Subgroups — C₂×C₁₃×#2502 #15721104

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2502	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#385	C₂	1	4	yes	maximal
7	C₂×C₁₃×#384	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
14	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#398	C₂²	1	32	yes	complemented
25	C₁₃×#391	C₂²	1	16	yes	complemented
26	C₁₃×#385	C₂²	1	32	yes	—
27	C₁₃×#384	C₂²	1	16	yes	complemented
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	8	yes	—
31	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×Q₈×C₁₃	—	2	4	no	—
33	C₂²×Q₈×C₁₃	—	2	8	no	—
34	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃	—	2	8	no	—
36	C₂³×C₄×C₁₃	—	2	8	no	—
37	C₂³×C₄×C₁₃	—	4	8	no	—
38	C₂³×C₄×C₁₃	D₄	1	8	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×C₂²⋊Q₈	—	2	32	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
53	C₂×C₁₃×C₄⋊C₄	—	4	16	no	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
60	C₂×C₁₃×C₂²⋊C₄	Q₈	1	16	yes	complemented
61	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
63	C₂×C₄²×C₁₃	—	2	8	no	—
64	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
65	C₁₃×#95	C₂³	1	8	yes	—
66	C₁₃×#95	C₂³	1	32	yes	—
67	C₂×#2502	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	2	4	no	—
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
71	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
72	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
73	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
74	C₂×Q₈×C₁₃	—	2	8	no	—
75	C₂×Q₈×C₁₃	—	2	16	no	—
76	C₂×Q₈×C₁₃	—	4	16	no	—
77	C₂²×C₄×C₁₃	—	2	8	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₃	—	2	32	no	—
81	C₂²×C₄×C₁₃	—	2	16	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	16	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₃	—	2	16	no	—
89	C₂²×C₄×C₁₃	—	4	16	no	—
90	C₂²×C₄×C₁₃	—	4	32	no	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	—
95	C₂²×C₄×C₁₃	#41	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	16	no	—
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	2	16	no	—
106	C₁₃×C₄⋊C₄	—	4	32	no	—
107	C₁₃×C₂²⋊C₄	—	2	16	no	—
108	C₁₃×C₂²⋊C₄	C₂×Q₈	1	32	yes	complemented
109	C₄²×C₁₃	—	2	16	no	—
110	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
111	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
112	#2502	C₂×C₁₃	1	16	yes	direct product factor
113	C₂×#398	C₂×C₁₃	1	4	yes	complemented
114	C₂×#391	C₂×C₁₃	1	2	yes	complemented
115	C₂×#385	C₂×C₁₃	1	4	yes	—
116	C₂×#384	C₂×C₁₃	1	2	yes	complemented
117	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
118	C₂³×C₁₃	—	2	8	no	—
119	C₂³×C₁₃	—	2	8	no	—
120	C₂³×C₁₃	—	2	32	no	—
121	C₂³×C₁₃	—	2	4	no	—
122	C₂³×C₁₃	—	2	4	no	—
123	C₂³×C₁₃	C₄⋊Q₈	1	16	yes	—
124	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
125	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
126	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
127	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
128	C₂³×C₁₃	C₂×#41	1	4	yes	—
129	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
130	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
131	Q₈×C₁₃	—	4	16	no	—
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	32	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	32	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	8	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	—	4	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	#123	1	16	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	—
152	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
153	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
154	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
155	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
156	C₂×C₂²⋊Q₈	—	2	8	no	—
157	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
158	C₂²×C₄⋊C₄	—	2	8	no	—
159	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
160	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
161	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
162	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
163	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
165	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
166	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
167	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
168	#398	C₂²×C₁₃	1	32	yes	complemented
169	#391	C₂²×C₁₃	1	16	yes	complemented
170	#385	C₂²×C₁₃	1	32	yes	—
171	#384	C₂²×C₁₃	1	16	yes	complemented
172	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
173	C₂×#95	C₂²×C₁₃	1	2	yes	—
174	C₂×#95	C₂²×C₁₃	1	8	yes	—
175	C₂²×C₁₃	—	2	4	no	—
176	C₂²×C₁₃	—	2	4	no	—
177	C₂²×C₁₃	—	2	16	no	—
178	C₂²×C₁₃	—	2	32	no	—
179	C₂²×C₁₃	C₂×#123	1	4	yes	—
180	C₂²×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
181	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
182	C₂²×C₁₃	#535	1	4	yes	—
183	C₂²×C₁₃	#554	1	16	yes	—
184	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
186	C₂²×C₁₃	C₂²×#41	1	2	yes	—
187	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
188	C₄×C₁₃	—	2	4	no	—
189	C₄×C₁₃	—	2	16	no	—
190	C₄×C₁₃	—	4	4	no	—
191	C₄×C₁₃	—	4	4	no	—
192	C₄×C₁₃	—	4	8	no	—
193	C₄×C₁₃	C₂×#123	1	8	yes	—
194	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
195	C₂²×Q₈	—	2	4	no	—
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
198	C₂³×C₄	—	2	8	no	—
199	C₂³×C₄	—	2	8	no	—
200	C₂³×C₄	—	4	8	no	—
201	C₂³×C₄	D₄×C₁₃	1	8	yes	—
202	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
203	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
204	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂²⋊Q₈	—	2	32	no	—
211	C₂×C₄⋊C₄	—	2	8	no	—
212	C₂×C₄⋊C₄	—	2	32	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₄⋊C₄	—	2	4	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	—	4	16	no	—
217	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
222	C₂×C₂²⋊C₄	—	2	8	no	—
223	C₂×C₂²⋊C₄	Q₈×C₁₃	1	16	yes	complemented
224	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
226	C₂×C₄²	—	2	8	no	—
227	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
228	#95	C₂³×C₁₃	1	8	yes	—
229	#95	C₂³×C₁₃	1	32	yes	—
230	C₂×C₁₃	—	2	8	no	—
231	C₂×C₁₃	#2502	1	8	yes	direct product factor
232	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
233	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
234	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
235	C₂×C₁₃	C₂×#554	1	4	yes	—
236	C₂⁴	—	2	4	no	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
239	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
240	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
241	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	2	16	no	—
244	C₂×Q₈	—	4	16	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	32	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	16	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	4	16	no	—
258	C₂²×C₄	—	4	32	no	—
259	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
261	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
262	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	—
263	C₂²×C₄	C₁₃×#41	1	8	yes	—
264	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
265	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
266	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
270	C₄⋊C₄	—	2	16	no	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	16	no	—
274	C₄⋊C₄	—	4	32	no	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂²⋊C₄	C₂×Q₈×C₁₃	1	32	yes	complemented
277	C₄²	—	2	16	no	—
278	C₁₃	C₂×#2502	1	1	yes	characteristic, direct product factor, Sylow
279	C₂³	—	2	8	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	4	no	—
284	C₂³	C₁₃×C₄⋊Q₈	1	16	yes	—
285	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
286	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
287	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
288	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
289	C₂³	C₂×C₁₃×#41	1	4	yes	—
290	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
291	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
292	Q₈	—	4	16	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	4	32	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	—	4	16	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₁₃×#123	1	16	yes	—
310	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
311	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
312	C₂×C₄	C₂²×Q₈×C₁₃	1	16	yes	—
313	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
314	C₂²	—	2	32	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	16	no	—
318	C₂²	C₂×C₁₃×#123	1	4	yes	—
319	C₂²	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
320	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
321	C₂²	C₁₃×#535	1	4	yes	—
322	C₂²	C₁₃×#554	1	16	yes	—
323	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
324	C₂²	C₂³×Q₈×C₁₃	1	2	yes	—
325	C₂²	C₂²×C₁₃×#41	1	2	yes	—
326	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	16	no	—
329	C₄	—	4	4	no	—
330	C₄	—	4	4	no	—
331	C₄	—	4	8	no	—
332	C₄	C₂×C₁₃×#123	1	8	yes	—
333	C₂	—	2	8	no	—
334	C₂	C₁₃×#2502	1	8	yes	direct product factor
335	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
336	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
337	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
338	C₂	C₂×C₁₃×#554	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2502	C₂	direct (N × H)
4. C₂×C₁₃×#398	C₂	semidirect
5. C₂×C₁₃×#391	C₂	semidirect
7. C₂×C₁₃×#384	C₂	semidirect
24. C₁₃×#398	C₂²	semidirect
25. C₁₃×#391	C₂²	semidirect
27. C₁₃×#384	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
67. C₂×#2502	C₁₃	direct (N × H)
108. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
112. #2502	C₂×C₁₃	direct (N × H)
113. C₂×#398	C₂×C₁₃	semidirect
114. C₂×#391	C₂×C₁₃	semidirect
116. C₂×#384	C₂×C₁₃	semidirect
168. #398	C₂²×C₁₃	semidirect
169. #391	C₂²×C₁₃	semidirect
171. #384	C₂²×C₁₃	semidirect
223. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
231. C₂×C₁₃	#2502	direct (N × H)
276. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
278. C₁₃	C₂×#2502	direct (N × H)
334. C₂	C₁₃×#2502	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×C₂²⋊Q₈	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2502	2
C₂×C₁₃×#398	2
C₂×C₁₃×#391	2
C₂×C₁₃×#385	2
C₂×C₁₃×#384	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2502	13

Subgroups — C2×C13×#2502 #15721104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2502 #15721104