Subgroups — C₂×C₁₃×#3170 #15747011

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	2	yes	maximal
2	C₁₃×#3170	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#467	C₂	1	4	yes	maximal
7	C₂×C₄×C₁₃×Q₁₆	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
10	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
11	C₁₃×#533	—	2	8	no	—
12	C₁₃×#533	C₂²	1	16	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#125	—	2	2	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
20	C₂×C₁₃×#117	—	2	2	no	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#500	C₂²	1	8	yes	complemented
23	C₁₃×#494	C₂²	1	8	yes	complemented
24	C₁₃×#487	C₂²	1	16	yes	complemented
25	C₁₃×#467	C₂²	1	32	yes	—
26	C₄×C₁₃×Q₁₆	C₂²	1	32	yes	complemented
27	C₂×C₁₃×#107	C₂²	1	4	yes	—
28	C₂×C₁₃×#103	C₂²	1	8	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	8	yes	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₁₃×Q₁₆	—	2	16	no	—
39	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
40	C₂²×C₈×C₁₃	—	2	8	no	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	—	2	4	no	—
46	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
47	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
48	C₁₃×#125	—	2	16	no	—
49	C₁₃×C₂²⋊Q₈	—	2	16	no	—
50	C₁₃×C₂²⋊Q₈	—	2	8	no	—
51	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
52	C₄×Q₈×C₁₃	—	2	16	no	—
53	C₄×Q₈×C₁₃	—	2	8	no	—
54	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
55	C₁₃×#117	—	2	16	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
63	C₂×C₄²×C₁₃	—	2	4	no	—
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	4	yes	—
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	C₂³	1	16	yes	—
71	C₁₃×#103	C₂³	1	32	yes	—
72	C₄×C₈×C₁₃	C₂³	1	8	yes	—
73	C₄×C₈×C₁₃	C₂³	1	4	yes	—
74	C₄×C₈×C₁₃	C₂³	1	4	yes	—
75	C₂×#3170	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	—	2	8	no	—
79	C₂×Q₈×C₁₃	—	2	16	no	—
80	C₂×Q₈×C₁₃	—	4	8	no	—
81	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	Q₁₆	1	8	yes	complemented
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₁₃×Q₁₆	—	2	32	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	16	no	—
100	C₂×C₈×C₁₃	#41	1	8	yes	—
101	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
102	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
103	C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₁₃×C₄⋊C₄	—	2	16	no	—
107	C₁₃×C₄⋊C₄	—	2	16	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
110	C₁₃×C₂²⋊C₄	—	2	16	no	—
111	C₄²×C₁₃	—	2	16	no	—
112	C₄²×C₁₃	C₂×D₄	1	4	yes	—
113	C₄²×C₁₃	C₂×D₄	1	2	yes	—
114	C₄²×C₁₃	C₂×D₄	1	4	yes	—
115	C₄²×C₁₃	C₂×D₄	1	2	yes	—
116	C₄²×C₁₃	C₂⁴	1	2	yes	—
117	C₄²×C₁₃	C₂⁴	1	2	yes	—
118	C₂×#533	C₂×C₁₃	1	2	yes	—
119	#3170	C₂×C₁₃	1	16	yes	direct product factor
120	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
122	C₂×#487	C₂×C₁₃	1	2	yes	complemented
123	C₂×#467	C₂×C₁₃	1	4	yes	—
124	C₂×C₄×Q₁₆	C₂×C₁₃	1	4	yes	complemented
125	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
129	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
130	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₁₃	—	2	16	no	—
132	Q₈×C₁₃	—	4	8	no	—
133	Q₈×C₁₃	—	4	16	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	4	8	no	—
142	C₂×C₄×C₁₃	—	4	8	no	—
143	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
144	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×Q₁₆	1	16	yes	complemented
146	C₂×C₄×C₁₃	#135	1	4	yes	—
147	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
154	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
155	C₈×C₁₃	—	2	4	no	—
156	C₈×C₁₃	C₂×#41	1	8	yes	—
157	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
158	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
159	#533	—	2	8	no	—
160	#533	C₂²×C₁₃	1	16	yes	—
161	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
162	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
163	C₂×#125	—	2	2	no	—
164	C₂×C₂²⋊Q₈	—	2	2	no	—
165	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
166	C₂×C₄×Q₈	—	2	2	no	—
167	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
168	C₂×#117	—	2	2	no	—
169	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
170	#500	C₂²×C₁₃	1	8	yes	complemented
171	#494	C₂²×C₁₃	1	8	yes	complemented
172	#487	C₂²×C₁₃	1	16	yes	complemented
173	#467	C₂²×C₁₃	1	32	yes	—
174	C₄×Q₁₆	C₂²×C₁₃	1	32	yes	complemented
175	C₂×#107	C₂²×C₁₃	1	4	yes	—
176	C₂×#103	C₂²×C₁₃	1	8	yes	—
177	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₁₃	1	8	yes	—
180	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	2	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	#532	1	2	yes	—
185	C₂²×C₁₃	C₂²×Q₁₆	1	4	yes	—
186	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
187	C₂²×C₁₃	C₂×#135	1	2	yes	—
188	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
189	C₄×C₁₃	—	2	2	no	—
190	C₄×C₁₃	—	2	2	no	—
191	C₄×C₁₃	—	4	8	no	—
192	C₄×C₁₃	—	4	8	no	—
193	C₄×C₁₃	#532	1	2	yes	—
194	C₄×C₁₃	C₂²×Q₁₆	1	4	yes	—
195	C₄×C₁₃	C₂²×Q₁₆	1	4	yes	—
196	C₄×C₁₃	C₂×#135	1	4	yes	—
197	C₄×C₁₃	C₂²×#41	1	2	yes	—
198	C₂²×Q₈	—	2	2	no	—
199	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
200	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
201	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
203	C₂×Q₁₆	—	2	16	no	—
204	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
205	C₂²×C₈	—	2	8	no	—
206	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
207	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
208	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
209	C₄⋊Q₈	—	2	4	no	—
210	C₄⋊Q₈	—	2	4	no	—
211	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
212	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
213	#125	—	2	16	no	—
214	C₂²⋊Q₈	—	2	16	no	—
215	C₂²⋊Q₈	—	2	8	no	—
216	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
217	C₄×Q₈	—	2	16	no	—
218	C₄×Q₈	—	2	8	no	—
219	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
220	#117	—	2	16	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₄²	—	2	4	no	—
229	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₁₃	1	4	yes	—
232	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
235	#107	C₂³×C₁₃	1	16	yes	—
236	#103	C₂³×C₁₃	1	32	yes	—
237	C₄×C₈	C₂³×C₁₃	1	8	yes	—
238	C₄×C₈	C₂³×C₁₃	1	4	yes	—
239	C₄×C₈	C₂³×C₁₃	1	4	yes	—
240	C₂×C₁₃	—	2	4	no	—
241	C₂×C₁₃	#3170	1	4	yes	direct product factor
242	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
243	C₂×C₁₃	C₂³×Q₁₆	1	1	yes	characteristic
244	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
245	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	8	no	—
248	C₂×Q₈	—	2	16	no	—
249	C₂×Q₈	—	4	8	no	—
250	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	C₁₃×Q₁₆	1	8	yes	complemented
256	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
266	Q₁₆	—	2	32	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	16	no	—
269	C₂×C₈	C₁₃×#41	1	8	yes	—
270	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
271	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	16	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
279	C₂²⋊C₄	—	2	16	no	—
280	C₄²	—	2	16	no	—
281	C₄²	C₂×D₄×C₁₃	1	4	yes	—
282	C₄²	C₂×D₄×C₁₃	1	2	yes	—
283	C₄²	C₂×D₄×C₁₃	1	4	yes	—
284	C₄²	C₂×D₄×C₁₃	1	2	yes	—
285	C₄²	C₂⁴×C₁₃	1	2	yes	—
286	C₄²	C₂⁴×C₁₃	1	2	yes	—
287	C₁₃	C₂×#3170	1	1	yes	characteristic, direct product factor, Sylow
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
291	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
292	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
293	Q₈	—	2	16	no	—
294	Q₈	—	4	8	no	—
295	Q₈	—	4	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
306	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
307	C₂×C₄	C₂×C₁₃×Q₁₆	1	16	yes	complemented
308	C₂×C₄	C₁₃×#135	1	4	yes	—
309	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
310	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
311	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
315	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
316	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
317	C₈	—	2	4	no	—
318	C₈	C₂×C₁₃×#41	1	8	yes	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	2	no	—
322	C₂²	C₁₃×#532	1	2	yes	—
323	C₂²	C₂²×C₁₃×Q₁₆	1	4	yes	—
324	C₂²	C₂²×C₁₃×Q₁₆	1	2	yes	—
325	C₂²	C₂×C₁₃×#135	1	2	yes	—
326	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	8	no	—
331	C₄	C₁₃×#532	1	2	yes	—
332	C₄	C₂²×C₁₃×Q₁₆	1	4	yes	—
333	C₄	C₂²×C₁₃×Q₁₆	1	4	yes	—
334	C₄	C₂×C₁₃×#135	1	4	yes	—
335	C₄	C₂²×C₁₃×#41	1	2	yes	—
336	C₂	—	2	4	no	—
337	C₂	C₁₃×#3170	1	4	yes	direct product factor
338	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
339	C₂	C₂³×C₁₃×Q₁₆	1	1	yes	characteristic
340	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×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
2. C₁₃×#3170	C₂	direct (N × H)
3. C₂×C₁₃×#500	C₂	semidirect
4. C₂×C₁₃×#494	C₂	semidirect
5. C₂×C₁₃×#487	C₂	semidirect
7. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
22. C₁₃×#500	C₂²	semidirect
23. C₁₃×#494	C₂²	semidirect
24. C₁₃×#487	C₂²	semidirect
26. C₄×C₁₃×Q₁₆	C₂²	semidirect
75. C₂×#3170	C₁₃	direct (N × H)
86. C₂²×C₄×C₁₃	Q₁₆	semidirect
119. #3170	C₂×C₁₃	direct (N × H)
120. C₂×#500	C₂×C₁₃	semidirect
121. C₂×#494	C₂×C₁₃	semidirect
122. C₂×#487	C₂×C₁₃	semidirect
124. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
145. C₂×C₄×C₁₃	C₂×Q₁₆	semidirect
170. #500	C₂²×C₁₃	semidirect
171. #494	C₂²×C₁₃	semidirect
172. #487	C₂²×C₁₃	semidirect
174. C₄×Q₁₆	C₂²×C₁₃	semidirect
241. C₂×C₁₃	#3170	direct (N × H)
255. C₂²×C₄	C₁₃×Q₁₆	semidirect
287. C₁₃	C₂×#3170	direct (N × H)
307. C₂×C₄	C₂×C₁₃×Q₁₆	semidirect
337. C₂	C₁₃×#3170	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₁₃×#3170	2
C₂×C₁₃×#500	2
C₂×C₁₃×#494	2
C₂×C₁₃×#487	2
C₂×C₁₃×#467	2
C₂×C₄×C₁₃×Q₁₆	2
C₂²×C₄×C₈×C₁₃	2
C₂×#3170	13

Subgroups — C2×C13×#3170 #15747011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3170 #15747011