#117	—	2	2	no	—
248	#117	—	4	1	no	—
249	D₁₆	—	2	2	no	—
250	D₁₆	—	4	2	no	—
251	M₃₂	—	4	2	no	—
252	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
255	#107	—	2	1	no	—
256	#107	C₂³×C₁₃	1	1	yes	characteristic
257	#107	C₂³×C₁₃	1	2	yes	—
258	#107	C₂³×C₁₃	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
261	#102	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
266	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₁₃	—	4	2	no	—
268	C₂×C₁₃	—	8	2	no	—
269	C₂×C₁₃	—	16	1	no	—
270	C₂×C₁₃	—	16	2	no	—
271	C₂×C₁₃	#3294	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
273	C₂×C₁₃	#3415	1	1	yes	characteristic
274	C₂⁴	—	4	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	4	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	8	2	no	—
286	C₂×D₄	—	8	4	no	—
287	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	—	2	1	no	—
294	D₈	—	2	1	no	—
295	D₈	—	2	2	no	—
296	D₈	—	4	4	no	—
297	D₈	—	8	1	no	—
298	D₈	C₁₃×#41	1	2	yes	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
303	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
315	C₄²	—	4	2	no	—
316	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	2	no	—
320	C₁₃	#33892	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	8	4	no	—
325	C₂³	—	8	4	no	—
326	C₂³	—	16	2	no	—
327	C₂³	C₂×C₁₃×D₈	1	2	yes	—
328	Q₈	—	16	1	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	2	no	—
339	D₄	—	16	1	no	—
340	D₄	—	16	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
349	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
350	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	C₈	—	2	2	no	—
353	C₈	—	2	1	no	—
354	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
355	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	8	1	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	8	no	—
369	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	1	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	2	no	—
375	C₄	C₁₃×#509	1	2	yes	—
376	C₄	C₁₃×#546	1	1	yes	characteristic
377	C₄	C₁₃×#577	1	1	yes	characteristic
378	C₂	—	4	2	no	—
379	C₂	—	8	2	no	—
380	C₂	—	16	2	no	—
381	C₂	—	16	1	no	—
382	C₂	C₁₃×#3294	1	1	yes	characteristic
383	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
384	C₂	C₁₃×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
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. C₁₃×#3341	C₂	semidirect
2. D₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2240	C₂	semidirect
4. C₁₃×#2234	C₂	semidirect
5. C₁₃×#2226	C₂	semidirect
6. C₁₃×#2218	C₂	semidirect
7. C₁₃×#2206	C₂	semidirect
8. C₁₃×#2184	C₂	semidirect
9. C₄×C₁₃×D₁₆	C₂	semidirect
10. C₁₃×#2169	C₂	semidirect
11. C₁₃×#2140	C₂	semidirect
16. C₂×C₁₃×D₁₆	C₂²	semidirect
17. C₂×C₁₃×M₃₂	C₂²	semidirect
18. C₁₃×#500	C₂²	semidirect
23. C₁₃×#466	C₂²	semidirect
27. C₄×C₁₃×D₈	C₂²	semidirect
29. C₁₃×#427	C₂²	semidirect
30. C₁₃×#367	C₂²	semidirect
31. C₁₃×#366	C₂²	semidirect
32. C₁₃×C₄⋊C₁₆	C₂²	semidirect
35. C₁₃×#357	C₂²	semidirect
36. C₁₃×#357	C₂²	semidirect
37. C₁₃×#357	C₂²	semidirect
38. C₁₃×#357	C₂²	semidirect
39. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₃×C₁₆	C₂²	semidirect
82. #33892	C₁₃	direct (N × H)
129. #3341	C₂×C₁₃	semidirect
130. D₄×D₈	C₂×C₁₃	semidirect
131. #2240	C₂×C₁₃	semidirect
132. #2234	C₂×C₁₃	semidirect
133. #2226	C₂×C₁₃	semidirect
134. #2218	C₂×C₁₃	semidirect
135. #2206	C₂×C₁₃	semidirect
136. #2184	C₂×C₁₃	semidirect
137. C₄×D₁₆	C₂×C₁₃	semidirect
138. #2169	C₂×C₁₃	semidirect
139. #2140	C₂×C₁₃	semidirect
179. C₂×D₁₆	C₂²×C₁₃	semidirect
180. C₂×M₃₂	C₂²×C₁₃	semidirect
181. #500	C₂²×C₁₃	semidirect
186. #466	C₂²×C₁₃	semidirect
190. C₄×D₈	C₂²×C₁₃	semidirect
192. #427	C₂²×C₁₃	semidirect
193. #367	C₂²×C₁₃	semidirect
194. #366	C₂²×C₁₃	semidirect
195. C₄⋊C₁₆	C₂²×C₁₃	semidirect
198. #357	C₂²×C₁₃	semidirect
199. #357	C₂²×C₁₃	semidirect
200. #357	C₂²×C₁₃	semidirect
201. #357	C₂²×C₁₃	semidirect
202. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
203. C₄×C₁₆	C₂²×C₁₃	semidirect
320. C₁₃	#33892	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×#3341	2
D₄×C₁₃×D₈	2
C₁₃×#2240	2
C₁₃×#2234	2
C₁₃×#2226	2
C₁₃×#2218	2
C₁₃×#2206	2
C₁₃×#2184	2
C₄×C₁₃×D₁₆	2
C₁₃×#2169	2
C₁₃×#2140	2
#33892	13

Subgroups — C13×#33892 #15720231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33892 #15720231