Subgroups — C₁₃×#33861 #15720200

Order 3328.

654 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	C₁₃×#3334	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×#2232	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2215	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	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#357	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₁₃×#547	—	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	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
18	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#493	C₂²	1	1	yes	characteristic
20	C₁₃×#480	—	2	2	no	—
21	C₁₃×#474	—	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	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
30	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#366	C₂²	1	2	yes	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	C₂×C₁₃×#41	—	4	1	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	4	1	no	—
44	C₂×C₁₃×D₈	—	2	4	no	—
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	—	4	2	no	—
48	C₂×C₁₃×D₈	C₂³	1	2	yes	—
49	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×#127	—	2	1	no	—
54	C₁₃×#123	—	4	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	1	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₁₃×#121	—	4	1	no	—
59	C₁₃×#120	—	4	2	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×D₁₆	—	2	2	no	—
65	C₁₃×D₁₆	—	4	2	no	—
66	C₂×C₁₃×C₁₆	—	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	2	no	—
71	C₁₃×#107	—	2	1	no	—
72	C₁₃×#107	C₂³	1	1	yes	characteristic
73	C₁₃×#107	C₂³	1	2	yes	—
74	C₁₃×#107	C₂³	1	1	yes	characteristic
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	#33861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	4	2	no	—
84	C₁₃×#41	—	8	4	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	4	4	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂×D₄×C₁₃	—	4	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	—	8	4	no	—
97	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₁₃×D₈	—	2	1	no	—
103	C₁₃×D₈	—	2	2	no	—
104	C₁₃×D₈	—	2	1	no	—
105	C₁₃×D₈	—	2	1	no	—
106	C₁₃×D₈	—	2	2	no	—
107	C₁₃×D₈	—	4	4	no	—
108	C₁₃×D₈	—	8	1	no	—
109	C₁₃×D₈	#41	1	2	yes	complemented
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₁₃×C₂²⋊C₄	—	4	1	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	2	no	—
125	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×C₁₆	—	2	1	no	—
128	C₁₃×C₁₆	—	2	1	no	—
129	C₁₃×C₁₆	—	2	2	no	—
130	#3334	C₂×C₁₃	1	1	yes	characteristic, complemented
131	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2240	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#2232	C₂×C₁₃	1	2	yes	complemented
134	#2224	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#2215	C₂×C₁₃	1	2	yes	complemented
136	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2184	C₂×C₁₃	1	2	yes	complemented
138	C₄×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
139	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×#357	C₂×C₁₃	1	2	yes	complemented
141	C₂³×C₁₃	—	4	1	no	—
142	C₂³×C₁₃	—	4	1	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	8	4	no	—
145	C₂³×C₁₃	—	8	4	no	—
146	C₂³×C₁₃	—	16	2	no	—
147	C₂³×C₁₃	C₂×D₈	1	2	yes	—
148	Q₈×C₁₃	—	8	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	4	no	—
158	D₄×C₁₃	—	8	2	no	—
159	D₄×C₁₃	—	16	1	no	—
160	D₄×C₁₃	D₁₆	1	4	yes	complemented
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	8	4	no	—
167	C₂×C₄×C₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₁₃	—	2	2	no	—
174	C₈×C₁₃	—	2	1	no	—
175	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
178	#547	—	2	1	no	—
179	D₄²	—	2	1	no	—
180	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
181	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
182	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
183	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
184	#493	C₂²×C₁₃	1	1	yes	characteristic
185	#480	—	2	2	no	—
186	#474	—	2	1	no	—
187	#466	C₂²×C₁₃	1	2	yes	—
188	#466	C₂²×C₁₃	1	2	yes	complemented
189	#459	—	2	1	no	—
190	#447	—	2	2	no	—
191	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
193	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
195	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
196	#366	C₂²×C₁₃	1	2	yes	complemented
197	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
198	#357	C₂²×C₁₃	1	1	yes	characteristic
199	#357	C₂²×C₁₃	1	2	yes	—
200	#357	C₂²×C₁₃	1	2	yes	complemented
201	#357	C₂²×C₁₃	1	2	yes	complemented
202	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
203	#357	C₂²×C₁₃	1	2	yes	complemented
204	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
205	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	4	2	no	—
209	C₂²×C₁₃	—	8	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	—	8	1	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	1	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	16	8	no	—
218	C₂²×C₁₃	C₂×D₁₆	1	4	yes	—
219	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	8	1	no	—
223	C₄×C₁₃	—	8	1	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	C₂×D₁₆	1	2	yes	—
226	C₄×C₁₃	#546	1	1	yes	characteristic
227	C₄×C₁₃	#577	1	1	yes	characteristic
228	C₂×#41	—	4	1	no	—
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	4	1	no	—
231	C₂×D₈	—	2	4	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	4	2	no	—
235	C₂×D₈	C₂³×C₁₃	1	2	yes	—
236	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
239	C₄⋊Q₈	—	2	1	no	—
240	#127	—	2	1	no	—
241	#123	—	4	2	no	—
242	C₂²⋊Q₈	—	4	1	no	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	#121	—	4	1	no	—
246	#120	—	4	2	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	2	2	no	—
251	D₁₆	—	2	2	no	—
252	D₁₆	—	4	2	no	—
253	C₂×C₁₆	—	4	2	no	—
254	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
257	#107	—	2	2	no	—
258	#107	—	2	1	no	—
259	#107	C₂³×C₁₃	1	1	yes	characteristic
260	#107	C₂³×C₁₃	1	2	yes	—
261	#107	C₂³×C₁₃	1	1	yes	characteristic
262	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
263	#102	—	2	1	no	—
264	#102	—	2	1	no	—
265	#102	—	2	2	no	—
266	#102	—	2	2	no	—
267	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
268	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₁₃	—	2	4	no	—
270	C₂×C₁₃	—	8	2	no	—
271	C₂×C₁₃	—	16	1	no	—
272	C₂×C₁₃	—	16	2	no	—
273	C₂×C₁₃	#3294	1	1	yes	characteristic
274	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
275	C₂×C₁₃	#3416	1	1	yes	characteristic
276	C₂⁴	—	4	2	no	—
277	#41	—	8	4	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	8	2	no	—
289	C₂×D₄	—	8	4	no	—
290	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	D₈	—	2	1	no	—
296	D₈	—	2	2	no	—
297	D₈	—	2	1	no	—
298	D₈	—	2	1	no	—
299	D₈	—	2	2	no	—
300	D₈	—	4	4	no	—
301	D₈	—	8	1	no	—
302	D₈	C₁₃×#41	1	2	yes	complemented
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
307	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
319	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₁₆	—	2	1	no	—
321	C₁₆	—	2	1	no	—
322	C₁₆	—	2	2	no	—
323	C₁₃	#33861	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	8	4	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	16	2	no	—
330	C₂³	C₂×C₁₃×D₈	1	2	yes	—
331	Q₈	—	8	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	1	no	—
338	D₄	—	8	4	no	—
339	D₄	—	8	4	no	—
340	D₄	—	8	4	no	—
341	D₄	—	8	2	no	—
342	D₄	—	16	1	no	—
343	D₄	C₁₃×D₁₆	1	4	yes	complemented
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	2	1	no	—
358	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
359	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	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	1	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	16	8	no	—
372	C₂²	C₂×C₁₃×D₁₆	1	4	yes	—
373	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	1	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	2	no	—
379	C₄	C₂×C₁₃×D₁₆	1	2	yes	—
380	C₄	C₁₃×#546	1	1	yes	characteristic
381	C₄	C₁₃×#577	1	1	yes	characteristic
382	C₂	—	2	4	no	—
383	C₂	—	8	2	no	—
384	C₂	—	16	2	no	—
385	C₂	—	16	1	no	—
386	C₂	C₁₃×#3294	1	1	yes	characteristic
387	C₂	C₂²×C₁₃×D₁₆	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
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×#3334	C₂	semidirect
2. D₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2240	C₂	semidirect
4. C₁₃×#2232	C₂	semidirect
5. C₁₃×#2224	C₂	semidirect
6. C₁₃×#2215	C₂	semidirect
7. C₁₃×#2206	C₂	semidirect
8. C₁₃×#2184	C₂	semidirect
9. C₄×C₁₃×D₁₆	C₂	semidirect
10. D₄×C₁₃×C₁₆	C₂	semidirect
11. C₂×C₁₃×#357	C₂	semidirect
16. C₂×C₁₃×D₁₆	C₂²	semidirect
17. C₂²×C₁₃×C₁₆	C₂²	semidirect
18. C₁₃×#500	C₂²	semidirect
23. C₁₃×#466	C₂²	semidirect
27. C₄×C₁₃×D₈	C₂²	semidirect
29. C₂×C₁₃×#107	C₂²	semidirect
30. C₁₃×#366	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. #33861	C₁₃	direct (N × H)
109. C₁₃×D₈	#41	semidirect
130. #3334	C₂×C₁₃	semidirect
131. D₄×D₈	C₂×C₁₃	semidirect
132. #2240	C₂×C₁₃	semidirect
133. #2232	C₂×C₁₃	semidirect
134. #2224	C₂×C₁₃	semidirect
135. #2215	C₂×C₁₃	semidirect
136. #2206	C₂×C₁₃	semidirect
137. #2184	C₂×C₁₃	semidirect
138. C₄×D₁₆	C₂×C₁₃	semidirect
139. D₄×C₁₆	C₂×C₁₃	semidirect
140. C₂×#357	C₂×C₁₃	semidirect
160. D₄×C₁₃	D₁₆	semidirect
181. C₂×D₁₆	C₂²×C₁₃	semidirect
182. C₂²×C₁₆	C₂²×C₁₃	semidirect
183. #500	C₂²×C₁₃	semidirect
188. #466	C₂²×C₁₃	semidirect
192. C₄×D₈	C₂²×C₁₃	semidirect
194. C₂×#107	C₂²×C₁₃	semidirect
195. #366	C₂²×C₁₃	semidirect
196. #366	C₂²×C₁₃	semidirect
197. C₄⋊C₁₆	C₂²×C₁₃	semidirect
200. #357	C₂²×C₁₃	semidirect
201. #357	C₂²×C₁₃	semidirect
202. #357	C₂²×C₁₃	semidirect
203. #357	C₂²×C₁₃	semidirect
204. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
205. C₄×C₁₆	C₂²×C₁₃	semidirect
302. D₈	C₁₃×#41	semidirect
323. C₁₃	#33861	direct (N × H)
343. D₄	C₁₃×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3334	2
D₄×C₁₃×D₈	2
C₁₃×#2240	2
C₁₃×#2232	2
C₁₃×#2224	2
C₁₃×#2215	2
C₁₃×#2206	2
C₁₃×#2184	2
C₄×C₁₃×D₁₆	2
D₄×C₁₃×C₁₆	2
C₂×C₁₃×#357	2
#33861	13

Subgroups — C13×#33861 #15720200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33861 #15720200