Subgroups — C₂×C₁₃×#3147 #15746971

Order 3328.

3366 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	4	yes	maximal, complemented
2	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3147	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#495	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#492	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	4	yes	—
10	C₂×C₁₃×#135	—	2	32	no	—
11	C₂×C₁₃×#135	C₂²	1	32	yes	complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
15	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#532	—	2	8	no	—
17	C₁₃×#532	C₂²	1	16	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#127	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	4	yes	—
21	C₂×C₁₃×#121	—	2	4	no	—
22	C₂×C₄×D₄×C₁₃	—	2	4	no	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#495	C₂²	1	32	yes	complemented
25	C₁₃×#494	C₂²	1	8	yes	complemented
26	C₁₃×#493	C₂²	1	8	yes	complemented
27	C₁₃×#492	C₂²	1	16	yes	complemented
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#41	—	2	8	no	—
33	C₂×C₁₃×#41	—	2	32	no	—
34	C₂×C₁₃×#41	C₂³	1	16	yes	—
35	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
36	C₂²×D₄×C₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₃	—	2	4	no	—
40	C₂³×C₄×C₁₃	D₄	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#135	—	2	128	no	—
43	C₂×C₁₃×Q₁₆	—	2	16	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
45	C₂×C₁₃×SD₁₆	—	2	32	no	—
46	C₂×C₁₃×SD₁₆	C₂³	1	32	yes	—
47	C₂×C₁₃×D₈	—	2	16	no	—
48	C₂×C₁₃×D₈	C₂³	1	16	yes	—
49	C₂²×C₈×C₁₃	D₄	1	16	yes	complemented
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
55	C₁₃×#127	—	2	4	no	—
56	C₁₃×#127	C₂³	1	8	yes	—
57	C₁₃×#124	—	2	8	no	—
58	C₁₃×#124	C₂³	1	16	yes	—
59	C₁₃×#121	—	2	32	no	—
60	C₄×D₄×C₁₃	—	2	32	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
63	C₂×C₄²×C₁₃	D₄	1	4	yes	—
64	C₂×C₄²×C₁₃	D₄	1	2	yes	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
68	C₄×C₈×C₁₃	C₂³	1	4	yes	—
69	C₄×C₈×C₁₃	C₂³	1	4	yes	—
70	C₄×C₈×C₁₃	C₂³	1	8	yes	—
71	C₂×#3147	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	4	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₁₃×#41	—	2	64	no	—
75	C₁₃×#41	—	4	32	no	—
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	16	no	—
78	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
79	C₂×D₄×C₁₃	—	2	16	no	—
80	C₂×D₄×C₁₃	—	2	16	no	—
81	C₂×D₄×C₁₃	—	2	16	no	—
82	C₂×D₄×C₁₃	—	2	4	no	—
83	C₂×D₄×C₁₃	—	4	16	no	—
84	C₂×D₄×C₁₃	—	4	16	no	—
85	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	16	no	—
89	C₂²×C₄×C₁₃	—	4	16	no	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
98	C₁₃×Q₁₆	—	2	32	no	—
99	C₁₃×SD₁₆	—	2	64	no	—
100	C₁₃×D₈	—	2	32	no	—
101	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
102	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
103	C₂×C₈×C₁₃	C₂×D₄	1	32	yes	complemented
104	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
106	C₁₃×C₄⋊C₄	—	2	16	no	—
107	C₁₃×C₂²⋊C₄	—	2	32	no	—
108	C₄²×C₁₃	C₂×D₄	1	8	yes	—
109	C₄²×C₁₃	C₂×D₄	1	2	yes	—
110	C₄²×C₁₃	C₂×D₄	1	2	yes	—
111	C₄²×C₁₃	C₂⁴	1	2	yes	—
112	C₄²×C₁₃	C₂⁴	1	2	yes	—
113	C₂²×#135	C₂×C₁₃	1	4	yes	complemented
114	C₂×#532	C₂×C₁₃	1	2	yes	complemented
115	#3147	C₂×C₁₃	1	16	yes	direct product factor
116	C₂×#495	C₂×C₁₃	1	4	yes	complemented
117	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×#492	C₂×C₁₃	1	2	yes	complemented
120	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂³×C₁₃	—	2	4	no	—
122	C₂³×C₁₃	—	2	8	no	—
123	C₂³×C₁₃	—	4	8	no	—
124	C₂³×C₁₃	—	4	16	no	—
125	C₂³×C₁₃	#127	1	4	yes	—
126	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
127	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
128	Q₈×C₁₃	—	2	16	no	—
129	Q₈×C₁₃	—	4	8	no	—
130	D₄×C₁₃	—	2	16	no	—
131	D₄×C₁₃	—	4	32	no	—
132	D₄×C₁₃	—	4	8	no	—
133	D₄×C₁₃	—	4	32	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	16	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	4	8	no	—
138	C₂×C₄×C₁₃	—	4	32	no	—
139	C₂×C₄×C₁₃	#127	1	4	yes	—
140	C₂×C₄×C₁₃	#127	1	8	yes	—
141	C₂×C₄×C₁₃	#135	1	8	yes	complemented
142	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
147	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
149	C₈×C₁₃	C₂²×D₄	1	8	yes	—
150	C₈×C₁₃	C₂²×D₄	1	8	yes	—
151	C₂²×#41	C₂²×C₁₃	1	4	yes	—
152	C₂×#135	—	2	32	no	—
153	C₂×#135	C₂²×C₁₃	1	32	yes	complemented
154	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
155	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	—
156	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
157	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
158	#532	—	2	8	no	—
159	#532	C₂²×C₁₃	1	16	yes	complemented
160	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
161	C₂×#127	C₂²×C₁₃	1	2	yes	—
162	C₂×#124	C₂²×C₁₃	1	4	yes	—
163	C₂×#121	—	2	4	no	—
164	C₂×C₄×D₄	—	2	4	no	—
165	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
166	#495	C₂²×C₁₃	1	32	yes	complemented
167	#494	C₂²×C₁₃	1	8	yes	complemented
168	#493	C₂²×C₁₃	1	8	yes	complemented
169	#492	C₂²×C₁₃	1	16	yes	complemented
170	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	8	yes	complemented
174	C₂²×C₁₃	—	2	8	no	—
175	C₂²×C₁₃	—	2	4	no	—
176	C₂²×C₁₃	—	4	8	no	—
177	C₂²×C₁₃	—	4	16	no	—
178	C₂²×C₁₃	—	8	16	no	—
179	C₂²×C₁₃	C₂×#127	1	4	yes	—
180	C₂²×C₁₃	C₂×#127	1	2	yes	—
181	C₂²×C₁₃	C₂×#135	1	4	yes	—
182	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
183	C₄×C₁₃	—	2	4	no	—
184	C₄×C₁₃	—	4	8	no	—
185	C₄×C₁₃	C₂×#127	1	4	yes	—
186	C₄×C₁₃	C₂×#127	1	2	yes	—
187	C₄×C₁₃	C₂×#135	1	8	yes	complemented
188	C₄×C₁₃	C₂³×D₄	1	2	yes	—
189	C₂×#41	—	2	8	no	—
190	C₂×#41	—	2	32	no	—
191	C₂×#41	C₂³×C₁₃	1	16	yes	—
192	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
193	C₂²×D₄	—	2	4	no	—
194	C₂²×D₄	—	2	4	no	—
195	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
196	C₂³×C₄	—	2	4	no	—
197	C₂³×C₄	D₄×C₁₃	1	2	yes	—
198	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
199	#135	—	2	128	no	—
200	C₂×Q₁₆	—	2	16	no	—
201	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
202	C₂×SD₁₆	—	2	32	no	—
203	C₂×SD₁₆	C₂³×C₁₃	1	32	yes	—
204	C₂×D₈	—	2	16	no	—
205	C₂×D₈	C₂³×C₁₃	1	16	yes	—
206	C₂²×C₈	D₄×C₁₃	1	16	yes	complemented
207	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
208	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
209	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
210	C₄⋊Q₈	—	2	4	no	—
211	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
212	#127	—	2	4	no	—
213	#127	C₂³×C₁₃	1	8	yes	—
214	#124	—	2	8	no	—
215	#124	C₂³×C₁₃	1	16	yes	—
216	#121	—	2	32	no	—
217	C₄×D₄	—	2	32	no	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₂²⋊C₄	—	2	8	no	—
220	C₂×C₄²	D₄×C₁₃	1	2	yes	—
221	C₂×C₄²	D₄×C₁₃	1	4	yes	—
222	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
225	C₄×C₈	C₂³×C₁₃	1	4	yes	—
226	C₄×C₈	C₂³×C₁₃	1	4	yes	—
227	C₄×C₈	C₂³×C₁₃	1	8	yes	—
228	C₂×C₁₃	—	2	4	no	—
229	C₂×C₁₃	—	8	8	no	—
230	C₂×C₁₃	#3147	1	4	yes	direct product factor
231	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
232	C₂×C₁₃	C₂²×#135	1	2	yes	—
233	C₂⁴	—	2	4	no	—
234	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
235	#41	—	2	64	no	—
236	#41	—	4	32	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	16	no	—
239	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
240	C₂×D₄	—	2	16	no	—
241	C₂×D₄	—	2	16	no	—
242	C₂×D₄	—	2	16	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	4	16	no	—
245	C₂×D₄	—	4	16	no	—
246	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	4	16	no	—
251	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
256	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
257	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
259	Q₁₆	—	2	32	no	—
260	SD₁₆	—	2	64	no	—
261	D₈	—	2	32	no	—
262	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
263	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
264	C₂×C₈	C₂×D₄×C₁₃	1	32	yes	complemented
265	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
266	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
267	C₄⋊C₄	—	2	16	no	—
268	C₂²⋊C₄	—	2	32	no	—
269	C₄²	C₂×D₄×C₁₃	1	8	yes	—
270	C₄²	C₂×D₄×C₁₃	1	2	yes	—
271	C₄²	C₂×D₄×C₁₃	1	2	yes	—
272	C₄²	C₂⁴×C₁₃	1	2	yes	—
273	C₄²	C₂⁴×C₁₃	1	2	yes	—
274	C₁₃	C₂×#3147	1	1	yes	characteristic, direct product factor, Sylow
275	C₂³	—	2	4	no	—
276	C₂³	—	2	8	no	—
277	C₂³	—	4	8	no	—
278	C₂³	—	4	16	no	—
279	C₂³	C₁₃×#127	1	4	yes	—
280	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
281	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
282	Q₈	—	2	16	no	—
283	Q₈	—	4	8	no	—
284	D₄	—	2	16	no	—
285	D₄	—	4	32	no	—
286	D₄	—	4	8	no	—
287	D₄	—	4	32	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	16	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	4	8	no	—
292	C₂×C₄	—	4	32	no	—
293	C₂×C₄	C₁₃×#127	1	4	yes	—
294	C₂×C₄	C₁₃×#127	1	8	yes	—
295	C₂×C₄	C₁₃×#135	1	8	yes	complemented
296	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
297	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
298	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
300	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
301	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
302	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
303	C₈	C₂²×D₄×C₁₃	1	8	yes	—
304	C₈	C₂²×D₄×C₁₃	1	8	yes	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	8	no	—
307	C₂²	—	4	16	no	—
308	C₂²	—	4	8	no	—
309	C₂²	—	8	16	no	—
310	C₂²	C₂×C₁₃×#127	1	4	yes	—
311	C₂²	C₂×C₁₃×#127	1	2	yes	—
312	C₂²	C₂×C₁₃×#135	1	4	yes	—
313	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
314	C₄	—	2	4	no	—
315	C₄	—	4	8	no	—
316	C₄	C₂×C₁₃×#127	1	4	yes	—
317	C₄	C₂×C₁₃×#127	1	2	yes	—
318	C₄	C₂×C₁₃×#135	1	8	yes	complemented
319	C₄	C₂³×D₄×C₁₃	1	2	yes	—
320	C₂	—	2	4	no	—
321	C₂	—	8	8	no	—
322	C₂	C₁₃×#3147	1	4	yes	direct product factor
323	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
324	C₂	C₂²×C₁₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3147	C₂	direct (N × H)
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#494	C₂	semidirect
6. C₂×C₁₃×#493	C₂	semidirect
7. C₂×C₁₃×#492	C₂	semidirect
8. C₂²×C₄×C₈×C₁₃	C₂	semidirect
11. C₂×C₁₃×#135	C₂²	semidirect
17. C₁₃×#532	C₂²	semidirect
24. C₁₃×#495	C₂²	semidirect
25. C₁₃×#494	C₂²	semidirect
26. C₁₃×#493	C₂²	semidirect
27. C₁₃×#492	C₂²	semidirect
31. C₂×C₄×C₈×C₁₃	C₂²	semidirect
49. C₂²×C₈×C₁₃	D₄	semidirect
71. C₂×#3147	C₁₃	direct (N × H)
103. C₂×C₈×C₁₃	C₂×D₄	semidirect
113. C₂²×#135	C₂×C₁₃	semidirect
114. C₂×#532	C₂×C₁₃	semidirect
115. #3147	C₂×C₁₃	direct (N × H)
116. C₂×#495	C₂×C₁₃	semidirect
117. C₂×#494	C₂×C₁₃	semidirect
118. C₂×#493	C₂×C₁₃	semidirect
119. C₂×#492	C₂×C₁₃	semidirect
120. C₂²×C₄×C₈	C₂×C₁₃	semidirect
141. C₂×C₄×C₁₃	#135	semidirect
153. C₂×#135	C₂²×C₁₃	semidirect
159. #532	C₂²×C₁₃	semidirect
166. #495	C₂²×C₁₃	semidirect
167. #494	C₂²×C₁₃	semidirect
168. #493	C₂²×C₁₃	semidirect
169. #492	C₂²×C₁₃	semidirect
173. C₂×C₄×C₈	C₂²×C₁₃	semidirect
187. C₄×C₁₃	C₂×#135	semidirect
206. C₂²×C₈	D₄×C₁₃	semidirect
230. C₂×C₁₃	#3147	direct (N × H)
264. C₂×C₈	C₂×D₄×C₁₃	semidirect
274. C₁₃	C₂×#3147	direct (N × H)
295. C₂×C₄	C₁₃×#135	semidirect
318. C₄	C₂×C₁₃×#135	semidirect
322. C₂	C₁₃×#3147	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×#135	2
C₂×C₁₃×#532	2
C₁₃×#3147	2
C₂×C₁₃×#495	2
C₂×C₁₃×#494	2
C₂×C₁₃×#493	2
C₂×C₁₃×#492	2
C₂²×C₄×C₈×C₁₃	2
C₂×#3147	13

Subgroups — C2×C13×#3147 #15746971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3147 #15746971