Subgroups — C₁₃×#34176 #15720515

Order 3328.

4110 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2342	C₂	1	16	yes	maximal, complemented
3	C₁₃×#2315	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2312	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2280	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#379	C₂	1	2	yes	maximal
7	C₁₃×#2273	C₂	1	2	yes	maximal, complemented
8	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
10	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
11	C₂²×C₁₃×C₂²⋊C₄	C₄	1	16	yes	complemented
12	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
14	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
18	C₁₃×#388	C₂²	1	32	yes	complemented
19	C₁₃×#385	C₂²	1	16	yes	complemented
20	C₁₃×#381	C₂²	1	8	yes	complemented
21	C₁₃×#380	C₂²	1	8	yes	complemented
22	C₁₃×#380	C₂²	1	8	yes	complemented
23	C₁₃×#379	C₂²	1	4	yes	—
24	C₁₃×#379	C₂²	1	4	yes	—
25	C₁₃×#379	C₂²	1	8	yes	—
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
29	C₂⁵×C₁₃	—	2	8	no	—
30	C₂⁵×C₁₃	—	4	8	no	—
31	C₂⁵×C₁₃	C₂×C₄	1	8	yes	—
32	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
33	C₂⁵×C₁₃	C₂³	1	4	yes	—
34	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	—	4	8	no	—
37	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
38	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₁₃×#117	—	4	16	no	—
44	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
45	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
46	C₂×C₁₃×C₂²⋊C₄	—	4	16	no	—
47	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
48	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
49	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	64	yes	complemented
50	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
51	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
52	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
53	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
57	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
59	C₁₃×#95	C₂³	1	16	yes	complemented
60	C₁₃×#95	C₂³	1	16	yes	complemented
61	#34176	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁴×C₁₃	—	2	4	no	—
63	C₂⁴×C₁₃	—	2	8	no	—
64	C₂⁴×C₁₃	—	2	32	no	—
65	C₂⁴×C₁₃	—	2	16	no	—
66	C₂⁴×C₁₃	—	2	4	no	—
67	C₂⁴×C₁₃	—	2	16	no	—
68	C₂⁴×C₁₃	—	4	32	no	—
69	C₂⁴×C₁₃	—	4	4	no	—
70	C₂⁴×C₁₃	—	4	8	no	—
71	C₂⁴×C₁₃	—	4	4	no	—
72	C₂⁴×C₁₃	—	4	64	no	—
73	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
75	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
76	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₁₃	#41	1	8	yes	—
78	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
79	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
82	C₂²×C₄×C₁₃	—	2	16	no	—
83	C₂²×C₄×C₁₃	—	2	16	no	—
84	C₂²×C₄×C₁₃	—	4	32	no	—
85	C₂²×C₄×C₁₃	—	4	4	no	—
86	C₂²×C₄×C₁₃	—	4	8	no	—
87	C₂²×C₄×C₁₃	—	4	4	no	—
88	C₂²×C₄×C₁₃	—	4	16	no	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
96	C₁₃×C₄⋊C₄	—	4	16	no	—
97	C₁₃×C₂²⋊C₄	—	2	16	no	—
98	C₁₃×C₂²⋊C₄	—	2	16	no	—
99	C₁₃×C₂²⋊C₄	—	2	32	no	—
100	C₁₃×C₂²⋊C₄	—	4	16	no	—
101	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
102	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
103	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
104	C₄²×C₁₃	—	4	16	no	—
105	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
106	#2342	C₂×C₁₃	1	16	yes	complemented
107	#2315	C₂×C₁₃	1	2	yes	complemented
108	#2312	C₂×C₁₃	1	4	yes	complemented
109	#2280	C₂×C₁₃	1	4	yes	complemented
110	C₂×#379	C₂×C₁₃	1	2	yes	—
111	#2273	C₂×C₁₃	1	2	yes	complemented
112	C₂³×C₁₃	—	2	32	no	—
113	C₂³×C₁₃	—	2	8	no	—
114	C₂³×C₁₃	—	2	16	no	—
115	C₂³×C₁₃	—	2	4	no	—
116	C₂³×C₁₃	—	2	4	no	—
117	C₂³×C₁₃	—	2	4	no	—
118	C₂³×C₁₃	—	2	8	no	—
119	C₂³×C₁₃	—	2	32	no	—
120	C₂³×C₁₃	—	2	8	no	—
121	C₂³×C₁₃	—	2	32	no	—
122	C₂³×C₁₃	—	2	4	no	—
123	C₂³×C₁₃	—	2	8	no	—
124	C₂³×C₁₃	—	4	8	no	—
125	C₂³×C₁₃	—	4	16	no	—
126	C₂³×C₁₃	—	4	8	no	—
127	C₂³×C₁₃	—	4	16	no	—
128	C₂³×C₁₃	—	4	64	no	—
129	C₂³×C₁₃	—	4	128	no	—
130	C₂³×C₁₃	—	4	16	no	—
131	C₂³×C₁₃	#117	1	16	yes	complemented
132	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
133	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
135	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
136	C₂³×C₁₃	C₂×#41	1	4	yes	—
137	C₂³×C₁₃	C₂×#41	1	8	yes	—
138	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
139	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
140	C₂×C₄×C₁₃	—	2	32	no	—
141	C₂×C₄×C₁₃	—	2	8	no	—
142	C₂×C₄×C₁₃	—	2	8	no	—
143	C₂×C₄×C₁₃	—	2	16	no	—
144	C₂×C₄×C₁₃	—	2	32	no	—
145	C₂×C₄×C₁₃	—	4	8	no	—
146	C₂×C₄×C₁₃	—	4	8	no	—
147	C₂×C₄×C₁₃	—	4	16	no	—
148	C₂×C₄×C₁₃	—	8	16	no	—
149	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
150	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
151	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
152	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
153	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
154	C₂²×C₂²⋊C₄	C₄×C₁₃	1	16	yes	complemented
155	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
156	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
157	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
158	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
159	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
160	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
161	#388	C₂²×C₁₃	1	32	yes	complemented
162	#385	C₂²×C₁₃	1	16	yes	complemented
163	#381	C₂²×C₁₃	1	8	yes	complemented
164	#380	C₂²×C₁₃	1	8	yes	complemented
165	#380	C₂²×C₁₃	1	8	yes	complemented
166	#379	C₂²×C₁₃	1	4	yes	—
167	#379	C₂²×C₁₃	1	8	yes	—
168	#379	C₂²×C₁₃	1	4	yes	—
169	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
170	C₄×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	complemented
171	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
172	C₂²×C₁₃	—	2	32	no	—
173	C₂²×C₁₃	—	2	4	no	—
174	C₂²×C₁₃	—	2	4	no	—
175	C₂²×C₁₃	—	2	4	no	—
176	C₂²×C₁₃	—	2	8	no	—
177	C₂²×C₁₃	—	2	16	no	—
178	C₂²×C₁₃	—	2	8	no	—
179	C₂²×C₁₃	—	2	16	no	—
180	C₂²×C₁₃	—	2	4	no	—
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	4	16	no	—
183	C₂²×C₁₃	—	4	64	no	—
184	C₂²×C₁₃	—	4	16	no	—
185	C₂²×C₁₃	—	4	8	no	—
186	C₂²×C₁₃	C₂×#117	1	4	yes	—
187	C₂²×C₁₃	C₂×#117	1	8	yes	—
188	C₂²×C₁₃	#518	1	8	yes	—
189	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
190	C₂²×C₁₃	C₂²×#41	1	2	yes	—
191	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
192	C₄×C₁₃	—	2	8	no	—
193	C₄×C₁₃	—	2	8	no	—
194	C₄×C₁₃	—	4	16	no	—
195	C₂⁵	—	2	8	no	—
196	C₂⁵	—	4	8	no	—
197	C₂⁵	C₂×C₄×C₁₃	1	8	yes	—
198	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
199	C₂⁵	C₂³×C₁₃	1	4	yes	—
200	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
201	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
202	C₂³×C₄	—	4	8	no	—
203	C₂³×C₄	C₂×C₄×C₁₃	1	16	yes	complemented
204	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
206	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
209	#117	—	4	16	no	—
210	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
211	C₂×C₂²⋊C₄	—	2	16	no	—
212	C₂×C₂²⋊C₄	—	4	16	no	—
213	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
214	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
215	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	64	yes	complemented
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
217	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
221	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
224	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
225	#95	C₂³×C₁₃	1	16	yes	complemented
226	#95	C₂³×C₁₃	1	16	yes	complemented
227	C₂×C₁₃	—	2	4	no	—
228	C₂×C₁₃	—	2	8	no	—
229	C₂×C₁₃	—	2	8	no	—
230	C₂×C₁₃	—	4	4	no	—
231	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
232	C₂×C₁₃	C₂×#518	1	2	yes	—
233	C₂×C₁₃	#3490	1	4	yes	—
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	32	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	16	no	—
240	C₂⁴	—	4	32	no	—
241	C₂⁴	—	4	4	no	—
242	C₂⁴	—	4	8	no	—
243	C₂⁴	—	4	4	no	—
244	C₂⁴	—	4	64	no	—
245	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
246	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	—
247	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
248	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
249	C₂⁴	C₁₃×#41	1	8	yes	—
250	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
251	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
252	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
253	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
254	C₂²×C₄	—	2	16	no	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	4	32	no	—
257	C₂²×C₄	—	4	4	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	—	4	16	no	—
261	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
265	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
266	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
268	C₄⋊C₄	—	4	16	no	—
269	C₂²⋊C₄	—	2	16	no	—
270	C₂²⋊C₄	—	2	16	no	—
271	C₂²⋊C₄	—	2	32	no	—
272	C₂²⋊C₄	—	4	16	no	—
273	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
274	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
275	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
276	C₄²	—	4	16	no	—
277	C₁₃	#34176	1	1	yes	characteristic, direct product factor, Sylow
278	C₂³	—	2	32	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	4	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	2	8	no	—
285	C₂³	—	2	32	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	2	32	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	4	8	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	4	8	no	—
293	C₂³	—	4	16	no	—
294	C₂³	—	4	64	no	—
295	C₂³	—	4	128	no	—
296	C₂³	—	4	16	no	—
297	C₂³	C₁₃×#117	1	16	yes	complemented
298	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
299	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
300	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
301	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
302	C₂³	C₂×C₁₃×#41	1	4	yes	—
303	C₂³	C₂×C₁₃×#41	1	8	yes	—
304	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
305	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
306	C₂×C₄	—	2	32	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	—	2	32	no	—
311	C₂×C₄	—	4	8	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	—	8	16	no	—
315	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
316	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
317	C₂²	—	2	32	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	16	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	4	16	no	—
328	C₂²	—	4	64	no	—
329	C₂²	—	4	16	no	—
330	C₂²	—	4	8	no	—
331	C₂²	C₂×C₁₃×#117	1	4	yes	—
332	C₂²	C₂×C₁₃×#117	1	8	yes	—
333	C₂²	C₁₃×#518	1	8	yes	—
334	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
335	C₂²	C₂²×C₁₃×#41	1	2	yes	—
336	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
337	C₄	—	2	8	no	—
338	C₄	—	2	8	no	—
339	C₄	—	4	16	no	—
340	C₂	—	2	4	no	—
341	C₂	—	2	8	no	—
342	C₂	—	2	8	no	—
343	C₂	—	4	4	no	—
344	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
345	C₂	C₂×C₁₃×#518	1	2	yes	—
346	C₂	C₁₃×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2342	C₂	semidirect
3. C₁₃×#2315	C₂	semidirect
4. C₁₃×#2312	C₂	semidirect
5. C₁₃×#2280	C₂	semidirect
7. C₁₃×#2273	C₂	semidirect
10. C₂×C₁₃×#117	C₂²	semidirect
11. C₂²×C₁₃×C₂²⋊C₄	C₄	semidirect
18. C₁₃×#388	C₂²	semidirect
19. C₁₃×#385	C₂²	semidirect
20. C₁₃×#381	C₂²	semidirect
21. C₁₃×#380	C₂²	semidirect
22. C₁₃×#380	C₂²	semidirect
26. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
37. C₂³×C₄×C₁₃	C₂×C₄	semidirect
44. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
49. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
50. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
58. C₂×C₄²×C₁₃	C₂³	semidirect
59. C₁₃×#95	C₂³	semidirect
60. C₁₃×#95	C₂³	semidirect
61. #34176	C₁₃	direct (N × H)
106. #2342	C₂×C₁₃	semidirect
107. #2315	C₂×C₁₃	semidirect
108. #2312	C₂×C₁₃	semidirect
109. #2280	C₂×C₁₃	semidirect
111. #2273	C₂×C₁₃	semidirect
131. C₂³×C₁₃	#117	semidirect
153. C₂×#117	C₂²×C₁₃	semidirect
154. C₂²×C₂²⋊C₄	C₄×C₁₃	semidirect
161. #388	C₂²×C₁₃	semidirect
162. #385	C₂²×C₁₃	semidirect
163. #381	C₂²×C₁₃	semidirect
164. #380	C₂²×C₁₃	semidirect
165. #380	C₂²×C₁₃	semidirect
169. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
170. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
171. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
203. C₂³×C₄	C₂×C₄×C₁₃	semidirect
210. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
215. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
216. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
224. C₂×C₄²	C₂³×C₁₃	semidirect
225. #95	C₂³×C₁₃	semidirect
226. #95	C₂³×C₁₃	semidirect
277. C₁₃	#34176	direct (N × H)
297. C₂³	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2342	2
C₁₃×#2315	2
C₁₃×#2312	2
C₁₃×#2280	2
C₂×C₁₃×#379	2
C₁₃×#2273	2
#34176	13

Subgroups — C13×#34176 #15720515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34176 #15720515