Subgroups — C₂×C₁₃×#3414 #15748970

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 332 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	2	yes	maximal, complemented
2	C₁₃×#3414	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#510	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#509	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#508	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#41	—	2	2	no	—
8	C₂×C₁₃×#135	—	2	2	no	—
9	C₂×C₁₃×#135	—	2	2	no	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	C₂²	1	4	yes	—
12	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
13	C₂×C₁₃×#135	C₂²	1	16	yes	complemented
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
15	C₂²×C₁₃×SD₁₆	—	2	2	no	—
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#510	C₂²	1	32	yes	complemented
19	C₁₃×#509	C₂²	1	32	yes	complemented
20	C₁₃×#508	C₂²	1	32	yes	complemented
21	C₂×C₁₃×Q₃₂	C₂²	1	4	yes	complemented
22	C₂×C₁₃×SD₃₂	C₂²	1	8	yes	complemented
23	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
24	C₂×C₁₃×M₃₂	C₂²	1	4	yes	complemented
25	C₂×C₁₃×M₃₂	C₂²	1	8	yes	complemented
26	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#41	—	2	4	no	—
28	C₂×C₁₃×#41	—	2	16	no	—
29	C₂×C₁₃×#41	—	2	4	no	—
30	C₂×C₁₃×#41	—	4	2	no	—
31	C₂×C₁₃×#41	—	4	8	no	—
32	C₂×C₁₃×#41	—	4	2	no	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₃	—	4	2	no	—
36	C₂³×C₄×C₁₃	—	4	2	no	—
37	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
38	C₁₃×#135	—	2	8	no	—
39	C₁₃×#135	—	2	16	no	—
40	C₁₃×#135	—	2	8	no	—
41	C₁₃×#135	—	2	16	no	—
42	C₁₃×#135	C₂³	1	16	yes	—
43	C₁₃×#135	C₂³	1	16	yes	complemented
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	—	2	4	no	—
46	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
47	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	16	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	4	no	—
53	C₂×C₁₃×D₈	C₂³	1	4	yes	—
54	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
55	C₂²×C₈×C₁₃	D₄	1	2	yes	—
56	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	D₄	1	4	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
61	C₁₃×Q₃₂	C₂³	1	16	yes	complemented
62	C₁₃×SD₃₂	C₂³	1	32	yes	complemented
63	C₁₃×D₁₆	C₂³	1	16	yes	complemented
64	C₁₃×M₃₂	C₂³	1	16	yes	complemented
65	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×C₁₆	C₂³	1	8	yes	complemented
67	C₂×#3414	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	4	2	no	—
69	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
70	C₁₃×#41	—	2	16	no	—
71	C₁₃×#41	—	2	16	no	—
72	C₁₃×#41	—	4	16	no	—
73	C₁₃×#41	—	4	8	no	—
74	C₁₃×#41	—	4	8	no	—
75	C₁₃×#41	—	4	16	no	—
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	—	2	8	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×Q₈×C₁₃	—	4	4	no	—
80	C₂×D₄×C₁₃	—	2	4	no	—
81	C₂×D₄×C₁₃	—	2	8	no	—
82	C₂×D₄×C₁₃	—	4	4	no	—
83	C₂×D₄×C₁₃	—	4	4	no	—
84	C₂×D₄×C₁₃	—	4	16	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	4	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	4	16	no	—
90	C₂²×C₄×C₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	D₈	1	4	yes	—
93	C₂²×C₄×C₁₃	D₈	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₁₃×Q₁₆	—	2	4	no	—
98	C₁₃×Q₁₆	—	2	8	no	—
99	C₁₃×Q₁₆	C₂⁴	1	8	yes	—
100	C₁₃×SD₁₆	—	2	16	no	—
101	C₁₃×SD₁₆	—	2	16	no	—
102	C₁₃×D₈	—	2	4	no	—
103	C₁₃×D₈	—	2	8	no	—
104	C₁₃×D₈	C₂⁴	1	8	yes	—
105	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
107	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
109	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
113	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
114	C₁₃×C₁₆	C₂⁴	1	8	yes	—
115	C₂²×#135	C₂×C₁₃	1	2	yes	complemented
116	#3414	C₂×C₁₃	1	16	yes	direct product factor
117	C₂×#510	C₂×C₁₃	1	4	yes	complemented
118	C₂×#509	C₂×C₁₃	1	4	yes	complemented
119	C₂×#508	C₂×C₁₃	1	4	yes	complemented
120	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂³×C₁₃	—	4	2	no	—
122	C₂³×C₁₃	—	4	8	no	—
123	C₂³×C₁₃	—	4	4	no	—
124	C₂³×C₁₃	—	8	8	no	—
125	C₂³×C₁₃	C₂×D₈	1	2	yes	—
126	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
127	C₂³×C₁₃	C₂×D₈	1	4	yes	—
128	Q₈×C₁₃	—	2	8	no	—
129	Q₈×C₁₃	—	4	8	no	—
130	Q₈×C₁₃	—	4	4	no	—
131	D₄×C₁₃	—	2	8	no	—
132	D₄×C₁₃	—	4	16	no	—
133	D₄×C₁₃	—	4	16	no	—
134	D₄×C₁₃	—	4	8	no	—
135	D₄×C₁₃	—	4	4	no	—
136	C₂×C₄×C₁₃	—	4	8	no	—
137	C₂×C₄×C₁₃	—	4	4	no	—
138	C₂×C₄×C₁₃	—	4	16	no	—
139	C₂×C₄×C₁₃	—	4	16	no	—
140	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
141	C₂×C₄×C₁₃	C₂×D₈	1	8	yes	—
142	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
143	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
149	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₁₃	C₂²×D₄	1	4	yes	—
151	C₈×C₁₃	C₂²×D₄	1	2	yes	—
152	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
153	C₂²×#41	—	2	2	no	—
154	C₂×#135	—	2	2	no	—
155	C₂×#135	—	2	2	no	—
156	C₂×#135	—	2	8	no	—
157	C₂×#135	C₂²×C₁₃	1	4	yes	—
158	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
159	C₂×#135	C₂²×C₁₃	1	16	yes	complemented
160	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
161	C₂²×SD₁₆	—	2	2	no	—
162	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
163	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
164	#510	C₂²×C₁₃	1	32	yes	complemented
165	#509	C₂²×C₁₃	1	32	yes	complemented
166	#508	C₂²×C₁₃	1	32	yes	complemented
167	C₂×Q₃₂	C₂²×C₁₃	1	4	yes	complemented
168	C₂×SD₃₂	C₂²×C₁₃	1	8	yes	complemented
169	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
170	C₂×M₃₂	C₂²×C₁₃	1	4	yes	complemented
171	C₂×M₃₂	C₂²×C₁₃	1	8	yes	complemented
172	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
173	C₂²×C₁₃	—	2	4	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	—	4	4	no	—
176	C₂²×C₁₃	—	4	8	no	—
177	C₂²×C₁₃	—	8	16	no	—
178	C₂²×C₁₃	—	8	8	no	—
179	C₂²×C₁₃	C₂²×D₈	1	4	yes	—
180	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
181	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₁₃	—	4	8	no	—
183	C₄×C₁₃	C₂²×D₈	1	2	yes	—
184	C₄×C₁₃	C₂²×D₈	1	4	yes	—
185	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
187	C₂×#41	—	2	4	no	—
188	C₂×#41	—	2	4	no	—
189	C₂×#41	—	2	16	no	—
190	C₂×#41	—	4	2	no	—
191	C₂×#41	—	4	2	no	—
192	C₂×#41	—	4	8	no	—
193	C₂²×Q₈	—	2	2	no	—
194	C₂²×D₄	—	2	2	no	—
195	C₂²×D₄	—	4	2	no	—
196	C₂³×C₄	—	4	2	no	—
197	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
198	#135	—	2	8	no	—
199	#135	—	2	16	no	—
200	#135	—	2	8	no	—
201	#135	—	2	16	no	—
202	#135	C₂³×C₁₃	1	16	yes	—
203	#135	C₂³×C₁₃	1	16	yes	complemented
204	C₂×Q₁₆	—	2	2	no	—
205	C₂×Q₁₆	—	2	4	no	—
206	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
207	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
208	C₂×SD₁₆	—	2	4	no	—
209	C₂×SD₁₆	—	2	4	no	—
210	C₂×SD₁₆	—	2	16	no	—
211	C₂×D₈	—	2	2	no	—
212	C₂×D₈	—	2	4	no	—
213	C₂×D₈	C₂³×C₁₃	1	4	yes	—
214	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
215	C₂²×C₈	D₄×C₁₃	1	2	yes	—
216	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
217	C₂²×C₈	D₄×C₁₃	1	4	yes	—
218	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
221	Q₃₂	C₂³×C₁₃	1	16	yes	complemented
222	SD₃₂	C₂³×C₁₃	1	32	yes	complemented
223	D₁₆	C₂³×C₁₃	1	16	yes	complemented
224	M₃₂	C₂³×C₁₃	1	16	yes	complemented
225	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
226	C₂×C₁₆	C₂³×C₁₃	1	8	yes	complemented
227	C₂×C₁₃	—	2	4	no	—
228	C₂×C₁₃	—	2	2	no	—
229	C₂×C₁₃	—	8	8	no	—
230	C₂×C₁₃	#3414	1	2	yes	direct product factor
231	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
232	C₂⁴	—	4	2	no	—
233	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
234	#41	—	2	16	no	—
235	#41	—	2	16	no	—
236	#41	—	4	16	no	—
237	#41	—	4	8	no	—
238	#41	—	4	8	no	—
239	#41	—	4	16	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	2	8	no	—
242	C₂×Q₈	—	4	2	no	—
243	C₂×Q₈	—	4	4	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	4	4	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂×D₄	—	4	16	no	—
249	C₂×D₄	—	4	2	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	16	no	—
255	C₂²×C₄	C₁₃×D₈	1	2	yes	—
256	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
257	C₂²×C₄	C₁₃×D₈	1	4	yes	—
258	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
261	Q₁₆	—	2	4	no	—
262	Q₁₆	—	2	8	no	—
263	Q₁₆	C₂⁴×C₁₃	1	8	yes	—
264	SD₁₆	—	2	16	no	—
265	SD₁₆	—	2	16	no	—
266	D₈	—	2	4	no	—
267	D₈	—	2	8	no	—
268	D₈	C₂⁴×C₁₃	1	8	yes	—
269	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
270	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
271	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
273	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
274	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
275	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
276	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
277	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
278	C₁₆	C₂⁴×C₁₃	1	8	yes	—
279	C₁₃	C₂×#3414	1	1	yes	characteristic, direct product factor, Sylow
280	C₂³	—	4	2	no	—
281	C₂³	—	4	8	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	8	8	no	—
284	C₂³	C₂×C₁₃×D₈	1	2	yes	—
285	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
286	C₂³	C₂×C₁₃×D₈	1	4	yes	—
287	Q₈	—	2	8	no	—
288	Q₈	—	4	8	no	—
289	Q₈	—	4	4	no	—
290	D₄	—	2	8	no	—
291	D₄	—	4	16	no	—
292	D₄	—	4	16	no	—
293	D₄	—	4	8	no	—
294	D₄	—	4	4	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	—	4	16	no	—
299	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
300	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
301	C₂×C₄	C₂×C₁₃×D₈	1	8	yes	—
302	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
303	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
304	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
305	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
308	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
309	C₈	C₂²×D₄×C₁₃	1	4	yes	—
310	C₈	C₂²×D₄×C₁₃	1	2	yes	—
311	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
312	C₂²	—	2	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	8	no	—
316	C₂²	—	8	16	no	—
317	C₂²	—	8	8	no	—
318	C₂²	C₂²×C₁₃×D₈	1	4	yes	—
319	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
320	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
321	C₄	—	4	8	no	—
322	C₄	C₂²×C₁₃×D₈	1	2	yes	—
323	C₄	C₂²×C₁₃×D₈	1	4	yes	—
324	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
325	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
326	C₂	—	2	4	no	—
327	C₂	—	2	2	no	—
328	C₂	—	8	8	no	—
329	C₂	C₁₃×#3414	1	2	yes	direct product factor
330	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×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. C₁₃×#3414	C₂	direct (N × H)
3. C₂×C₁₃×#510	C₂	semidirect
4. C₂×C₁₃×#509	C₂	semidirect
5. C₂×C₁₃×#508	C₂	semidirect
6. C₂²×C₁₃×M₃₂	C₂	semidirect
12. C₂×C₁₃×#135	C₂²	semidirect
13. C₂×C₁₃×#135	C₂²	semidirect
14. C₂²×C₁₃×Q₁₆	C₂²	semidirect
16. C₂²×C₁₃×D₈	C₂²	semidirect
18. C₁₃×#510	C₂²	semidirect
19. C₁₃×#509	C₂²	semidirect
20. C₁₃×#508	C₂²	semidirect
21. C₂×C₁₃×Q₃₂	C₂²	semidirect
22. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₂×C₁₃×D₁₆	C₂²	semidirect
24. C₂×C₁₃×M₃₂	C₂²	semidirect
25. C₂×C₁₃×M₃₂	C₂²	semidirect
26. C₂²×C₁₃×C₁₆	C₂²	semidirect
43. C₁₃×#135	C₂³	semidirect
47. C₂×C₁₃×Q₁₆	C₂³	semidirect
54. C₂×C₁₃×D₈	C₂³	semidirect
61. C₁₃×Q₃₂	C₂³	semidirect
62. C₁₃×SD₃₂	C₂³	semidirect
63. C₁₃×D₁₆	C₂³	semidirect
64. C₁₃×M₃₂	C₂³	semidirect
66. C₂×C₁₃×C₁₆	C₂³	semidirect
67. C₂×#3414	C₁₃	direct (N × H)
115. C₂²×#135	C₂×C₁₃	semidirect
116. #3414	C₂×C₁₃	direct (N × H)
117. C₂×#510	C₂×C₁₃	semidirect
118. C₂×#509	C₂×C₁₃	semidirect
119. C₂×#508	C₂×C₁₃	semidirect
120. C₂²×M₃₂	C₂×C₁₃	semidirect
158. C₂×#135	C₂²×C₁₃	semidirect
159. C₂×#135	C₂²×C₁₃	semidirect
160. C₂²×Q₁₆	C₂²×C₁₃	semidirect
162. C₂²×D₈	C₂²×C₁₃	semidirect
164. #510	C₂²×C₁₃	semidirect
165. #509	C₂²×C₁₃	semidirect
166. #508	C₂²×C₁₃	semidirect
167. C₂×Q₃₂	C₂²×C₁₃	semidirect
168. C₂×SD₃₂	C₂²×C₁₃	semidirect
169. C₂×D₁₆	C₂²×C₁₃	semidirect
170. C₂×M₃₂	C₂²×C₁₃	semidirect
171. C₂×M₃₂	C₂²×C₁₃	semidirect
172. C₂²×C₁₆	C₂²×C₁₃	semidirect
203. #135	C₂³×C₁₃	semidirect
207. C₂×Q₁₆	C₂³×C₁₃	semidirect
214. C₂×D₈	C₂³×C₁₃	semidirect
221. Q₃₂	C₂³×C₁₃	semidirect
222. SD₃₂	C₂³×C₁₃	semidirect
223. D₁₆	C₂³×C₁₃	semidirect
224. M₃₂	C₂³×C₁₃	semidirect
226. C₂×C₁₆	C₂³×C₁₃	semidirect
230. C₂×C₁₃	#3414	direct (N × H)
279. C₁₃	C₂×#3414	direct (N × H)
329. C₂	C₁₃×#3414	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
C₁₃×#3414	2
C₂×C₁₃×#510	2
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₂²×C₁₃×M₃₂	2
C₂×#3414	13

Subgroups — C2×C13×#3414 #15748970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3414 #15748970