Subgroups — C₂×C₁₃×#3177 #15747020

Order 3328.

1842 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	2	yes	maximal
2	C₁₃×#3177	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#491	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#470	C₂	1	2	yes	maximal
7	C₂×C₁₃×#467	C₂	1	2	yes	maximal
8	C₂×C₁₃×#441	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#541	—	2	8	no	—
16	C₁₃×#541	C₂²	1	16	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#126	—	2	4	no	—
19	C₂×C₁₃×#125	—	2	4	no	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₁₃×#499	C₂²	1	8	yes	complemented
25	C₁₃×#494	C₂²	1	8	yes	complemented
26	C₁₃×#491	C₂²	1	16	yes	complemented
27	C₁₃×#470	C₂²	1	16	yes	—
28	C₁₃×#467	C₂²	1	16	yes	—
29	C₁₃×#441	C₂²	1	16	yes	complemented
30	C₄×C₁₃×Q₁₆	C₂²	1	16	yes	complemented
31	C₂×C₁₃×#107	C₂²	1	2	yes	—
32	C₂×C₁₃×#106	C₂²	1	2	yes	—
33	C₂×C₁₃×#103	C₂²	1	4	yes	—
34	C₂×C₁₃×#103	C₂²	1	4	yes	—
35	C₁₃×#405	C₂²	1	8	yes	—
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₁₃×Q₁₆	—	2	8	no	—
43	C₂×C₁₃×Q₁₆	—	2	8	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
45	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
46	C₂×C₁₃×M₁₆	—	2	4	no	—
47	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
56	C₁₃×#126	—	2	32	no	—
57	C₁₃×#125	—	2	32	no	—
58	C₁₃×#125	—	2	4	no	—
59	C₁₃×#125	C₂³	1	8	yes	—
60	C₁₃×C₂²⋊Q₈	—	2	8	no	—
61	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
62	C₄×Q₈×C₁₃	—	2	8	no	—
63	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
64	C₁₃×#117	D₄	1	4	yes	—
65	C₁₃×#117	C₂³	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	—	2	4	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	8	yes	—
78	C₁₃×#106	C₂³	1	8	yes	—
79	C₁₃×#103	C₂³	1	16	yes	—
80	C₁₃×#103	C₂³	1	16	yes	—
81	C₁₃×#97	C₂³	1	4	yes	—
82	C₁₃×#97	C₂³	1	4	yes	—
83	C₄×C₈×C₁₃	C₂³	1	4	yes	—
84	C₄×C₈×C₁₃	C₂³	1	4	yes	—
85	C₂×#3177	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	8	no	—
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×Q₁₆	—	2	16	no	—
102	C₁₃×Q₁₆	—	2	16	no	—
103	C₁₃×M₁₆	—	2	8	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	8	no	—
107	C₂×C₈×C₁₃	#41	1	4	yes	—
108	C₂×C₈×C₁₃	#41	1	4	yes	—
109	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
110	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
111	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
112	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
113	C₁₃×C₄⋊C₄	—	2	16	no	—
114	C₁₃×C₄⋊C₄	—	2	16	no	—
115	C₁₃×C₄⋊C₄	—	2	16	no	—
116	C₁₃×C₄⋊C₄	—	2	16	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
119	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
120	C₁₃×C₂²⋊C₄	—	2	16	no	—
121	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
122	C₄²×C₁₃	—	2	16	no	—
123	C₄²×C₁₃	C₂×D₄	1	2	yes	—
124	C₄²×C₁₃	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃	C₂⁴	1	2	yes	—
126	C₄²×C₁₃	C₂⁴	1	2	yes	—
127	C₂×#541	C₂×C₁₃	1	2	yes	—
128	#3177	C₂×C₁₃	1	16	yes	direct product factor
129	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂×#491	C₂×C₁₃	1	2	yes	complemented
132	C₂×#470	C₂×C₁₃	1	2	yes	—
133	C₂×#467	C₂×C₁₃	1	2	yes	—
134	C₂×#441	C₂×C₁₃	1	2	yes	complemented
135	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
136	C₂×#405	C₂×C₁₃	1	1	yes	characteristic
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	4	no	—
139	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
140	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₃	—	2	8	no	—
142	Q₈×C₁₃	—	2	8	no	—
143	Q₈×C₁₃	—	4	8	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	8	no	—
151	C₂×C₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	—	4	8	no	—
154	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
160	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
161	C₈×C₁₃	—	2	2	no	—
162	C₈×C₁₃	—	2	2	no	—
163	C₈×C₁₃	C₂×#41	1	4	yes	—
164	C₈×C₁₃	C₂×#41	1	4	yes	—
165	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
166	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
167	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
168	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
169	#541	—	2	8	no	—
170	#541	C₂²×C₁₃	1	16	yes	—
171	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
172	C₂×#126	—	2	4	no	—
173	C₂×#125	—	2	4	no	—
174	C₂×#125	C₂²×C₁₃	1	2	yes	—
175	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
176	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
177	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
178	#499	C₂²×C₁₃	1	8	yes	complemented
179	#494	C₂²×C₁₃	1	8	yes	complemented
180	#491	C₂²×C₁₃	1	16	yes	complemented
181	#470	C₂²×C₁₃	1	16	yes	—
182	#467	C₂²×C₁₃	1	16	yes	—
183	#441	C₂²×C₁₃	1	16	yes	complemented
184	C₄×Q₁₆	C₂²×C₁₃	1	16	yes	complemented
185	C₂×#107	C₂²×C₁₃	1	2	yes	—
186	C₂×#106	C₂²×C₁₃	1	2	yes	—
187	C₂×#103	C₂²×C₁₃	1	4	yes	—
188	C₂×#103	C₂²×C₁₃	1	4	yes	—
189	#405	C₂²×C₁₃	1	8	yes	—
190	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂²×C₁₃	—	2	2	no	—
195	C₂²×C₁₃	—	2	4	no	—
196	C₂²×C₁₃	—	4	4	no	—
197	C₂²×C₁₃	#532	1	2	yes	—
198	C₂²×C₁₃	#578	1	4	yes	—
199	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	4	8	no	—
204	C₄×C₁₃	—	4	8	no	—
205	C₄×C₁₃	#532	1	2	yes	—
206	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
207	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
208	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂×Q₁₆	—	2	8	no	—
211	C₂×Q₁₆	—	2	8	no	—
212	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
213	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
216	C₂²×C₈	—	2	4	no	—
217	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
219	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
222	C₄⋊Q₈	—	2	4	no	—
223	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
224	#126	—	2	32	no	—
225	#125	—	2	32	no	—
226	#125	—	2	4	no	—
227	#125	C₂³×C₁₃	1	8	yes	—
228	C₂²⋊Q₈	—	2	8	no	—
229	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
230	C₄×Q₈	—	2	8	no	—
231	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
232	#117	D₄×C₁₃	1	4	yes	—
233	#117	C₂³×C₁₃	1	4	yes	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
242	C₂×C₄²	—	2	4	no	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	#107	C₂³×C₁₃	1	8	yes	—
246	#106	C₂³×C₁₃	1	8	yes	—
247	#103	C₂³×C₁₃	1	16	yes	—
248	#103	C₂³×C₁₃	1	16	yes	—
249	#97	C₂³×C₁₃	1	4	yes	—
250	#97	C₂³×C₁₃	1	4	yes	—
251	C₄×C₈	C₂³×C₁₃	1	4	yes	—
252	C₄×C₈	C₂³×C₁₃	1	4	yes	—
253	C₂×C₁₃	—	4	2	no	—
254	C₂×C₁₃	#3177	1	4	yes	direct product factor
255	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#578	1	2	yes	—
257	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
272	Q₁₆	—	2	16	no	—
273	Q₁₆	—	2	16	no	—
274	M₁₆	—	2	8	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	C₁₃×#41	1	4	yes	—
279	C₂×C₈	C₁₃×#41	1	4	yes	—
280	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
281	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
282	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
283	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
284	C₄⋊C₄	—	2	16	no	—
285	C₄⋊C₄	—	2	16	no	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
290	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
291	C₂²⋊C₄	—	2	16	no	—
292	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
293	C₄²	—	2	16	no	—
294	C₄²	C₂×D₄×C₁₃	1	2	yes	—
295	C₄²	C₂×D₄×C₁₃	1	2	yes	—
296	C₄²	C₂⁴×C₁₃	1	2	yes	—
297	C₄²	C₂⁴×C₁₃	1	2	yes	—
298	C₁₃	C₂×#3177	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
302	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
303	Q₈	—	2	8	no	—
304	Q₈	—	2	8	no	—
305	Q₈	—	4	8	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	4	8	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
317	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
318	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
319	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
321	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
322	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
323	C₈	—	2	2	no	—
324	C₈	—	2	2	no	—
325	C₈	C₂×C₁₃×#41	1	4	yes	—
326	C₈	C₂×C₁₃×#41	1	4	yes	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	C₁₃×#532	1	2	yes	—
331	C₂²	C₁₃×#578	1	4	yes	—
332	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	8	no	—
337	C₄	—	4	8	no	—
338	C₄	C₁₃×#532	1	2	yes	—
339	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
340	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
341	C₂	—	4	2	no	—
342	C₂	C₁₃×#3177	1	4	yes	direct product factor
343	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
344	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3177	C₂	direct (N × H)
3. C₂×C₁₃×#499	C₂	semidirect
4. C₂×C₁₃×#494	C₂	semidirect
5. C₂×C₁₃×#491	C₂	semidirect
8. C₂×C₁₃×#441	C₂	semidirect
9. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
24. C₁₃×#499	C₂²	semidirect
25. C₁₃×#494	C₂²	semidirect
26. C₁₃×#491	C₂²	semidirect
29. C₁₃×#441	C₂²	semidirect
30. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₂×#3177	C₁₃	direct (N × H)
128. #3177	C₂×C₁₃	direct (N × H)
129. C₂×#499	C₂×C₁₃	semidirect
130. C₂×#494	C₂×C₁₃	semidirect
131. C₂×#491	C₂×C₁₃	semidirect
134. C₂×#441	C₂×C₁₃	semidirect
135. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
178. #499	C₂²×C₁₃	semidirect
179. #494	C₂²×C₁₃	semidirect
180. #491	C₂²×C₁₃	semidirect
183. #441	C₂²×C₁₃	semidirect
184. C₄×Q₁₆	C₂²×C₁₃	semidirect
254. C₂×C₁₃	#3177	direct (N × H)
298. C₁₃	C₂×#3177	direct (N × H)
342. C₂	C₁₃×#3177	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×#541	2
C₁₃×#3177	2
C₂×C₁₃×#499	2
C₂×C₁₃×#494	2
C₂×C₁₃×#491	2
C₂×C₁₃×#470	2
C₂×C₁₃×#467	2
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₁₃×#405	2
C₂×#3177	13

Subgroups — C2×C13×#3177 #15747020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3177 #15747020