Subgroups — C₂×C₁₃×#2372 #15720486

Order 3328.

3158 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2372	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#388	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#386	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#376	C₂	1	2	yes	maximal, complemented
8	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
11	C₂×C₁₃×#124	C₄	1	16	yes	complemented
12	C₂×C₁₃×#124	C₂²	1	8	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#391	C₂²	1	16	yes	complemented
21	C₁₃×#388	C₂²	1	32	yes	complemented
22	C₁₃×#386	C₂²	1	16	yes	—
23	C₄×C₁₃×C₂²⋊C₄	C₂²	1	32	yes	complemented
24	C₁₃×#376	C₂²	1	16	yes	complemented
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂×C₁₃×#95	C₂²	1	4	yes	—
27	C₂×C₁₃×#95	C₂²	1	2	yes	—
28	C₂×C₁₃×#95	C₂²	1	4	yes	—
29	C₂⁵×C₁₃	C₂³	1	2	yes	—
30	C₂²×Q₈×C₁₃	—	4	2	no	—
31	C₂²×Q₈×C₁₃	—	4	2	no	—
32	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
33	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
34	C₂²×D₄×C₁₃	—	4	2	no	—
35	C₂²×D₄×C₁₃	—	4	2	no	—
36	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
37	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₃	—	2	16	no	—
39	C₂³×C₄×C₁₃	—	4	4	no	—
40	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
46	C₁₃×#124	C₂×C₄	1	64	yes	complemented
47	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
50	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
51	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	32	yes	complemented
52	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
53	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
55	C₂×C₄²×C₁₃	—	2	16	no	—
56	C₂×C₄²×C₁₃	—	4	4	no	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
58	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
61	C₁₃×#95	C₂³	1	8	yes	—
62	C₁₃×#95	C₂³	1	16	yes	—
63	C₁₃×#95	C₂³	1	16	yes	—
64	C₁₃×#95	C₂³	1	8	yes	—
65	C₂×#2372	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	—	2	8	no	—
67	C₂⁴×C₁₃	—	2	8	no	—
68	C₂⁴×C₁₃	—	2	4	no	—
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
71	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
72	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₁₃	—	4	16	no	—
74	C₂×Q₈×C₁₃	—	4	4	no	—
75	C₂×Q₈×C₁₃	—	4	4	no	—
76	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	complemented
77	C₂×D₄×C₁₃	—	4	16	no	—
78	C₂×D₄×C₁₃	—	4	4	no	—
79	C₂×D₄×C₁₃	—	4	4	no	—
80	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
81	C₂²×C₄×C₁₃	—	2	8	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	8	no	—
91	C₂²×C₄×C₁₃	—	2	32	no	—
92	C₂²×C₄×C₁₃	—	4	8	no	—
93	C₂²×C₄×C₁₃	—	4	32	no	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₁₃	#41	1	16	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
103	C₁₃×C₄⋊C₄	—	4	8	no	—
104	C₁₃×C₂²⋊C₄	—	2	32	no	—
105	C₁₃×C₂²⋊C₄	—	4	8	no	—
106	C₁₃×C₂²⋊C₄	C₂²×C₄	1	64	yes	complemented
107	C₄²×C₁₃	—	2	32	no	—
108	C₄²×C₁₃	—	4	8	no	—
109	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
110	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
111	#2372	C₂×C₁₃	1	16	yes	direct product factor
112	C₂×#391	C₂×C₁₃	1	2	yes	complemented
113	C₂×#388	C₂×C₁₃	1	4	yes	complemented
114	C₂×#386	C₂×C₁₃	1	2	yes	—
115	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
116	C₂×#376	C₂×C₁₃	1	2	yes	complemented
117	C₂³×C₁₃	—	2	32	no	—
118	C₂³×C₁₃	—	2	16	no	—
119	C₂³×C₁₃	—	2	8	no	—
120	C₂³×C₁₃	—	2	8	no	—
121	C₂³×C₁₃	—	2	4	no	—
122	C₂³×C₁₃	—	2	4	no	—
123	C₂³×C₁₃	—	4	8	no	—
124	C₂³×C₁₃	—	4	8	no	—
125	C₂³×C₁₃	—	4	16	no	—
126	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
127	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
128	C₂³×C₁₃	C₂×#41	1	8	yes	—
129	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
130	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
131	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
132	Q₈×C₁₃	—	4	16	no	—
133	D₄×C₁₃	—	4	16	no	—
134	C₂×C₄×C₁₃	—	2	16	no	—
135	C₂×C₄×C₁₃	—	2	8	no	—
136	C₂×C₄×C₁₃	—	2	16	no	—
137	C₂×C₄×C₁₃	—	2	32	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	8	no	—
148	C₂×C₄×C₁₃	—	4	32	no	—
149	C₂×C₄×C₁₃	—	4	16	no	—
150	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
151	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
153	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
154	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
155	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
156	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
157	C₂×#124	C₄×C₁₃	1	16	yes	complemented
158	C₂×#124	C₂²×C₁₃	1	8	yes	—
159	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
160	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
161	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
162	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
163	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
164	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
165	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
166	#391	C₂²×C₁₃	1	16	yes	complemented
167	#388	C₂²×C₁₃	1	32	yes	complemented
168	#386	C₂²×C₁₃	1	16	yes	—
169	C₄×C₂²⋊C₄	C₂²×C₁₃	1	32	yes	complemented
170	#376	C₂²×C₁₃	1	16	yes	complemented
171	C₂×#95	C₂²×C₁₃	1	2	yes	—
172	C₂×#95	C₂²×C₁₃	1	4	yes	—
173	C₂×#95	C₂²×C₁₃	1	2	yes	—
174	C₂×#95	C₂²×C₁₃	1	4	yes	—
175	C₂²×C₁₃	—	2	16	no	—
176	C₂²×C₁₃	—	2	8	no	—
177	C₂²×C₁₃	—	4	32	no	—
178	C₂²×C₁₃	—	4	4	no	—
179	C₂²×C₁₃	—	4	4	no	—
180	C₂²×C₁₃	—	4	8	no	—
181	C₂²×C₁₃	C₄×#41	1	8	yes	—
182	C₂²×C₁₃	#518	1	4	yes	—
183	C₂²×C₁₃	#551	1	8	yes	—
184	C₂²×C₁₃	#555	1	8	yes	—
185	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
186	C₂²×C₁₃	C₂²×#41	1	4	yes	—
187	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
189	C₄×C₁₃	—	2	8	no	—
190	C₄×C₁₃	—	2	4	no	—
191	C₄×C₁₃	—	2	8	no	—
192	C₄×C₁₃	—	2	16	no	—
193	C₄×C₁₃	—	4	8	no	—
194	C₂⁵	C₂³×C₁₃	1	2	yes	—
195	C₂²×Q₈	—	4	2	no	—
196	C₂²×Q₈	—	4	2	no	—
197	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
198	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
199	C₂²×D₄	—	4	2	no	—
200	C₂²×D₄	—	4	2	no	—
201	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
202	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
203	C₂³×C₄	—	2	16	no	—
204	C₂³×C₄	—	4	4	no	—
205	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
206	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
211	#124	C₂×C₄×C₁₃	1	64	yes	complemented
212	C₂×C₄⋊C₄	—	4	4	no	—
213	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
214	C₂×C₂²⋊C₄	—	2	16	no	—
215	C₂×C₂²⋊C₄	—	4	4	no	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	32	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	16	yes	—
220	C₂×C₄²	—	2	16	no	—
221	C₂×C₄²	—	4	4	no	—
222	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
223	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
224	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
225	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
226	#95	C₂³×C₁₃	1	8	yes	—
227	#95	C₂³×C₁₃	1	16	yes	—
228	#95	C₂³×C₁₃	1	8	yes	—
229	#95	C₂³×C₁₃	1	16	yes	—
230	C₂×C₁₃	—	4	8	no	—
231	C₂×C₁₃	#2372	1	8	yes	direct product factor
232	C₂×C₁₃	C₂×C₄×#41	1	2	yes	—
233	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
234	C₂×C₁₃	C₂×#551	1	2	yes	—
235	C₂×C₁₃	C₂×#555	1	2	yes	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	—	2	4	no	—
240	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
241	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
242	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
243	C₂×Q₈	—	4	16	no	—
244	C₂×Q₈	—	4	4	no	—
245	C₂×Q₈	—	4	4	no	—
246	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	complemented
247	C₂×D₄	—	4	16	no	—
248	C₂×D₄	—	4	4	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	32	no	—
262	C₂²×C₄	—	4	8	no	—
263	C₂²×C₄	—	4	32	no	—
264	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
267	C₂²×C₄	C₁₃×#41	1	16	yes	—
268	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
273	C₄⋊C₄	—	4	8	no	—
274	C₂²⋊C₄	—	2	32	no	—
275	C₂²⋊C₄	—	4	8	no	—
276	C₂²⋊C₄	C₂²×C₄×C₁₃	1	64	yes	complemented
277	C₄²	—	2	32	no	—
278	C₄²	—	4	8	no	—
279	C₄²	C₂²×C₄×C₁₃	1	16	yes	complemented
280	C₁₃	C₂×#2372	1	1	yes	characteristic, direct product factor, Sylow
281	C₂³	—	2	32	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	8	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	8	no	—
289	C₂³	—	4	16	no	—
290	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
291	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
292	C₂³	C₂×C₁₃×#41	1	8	yes	—
293	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
294	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
295	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
296	Q₈	—	4	16	no	—
297	D₄	—	4	16	no	—
298	C₂×C₄	—	2	16	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	16	no	—
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	4	32	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
315	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
316	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
317	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
318	C₂²	—	2	16	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	4	32	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	8	no	—
324	C₂²	C₄×C₁₃×#41	1	8	yes	—
325	C₂²	C₁₃×#518	1	4	yes	—
326	C₂²	C₁₃×#551	1	8	yes	—
327	C₂²	C₁₃×#555	1	8	yes	—
328	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
329	C₂²	C₂²×C₁₃×#41	1	4	yes	—
330	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	16	no	—
336	C₄	—	4	8	no	—
337	C₂	—	4	8	no	—
338	C₂	C₁₃×#2372	1	8	yes	direct product factor
339	C₂	C₂×C₄×C₁₃×#41	1	2	yes	—
340	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
341	C₂	C₂×C₁₃×#551	1	2	yes	—
342	C₂	C₂×C₁₃×#555	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2372	C₂	direct (N × H)
3. C₂×C₁₃×#391	C₂	semidirect
4. C₂×C₁₃×#388	C₂	semidirect
6. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₂×C₁₃×#376	C₂	semidirect
11. C₂×C₁₃×#124	C₄	semidirect
20. C₁₃×#391	C₂²	semidirect
21. C₁₃×#388	C₂²	semidirect
23. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
24. C₁₃×#376	C₂²	semidirect
32. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
46. C₁₃×#124	C₂×C₄	semidirect
51. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
57. C₂×C₄²×C₁₃	C₂×C₄	semidirect
65. C₂×#2372	C₁₃	direct (N × H)
76. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
106. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
109. C₄²×C₁₃	C₂²×C₄	semidirect
111. #2372	C₂×C₁₃	direct (N × H)
112. C₂×#391	C₂×C₁₃	semidirect
113. C₂×#388	C₂×C₁₃	semidirect
115. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
116. C₂×#376	C₂×C₁₃	semidirect
157. C₂×#124	C₄×C₁₃	semidirect
166. #391	C₂²×C₁₃	semidirect
167. #388	C₂²×C₁₃	semidirect
169. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
170. #376	C₂²×C₁₃	semidirect
197. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
211. #124	C₂×C₄×C₁₃	semidirect
216. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
222. C₂×C₄²	C₂×C₄×C₁₃	semidirect
231. C₂×C₁₃	#2372	direct (N × H)
246. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
276. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
279. C₄²	C₂²×C₄×C₁₃	semidirect
280. C₁₃	C₂×#2372	direct (N × H)
338. C₂	C₁₃×#2372	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#124	2
C₁₃×#2372	2
C₂×C₁₃×#391	2
C₂×C₁₃×#388	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×C₁₃×#376	2
C₂×#2372	13

Subgroups — C2×C13×#2372 #15720486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2372 #15720486