Subgroups — C₁₃×#33862 #15720201

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2233	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×SD₃₂	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×#554	—	2	1	no	—
14	D₄²×C₁₃	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×SD₃₂	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×#484	—	2	2	no	—
21	C₁₃×#477	—	2	1	no	—
22	C₁₃×#467	C₂²	1	2	yes	complemented
23	C₁₃×#466	C₂²	1	2	yes	—
24	C₁₃×#459	—	2	1	no	—
25	C₁₃×#447	—	2	2	no	—
26	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
30	C₁₃×#367	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#367	C₂²	1	2	yes	complemented
32	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#357	C₂²	1	1	yes	characteristic
35	C₁₃×#357	C₂²	1	2	yes	—
36	C₁₃×#357	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	complemented
38	C₁₃×#357	C₂²	1	2	yes	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×Q₁₆	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×#127	—	2	1	no	—
53	C₁₃×#125	—	4	1	no	—
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#121	—	4	1	no	—
58	C₁₃×#120	—	4	2	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	4	1	no	—
62	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×SD₃₂	—	2	2	no	—
65	C₁₃×SD₃₂	—	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×#103	—	2	1	no	—
77	C₁₃×#103	—	2	2	no	—
78	C₁₃×#102	—	2	1	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	#33862	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	4	2	no	—
84	C₂×Q₈×C₁₃	—	2	1	no	—
85	C₂×Q₈×C₁₃	—	4	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	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	8	4	no	—
95	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₁₃×Q₁₆	—	2	1	no	—
100	C₁₃×Q₁₆	—	2	1	no	—
101	C₁₃×D₈	—	2	2	no	—
102	C₁₃×D₈	—	2	1	no	—
103	C₁₃×D₈	—	2	2	no	—
104	C₁₃×D₈	—	4	4	no	—
105	C₁₃×D₈	—	8	1	no	—
106	C₁₃×D₈	#41	1	2	yes	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
120	C₁₃×C₂²⋊C₄	—	4	2	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	1	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	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
130	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic
131	#2240	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2233	C₂×C₁₃	1	2	yes	complemented
133	#2226	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2217	C₂×C₁₃	1	2	yes	complemented
135	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2187	C₂×C₁₃	1	2	yes	complemented
137	C₄×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
138	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂×#357	C₂×C₁₃	1	2	yes	complemented
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	8	4	no	—
143	C₂³×C₁₃	—	8	4	no	—
144	C₂³×C₁₃	—	16	2	no	—
145	C₂³×C₁₃	C₂×D₈	1	2	yes	—
146	Q₈×C₁₃	—	4	1	no	—
147	Q₈×C₁₃	—	4	1	no	—
148	Q₈×C₁₃	—	16	1	no	—
149	D₄×C₁₃	—	2	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	8	4	no	—
154	D₄×C₁₃	—	8	4	no	—
155	D₄×C₁₃	—	8	2	no	—
156	D₄×C₁₃	—	16	1	no	—
157	D₄×C₁₃	SD₃₂	1	4	yes	complemented
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	16	2	no	—
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
175	#554	—	2	1	no	—
176	D₄²	—	2	1	no	—
177	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
179	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
180	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
181	#493	C₂²×C₁₃	1	1	yes	characteristic
182	#484	—	2	2	no	—
183	#477	—	2	1	no	—
184	#467	C₂²×C₁₃	1	2	yes	complemented
185	#466	C₂²×C₁₃	1	2	yes	—
186	#459	—	2	1	no	—
187	#447	—	2	2	no	—
188	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
189	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
192	#367	C₂²×C₁₃	1	1	yes	characteristic, complemented
193	#367	C₂²×C₁₃	1	2	yes	complemented
194	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	#358	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	2	yes	complemented
201	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
202	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	4	2	no	—
206	C₂²×C₁₃	—	8	1	no	—
207	C₂²×C₁₃	—	8	1	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	16	8	no	—
212	C₂²×C₁₃	C₂×SD₃₂	1	4	yes	—
213	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	8	1	no	—
217	C₄×C₁₃	—	8	1	no	—
218	C₄×C₁₃	—	8	2	no	—
219	C₄×C₁₃	—	8	1	no	—
220	C₄×C₁₃	C₂×SD₃₂	1	2	yes	—
221	C₄×C₁₃	#546	1	1	yes	characteristic
222	C₄×C₁₃	#577	1	1	yes	characteristic
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	4	1	no	—
225	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×D₈	—	2	4	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	4	2	no	—
230	C₂×D₈	C₂³×C₁₃	1	2	yes	—
231	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
233	C₄⋊Q₈	—	2	1	no	—
234	#127	—	2	1	no	—
235	#125	—	4	1	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	4	2	no	—
238	#121	—	2	2	no	—
239	#121	—	4	1	no	—
240	#120	—	4	2	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	4	1	no	—
244	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	—	2	2	no	—
246	SD₃₂	—	2	2	no	—
247	SD₃₂	—	4	2	no	—
248	C₂×C₁₆	—	4	2	no	—
249	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
252	#107	—	2	2	no	—
253	#107	—	2	1	no	—
254	#107	C₂³×C₁₃	1	1	yes	characteristic
255	#107	C₂³×C₁₃	1	2	yes	—
256	#107	C₂³×C₁₃	1	1	yes	characteristic
257	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
258	#103	—	2	1	no	—
259	#103	—	2	2	no	—
260	#102	—	2	1	no	—
261	#102	—	2	2	no	—
262	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
263	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₁₃	—	2	4	no	—
265	C₂×C₁₃	—	8	2	no	—
266	C₂×C₁₃	—	16	2	no	—
267	C₂×C₁₃	#3294	1	1	yes	characteristic
268	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
269	C₂×C₁₃	#3415	1	1	yes	characteristic
270	C₂⁴	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	8	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
286	Q₁₆	—	2	1	no	—
287	Q₁₆	—	2	1	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	1	no	—
290	D₈	—	2	2	no	—
291	D₈	—	4	4	no	—
292	D₈	—	8	1	no	—
293	D₈	C₁₃×#41	1	2	yes	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
298	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
311	C₄²	—	4	1	no	—
312	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	2	no	—
316	C₁₃	#33862	1	1	yes	characteristic, direct product factor, Sylow
317	C₂³	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	16	2	no	—
322	C₂³	C₂×C₁₃×D₈	1	2	yes	—
323	Q₈	—	4	1	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	16	1	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	16	1	no	—
334	D₄	C₁₃×SD₃₂	1	4	yes	complemented
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	16	2	no	—
343	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
345	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	1	no	—
349	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
350	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	16	8	no	—
360	C₂²	C₂×C₁₃×SD₃₂	1	4	yes	—
361	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	2	no	—
368	C₄	C₂×C₁₃×SD₃₂	1	2	yes	—
369	C₄	C₁₃×#546	1	1	yes	characteristic
370	C₄	C₁₃×#577	1	1	yes	characteristic
371	C₂	—	2	4	no	—
372	C₂	—	8	2	no	—
373	C₂	—	16	2	no	—
374	C₂	C₁₃×#3294	1	1	yes	characteristic
375	C₂	C₂²×C₁₃×SD₃₂	1	1	yes	characteristic
376	C₂	C₁₃×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	D₄×C₁₃×D₈	C₂
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×#3338	C₂	semidirect
3. C₁₃×#2240	C₂	semidirect
4. C₁₃×#2233	C₂	semidirect
5. C₁₃×#2226	C₂	semidirect
6. C₁₃×#2217	C₂	semidirect
7. C₁₃×#2207	C₂	semidirect
8. C₁₃×#2187	C₂	semidirect
9. C₄×C₁₃×SD₃₂	C₂	semidirect
10. D₄×C₁₃×C₁₆	C₂	semidirect
11. C₂×C₁₃×#357	C₂	semidirect
16. C₂×C₁₃×SD₃₂	C₂²	semidirect
17. C₂²×C₁₃×C₁₆	C₂²	semidirect
18. C₁₃×#500	C₂²	semidirect
22. C₁₃×#467	C₂²	semidirect
26. C₄×C₁₃×Q₁₆	C₂²	semidirect
29. C₂×C₁₃×#107	C₂²	semidirect
30. C₁₃×#367	C₂²	semidirect
31. C₁₃×#367	C₂²	semidirect
32. C₁₃×C₄⋊C₁₆	C₂²	semidirect
33. C₁₃×#358	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. #33862	C₁₃	direct (N × H)
129. #3338	C₂×C₁₃	semidirect
131. #2240	C₂×C₁₃	semidirect
132. #2233	C₂×C₁₃	semidirect
133. #2226	C₂×C₁₃	semidirect
134. #2217	C₂×C₁₃	semidirect
135. #2207	C₂×C₁₃	semidirect
136. #2187	C₂×C₁₃	semidirect
137. C₄×SD₃₂	C₂×C₁₃	semidirect
138. D₄×C₁₆	C₂×C₁₃	semidirect
139. C₂×#357	C₂×C₁₃	semidirect
157. D₄×C₁₃	SD₃₂	semidirect
178. C₂×SD₃₂	C₂²×C₁₃	semidirect
179. C₂²×C₁₆	C₂²×C₁₃	semidirect
180. #500	C₂²×C₁₃	semidirect
184. #467	C₂²×C₁₃	semidirect
188. C₄×Q₁₆	C₂²×C₁₃	semidirect
191. C₂×#107	C₂²×C₁₃	semidirect
192. #367	C₂²×C₁₃	semidirect
193. #367	C₂²×C₁₃	semidirect
194. C₄⋊C₁₆	C₂²×C₁₃	semidirect
195. #358	C₂²×C₁₃	semidirect
198. #357	C₂²×C₁₃	semidirect
199. #357	C₂²×C₁₃	semidirect
200. #357	C₂²×C₁₃	semidirect
201. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
202. C₄×C₁₆	C₂²×C₁₃	semidirect
316. C₁₃	#33862	direct (N × H)
334. D₄	C₁₃×SD₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3338	2
D₄×C₁₃×D₈	2
C₁₃×#2240	2
C₁₃×#2233	2
C₁₃×#2226	2
C₁₃×#2217	2
C₁₃×#2207	2
C₁₃×#2187	2
C₄×C₁₃×SD₃₂	2
D₄×C₁₃×C₁₆	2
C₂×C₁₃×#357	2
#33862	13

Subgroups — C13×#33862 #15720201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33862 #15720201