Subgroups — C₂×C₁₃×#3444 #15749007

Order 3328.

8518 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#533	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×#529	C₂	1	12	yes	maximal, complemented
5	C₂×C₁₃×#525	C₂	1	6	yes	maximal, complemented
6	C₂×C₄×C₁₃×#41	C₂	1	6	yes	maximal, complemented
7	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#41	C₂²	1	6	yes	—
9	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
10	C₁₃×#533	C₂²	1	48	yes	complemented
11	C₁₃×#532	C₂²	1	48	yes	complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#529	C₂²	1	192	yes	complemented
15	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#125	C₂²	1	6	yes	complemented
17	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
18	C₁₃×#525	C₂²	1	96	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	12	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	—
21	C₂×C₁₃×#121	C₂²	1	12	yes	—
22	C₂×C₁₃×#120	C₂²	1	4	yes	—
23	C₄×C₁₃×#41	C₂²	1	96	yes	complemented
24	C₂×C₄×Q₈×C₁₃	C₂²	1	12	yes	complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	6	yes	—
28	C₂×C₁₃×#117	C₂²	1	12	yes	complemented
29	C₂²×C₄²×C₁₃	C₂²	1	6	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	16	yes	complemented
33	C₂²×C₄²×C₁₃	C₂²	1	4	yes	complemented
34	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₁₃×#41	—	2	48	no	—
36	C₂×C₁₃×#41	C₂³	1	48	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
38	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
39	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
40	C₂³×C₄×C₁₃	—	2	24	no	—
41	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
47	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
48	C₁₃×#127	C₂³	1	8	yes	complemented
49	C₁₃×#126	C₂³	1	64	yes	complemented
50	C₁₃×#125	C₂³	1	48	yes	complemented
51	C₁₃×#124	C₂³	1	48	yes	complemented
52	C₁₃×#123	C₂³	1	96	yes	—
53	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	—
54	C₁₃×#121	C₂³	1	96	yes	—
55	C₁₃×#120	C₂³	1	32	yes	—
56	C₄×Q₈×C₁₃	C₂³	1	96	yes	complemented
57	C₄×D₄×C₁₃	C₂³	1	192	yes	—
58	C₄×D₄×C₁₃	C₂³	1	96	yes	complemented
59	C₁₃×#117	C₂³	1	48	yes	—
60	C₁₃×#117	C₂³	1	96	yes	complemented
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
63	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
65	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	48	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	32	yes	complemented
76	C₂×#3444	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	12	no	—
78	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
79	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
81	C₁₃×#41	—	2	192	no	—
82	C₂×Q₈×C₁₃	—	2	24	no	—
83	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
84	C₂×D₄×C₁₃	—	2	48	no	—
85	C₂×D₄×C₁₃	—	2	24	no	—
86	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
87	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
88	C₂²×C₄×C₁₃	—	2	12	no	—
89	C₂²×C₄×C₁₃	—	2	24	no	—
90	C₂²×C₄×C₁₃	—	2	24	no	—
91	C₂²×C₄×C₁₃	—	2	48	no	—
92	C₂²×C₄×C₁₃	—	2	96	no	—
93	C₂²×C₄×C₁₃	#41	1	24	yes	complemented
94	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	48	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
103	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
104	C₁₃×C₄⋊C₄	C₂⁴	1	96	yes	—
105	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
106	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
107	C₄²×C₁₃	C₂⁴	1	12	yes	—
108	C₄²×C₁₃	C₂⁴	1	24	yes	—
109	C₄²×C₁₃	C₂⁴	1	12	yes	—
110	C₄²×C₁₃	C₂⁴	1	8	yes	—
111	C₄²×C₁₃	C₂⁴	1	4	yes	—
112	C₄²×C₁₃	C₂⁴	1	4	yes	—
113	C₄²×C₁₃	C₂⁴	1	48	yes	—
114	#3444	C₂×C₁₃	1	32	yes	direct product factor
115	C₂×#533	C₂×C₁₃	1	3	yes	complemented
116	C₂×#532	C₂×C₁₃	1	3	yes	complemented
117	C₂×#529	C₂×C₁₃	1	12	yes	complemented
118	C₂×#525	C₂×C₁₃	1	6	yes	complemented
119	C₂×C₄×#41	C₂×C₁₃	1	6	yes	complemented
120	C₂³×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂³×C₁₃	—	2	32	no	—
122	C₂³×C₁₃	—	2	24	no	—
123	C₂³×C₁₃	—	2	12	no	—
124	C₂³×C₁₃	—	2	24	no	—
125	C₂³×C₁₃	C₂×#41	1	12	yes	—
126	C₂³×C₁₃	C₂⁵	1	8	yes	—
127	C₂³×C₁₃	C₂⁵	1	6	yes	—
128	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
129	Q₈×C₁₃	—	2	48	no	—
130	D₄×C₁₃	—	2	96	no	—
131	D₄×C₁₃	—	2	48	no	—
132	C₂×C₄×C₁₃	—	2	24	no	—
133	C₂×C₄×C₁₃	—	2	12	no	—
134	C₂×C₄×C₁₃	—	2	24	no	—
135	C₂×C₄×C₁₃	—	2	48	no	—
136	C₂×C₄×C₁₃	—	2	48	no	—
137	C₂×C₄×C₁₃	—	2	96	no	—
138	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
139	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
140	C₂×C₄×C₁₃	C₂×#41	1	48	yes	complemented
141	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
142	C₂×C₄×C₁₃	C₂⁵	1	24	yes	—
143	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
144	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
145	C₂²×#41	C₂²×C₁₃	1	6	yes	—
146	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
147	#533	C₂²×C₁₃	1	48	yes	complemented
148	#532	C₂²×C₁₃	1	48	yes	complemented
149	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
150	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
151	#529	C₂²×C₁₃	1	192	yes	complemented
152	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
153	C₂×#125	C₂²×C₁₃	1	6	yes	complemented
154	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
155	#525	C₂²×C₁₃	1	96	yes	complemented
156	C₂×#123	C₂²×C₁₃	1	12	yes	—
157	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	—
158	C₂×#121	C₂²×C₁₃	1	12	yes	—
159	C₂×#120	C₂²×C₁₃	1	4	yes	—
160	C₄×#41	C₂²×C₁₃	1	96	yes	complemented
161	C₂×C₄×Q₈	C₂²×C₁₃	1	12	yes	complemented
162	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	—
163	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
164	C₂×#117	C₂²×C₁₃	1	6	yes	—
165	C₂×#117	C₂²×C₁₃	1	12	yes	complemented
166	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
167	C₂²×C₄²	C₂²×C₁₃	1	6	yes	—
168	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
169	C₂²×C₄²	C₂²×C₁₃	1	16	yes	complemented
170	C₂²×C₄²	C₂²×C₁₃	1	4	yes	complemented
171	C₂²×C₁₃	—	2	32	no	—
172	C₂²×C₁₃	—	2	12	no	—
173	C₂²×C₁₃	—	2	24	no	—
174	C₂²×C₁₃	—	2	24	no	—
175	C₂²×C₁₃	—	4	16	no	—
176	C₂²×C₁₃	C₂²×#41	1	12	yes	—
177	C₂²×C₁₃	C₂²×#41	1	6	yes	—
178	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
179	C₄×C₁₃	—	2	12	no	—
180	C₄×C₁₃	—	2	24	no	—
181	C₄×C₁₃	C₂²×#41	1	12	yes	—
182	C₄×C₁₃	C₂²×#41	1	12	yes	—
183	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
184	C₂×#41	—	2	48	no	—
185	C₂×#41	C₂³×C₁₃	1	48	yes	—
186	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
187	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
188	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
189	C₂³×C₄	—	2	24	no	—
190	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
191	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
192	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
193	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
194	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
195	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
196	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
197	#127	C₂³×C₁₃	1	8	yes	complemented
198	#126	C₂³×C₁₃	1	64	yes	complemented
199	#125	C₂³×C₁₃	1	48	yes	complemented
200	#124	C₂³×C₁₃	1	48	yes	complemented
201	#123	C₂³×C₁₃	1	96	yes	—
202	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	—
203	#121	C₂³×C₁₃	1	96	yes	—
204	#120	C₂³×C₁₃	1	32	yes	—
205	C₄×Q₈	C₂³×C₁₃	1	96	yes	complemented
206	C₄×D₄	C₂³×C₁₃	1	192	yes	—
207	C₄×D₄	C₂³×C₁₃	1	96	yes	complemented
208	#117	C₂³×C₁₃	1	48	yes	—
209	#117	C₂³×C₁₃	1	96	yes	complemented
210	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
211	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
212	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
214	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
215	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
216	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
217	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
218	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
219	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
220	C₂×C₄²	C₂³×C₁₃	1	48	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
223	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₃	1	32	yes	complemented
225	C₂×C₁₃	—	2	12	no	—
226	C₂×C₁₃	—	4	8	no	—
227	C₂×C₁₃	#3444	1	4	yes	direct product factor
228	C₂×C₁₃	C₂³×#41	1	3	yes	—
229	C₂⁴	—	2	12	no	—
230	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
231	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
232	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
233	#41	—	2	192	no	—
234	C₂×Q₈	—	2	24	no	—
235	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
236	C₂×D₄	—	2	48	no	—
237	C₂×D₄	—	2	24	no	—
238	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
239	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
240	C₂²×C₄	—	2	12	no	—
241	C₂²×C₄	—	2	24	no	—
242	C₂²×C₄	—	2	24	no	—
243	C₂²×C₄	—	2	48	no	—
244	C₂²×C₄	—	2	96	no	—
245	C₂²×C₄	C₁₃×#41	1	24	yes	complemented
246	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
247	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
248	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
249	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
250	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
251	C₂²×C₄	C₂⁴×C₁₃	1	48	yes	—
252	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
253	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
254	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
255	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
256	C₄⋊C₄	C₂⁴×C₁₃	1	96	yes	—
257	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
258	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
259	C₄²	C₂⁴×C₁₃	1	4	yes	—
260	C₄²	C₂⁴×C₁₃	1	12	yes	—
261	C₄²	C₂⁴×C₁₃	1	24	yes	—
262	C₄²	C₂⁴×C₁₃	1	12	yes	—
263	C₄²	C₂⁴×C₁₃	1	8	yes	—
264	C₄²	C₂⁴×C₁₃	1	4	yes	—
265	C₄²	C₂⁴×C₁₃	1	48	yes	—
266	C₁₃	C₂×#3444	1	1	yes	characteristic, direct product factor, Sylow
267	C₂³	—	2	32	no	—
268	C₂³	—	2	24	no	—
269	C₂³	—	2	12	no	—
270	C₂³	—	2	24	no	—
271	C₂³	C₂×C₁₃×#41	1	12	yes	—
272	C₂³	C₂⁵×C₁₃	1	8	yes	—
273	C₂³	C₂⁵×C₁₃	1	6	yes	—
274	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
275	Q₈	—	2	48	no	—
276	D₄	—	2	96	no	—
277	D₄	—	2	48	no	—
278	C₂×C₄	—	2	24	no	—
279	C₂×C₄	—	2	12	no	—
280	C₂×C₄	—	2	24	no	—
281	C₂×C₄	—	2	48	no	—
282	C₂×C₄	—	2	48	no	—
283	C₂×C₄	—	2	96	no	—
284	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
285	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
286	C₂×C₄	C₂×C₁₃×#41	1	48	yes	complemented
287	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
288	C₂×C₄	C₂⁵×C₁₃	1	24	yes	—
289	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
290	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
291	C₂²	—	2	32	no	—
292	C₂²	—	2	12	no	—
293	C₂²	—	2	24	no	—
294	C₂²	—	2	24	no	—
295	C₂²	—	4	16	no	—
296	C₂²	C₂²×C₁₃×#41	1	12	yes	—
297	C₂²	C₂²×C₁₃×#41	1	6	yes	—
298	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
299	C₄	—	2	12	no	—
300	C₄	—	2	24	no	—
301	C₄	C₂²×C₁₃×#41	1	12	yes	—
302	C₄	C₂²×C₁₃×#41	1	12	yes	—
303	C₂	—	2	12	no	—
304	C₂	—	4	8	no	—
305	C₂	C₁₃×#3444	1	4	yes	direct product factor
306	C₂	C₂³×C₁₃×#41	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	direct (N × H)
2. C₂×C₁₃×#533	C₂	semidirect
3. C₂×C₁₃×#532	C₂	semidirect
4. C₂×C₁₃×#529	C₂	semidirect
5. C₂×C₁₃×#525	C₂	semidirect
6. C₂×C₄×C₁₃×#41	C₂	semidirect
7. C₂³×C₄²×C₁₃	C₂	semidirect
10. C₁₃×#533	C₂²	semidirect
11. C₁₃×#532	C₂²	semidirect
12. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
13. C₂×C₁₃×#127	C₂²	semidirect
14. C₁₃×#529	C₂²	semidirect
15. C₂×C₁₃×#126	C₂²	semidirect
16. C₂×C₁₃×#125	C₂²	semidirect
17. C₂×C₁₃×#124	C₂²	semidirect
18. C₁₃×#525	C₂²	semidirect
23. C₄×C₁₃×#41	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. C₂×C₁₃×#117	C₂²	semidirect
32. C₂²×C₄²×C₁₃	C₂²	semidirect
33. C₂²×C₄²×C₁₃	C₂²	semidirect
47. C₁₃×C₄⋊Q₈	C₂³	semidirect
48. C₁₃×#127	C₂³	semidirect
49. C₁₃×#126	C₂³	semidirect
50. C₁₃×#125	C₂³	semidirect
51. C₁₃×#124	C₂³	semidirect
56. C₄×Q₈×C₁₃	C₂³	semidirect
58. C₄×D₄×C₁₃	C₂³	semidirect
60. C₁₃×#117	C₂³	semidirect
75. C₂×C₄²×C₁₃	C₂³	semidirect
76. C₂×#3444	C₁₃	direct (N × H)
93. C₂²×C₄×C₁₃	#41	semidirect
114. #3444	C₂×C₁₃	direct (N × H)
115. C₂×#533	C₂×C₁₃	semidirect
116. C₂×#532	C₂×C₁₃	semidirect
117. C₂×#529	C₂×C₁₃	semidirect
118. C₂×#525	C₂×C₁₃	semidirect
119. C₂×C₄×#41	C₂×C₁₃	semidirect
120. C₂³×C₄²	C₂×C₁₃	semidirect
140. C₂×C₄×C₁₃	C₂×#41	semidirect
147. #533	C₂²×C₁₃	semidirect
148. #532	C₂²×C₁₃	semidirect
149. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
150. C₂×#127	C₂²×C₁₃	semidirect
151. #529	C₂²×C₁₃	semidirect
152. C₂×#126	C₂²×C₁₃	semidirect
153. C₂×#125	C₂²×C₁₃	semidirect
154. C₂×#124	C₂²×C₁₃	semidirect
155. #525	C₂²×C₁₃	semidirect
160. C₄×#41	C₂²×C₁₃	semidirect
161. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
163. C₂×C₄×D₄	C₂²×C₁₃	semidirect
165. C₂×#117	C₂²×C₁₃	semidirect
169. C₂²×C₄²	C₂²×C₁₃	semidirect
170. C₂²×C₄²	C₂²×C₁₃	semidirect
196. C₄⋊Q₈	C₂³×C₁₃	semidirect
197. #127	C₂³×C₁₃	semidirect
198. #126	C₂³×C₁₃	semidirect
199. #125	C₂³×C₁₃	semidirect
200. #124	C₂³×C₁₃	semidirect
205. C₄×Q₈	C₂³×C₁₃	semidirect
207. C₄×D₄	C₂³×C₁₃	semidirect
209. #117	C₂³×C₁₃	semidirect
224. C₂×C₄²	C₂³×C₁₃	semidirect
227. C₂×C₁₃	#3444	direct (N × H)
245. C₂²×C₄	C₁₃×#41	semidirect
266. C₁₃	C₂×#3444	direct (N × H)
286. C₂×C₄	C₂×C₁₃×#41	semidirect
305. C₂	C₁₃×#3444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3444	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂×C₄×C₁₃×#41	2
C₂³×C₄²×C₁₃	2
C₂×#3444	13

Subgroups — C2×C13×#3444 #15749007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3444 #15749007