Subgroups — C₁₃×#34876 #15721215

Order 3328.

2614 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2611	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2610	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2604	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2603	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2543	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2498	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2430	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2397	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
16	C₁₃×#2290	C₂	1	4	yes	maximal, complemented
17	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₁₃×#529	—	2	8	no	—
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	4	yes	—
27	C₄×C₁₃×#41	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#117	C₂²	1	2	yes	—
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#400	C₂²	1	2	yes	—
45	C₁₃×#400	C₂²	1	2	yes	—
46	C₁₃×#399	C₂²	1	2	yes	—
47	C₁₃×#399	C₂²	1	2	yes	—
48	C₁₃×#398	C₂²	1	2	yes	—
49	C₁₃×#398	C₂²	1	2	yes	—
50	C₁₃×#397	C₂²	1	2	yes	—
51	C₁₃×#397	C₂²	1	2	yes	—
52	C₁₃×#395	C₂²	1	2	yes	—
53	C₁₃×#395	C₂²	1	2	yes	—
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#393	C₂²	1	2	yes	—
57	C₁₃×#393	C₂²	1	2	yes	—
58	C₁₃×#392	C₂²	1	2	yes	—
59	C₁₃×#392	C₂²	1	2	yes	—
60	C₁₃×#390	C₂²	1	4	yes	—
61	C₁₃×#389	C₂²	1	4	yes	—
62	C₁₃×#388	C₂²	1	4	yes	—
63	C₁₃×#388	C₂²	1	4	yes	—
64	C₁₃×#388	C₂²	1	4	yes	—
65	C₁₃×#388	C₂²	1	4	yes	—
66	C₁₃×#387	C₂²	1	4	yes	—
67	C₁₃×#387	C₂²	1	4	yes	—
68	C₁₃×#386	C₂²	1	4	yes	—
69	C₁₃×#386	C₂²	1	4	yes	—
70	C₁₃×#386	C₂²	1	4	yes	—
71	C₁₃×#386	C₂²	1	4	yes	—
72	C₁₃×#385	C₂²	1	4	yes	—
73	C₁₃×#385	C₂²	1	4	yes	—
74	C₁₃×#380	C₂²	1	4	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₁₃×#376	C₂²	1	2	yes	—
79	C₁₃×#376	C₂²	1	2	yes	—
80	C₁₃×#376	C₂²	1	2	yes	—
81	C₁₃×#376	C₂²	1	1	yes	characteristic
82	C₁₃×#376	C₂²	1	1	yes	characteristic
83	C₂×C₁₃×#95	C₂²	1	2	yes	—
84	C₂×C₁₃×#95	C₂²	1	2	yes	—
85	C₂×C₁₃×#41	—	2	8	no	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#126	—	2	8	no	—
103	C₁₃×#125	—	2	4	no	—
104	C₁₃×#124	—	2	4	no	—
105	C₁₃×#123	—	2	8	no	—
106	C₁₃×C₂²⋊Q₈	—	2	4	no	—
107	C₁₃×#121	—	2	16	no	—
108	C₁₃×#121	—	2	4	no	—
109	C₄×Q₈×C₁₃	—	2	4	no	—
110	C₄×Q₈×C₁₃	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	8	no	—
113	C₄×D₄×C₁₃	—	2	8	no	—
114	C₄×D₄×C₁₃	—	2	8	no	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	16	no	—
119	C₁₃×#117	—	2	4	no	—
120	C₁₃×#117	—	2	8	no	—
121	C₁₃×#117	—	2	8	no	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃	—	2	8	no	—
150	C₂×C₄²×C₁₃	—	2	8	no	—
151	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	C₁₃×#95	C₂³	1	4	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	#34876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×#41	—	2	32	no	—
180	C₂×Q₈×C₁₃	—	2	2	no	—
181	C₂×Q₈×C₁₃	—	2	2	no	—
182	C₂×Q₈×C₁₃	—	2	4	no	—
183	C₂×Q₈×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	2	8	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	2	no	—
195	C₂×D₄×C₁₃	#41	1	8	yes	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	8	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	8	no	—
206	C₂²×C₄×C₁₃	—	2	8	no	—
207	C₂²×C₄×C₁₃	—	2	8	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	2	no	—
210	C₂²×C₄×C₁₃	—	4	4	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	8	no	—
239	C₁₃×C₄⋊C₄	—	2	8	no	—
240	C₁₃×C₄⋊C₄	—	4	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	8	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	8	no	—
251	C₁₃×C₂²⋊C₄	—	2	8	no	—
252	C₁₃×C₂²⋊C₄	—	2	8	no	—
253	C₁₃×C₂²⋊C₄	—	4	4	no	—
254	C₁₃×C₂²⋊C₄	—	4	4	no	—
255	C₄²×C₁₃	—	2	4	no	—
256	C₄²×C₁₃	—	2	4	no	—
257	C₄²×C₁₃	—	2	4	no	—
258	C₄²×C₁₃	—	2	4	no	—
259	C₄²×C₁₃	—	2	8	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	C₂×D₄	1	4	yes	—
262	C₄²×C₁₃	C₂×D₄	1	4	yes	—
263	C₄²×C₁₃	C₂×D₄	1	4	yes	—
264	C₄²×C₁₃	C₂×D₄	1	4	yes	—
265	C₄²×C₁₃	#41	1	8	yes	complemented
266	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2611	C₂×C₁₃	1	2	yes	complemented
269	#2610	C₂×C₁₃	1	2	yes	complemented
270	#2604	C₂×C₁₃	1	2	yes	complemented
271	#2603	C₂×C₁₃	1	2	yes	complemented
272	#2564	C₂×C₁₃	1	2	yes	complemented
273	#2543	C₂×C₁₃	1	2	yes	complemented
274	#2498	C₂×C₁₃	1	2	yes	complemented
275	#2430	C₂×C₁₃	1	2	yes	complemented
276	#2399	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2398	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2398	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2397	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₄×#121	C₂×C₁₃	1	4	yes	complemented
281	#2290	C₂×C₁₃	1	4	yes	complemented
282	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	4	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	2	4	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂³×C₁₃	C₂×#41	1	4	yes	—
296	C₂³×C₁₃	C₂×#41	1	4	yes	—
297	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
298	Q₈×C₁₃	—	2	8	no	—
299	Q₈×C₁₃	—	4	4	no	—
300	D₄×C₁₃	—	2	8	no	—
301	D₄×C₁₃	—	2	16	no	—
302	D₄×C₁₃	—	4	16	no	—
303	D₄×C₁₃	—	4	4	no	—
304	D₄×C₁₃	—	4	8	no	—
305	C₂×C₄×C₁₃	—	2	16	no	—
306	C₂×C₄×C₁₃	—	2	8	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	8	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	4	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	4	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	16	no	—
333	C₂×C₄×C₁₃	—	4	8	no	—
334	C₂×C₄×C₁₃	—	4	8	no	—
335	C₂×C₄×C₁₃	—	4	8	no	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
343	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
344	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
345	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
346	#529	—	2	8	no	—
347	C₂×#126	C₂²×C₁₃	1	2	yes	—
348	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#123	C₂²×C₁₃	1	2	yes	—
351	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#121	C₂²×C₁₃	1	4	yes	—
354	C₄×#41	—	2	8	no	—
355	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
359	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
363	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
364	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
365	C₂×#117	C₂²×C₁₃	1	2	yes	—
366	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#117	C₂²×C₁₃	1	2	yes	—
368	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
369	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
370	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
371	#400	C₂²×C₁₃	1	2	yes	—
372	#400	C₂²×C₁₃	1	2	yes	—
373	#399	C₂²×C₁₃	1	2	yes	—
374	#399	C₂²×C₁₃	1	2	yes	—
375	#398	C₂²×C₁₃	1	2	yes	—
376	#398	C₂²×C₁₃	1	2	yes	—
377	#397	C₂²×C₁₃	1	2	yes	—
378	#397	C₂²×C₁₃	1	2	yes	—
379	#395	C₂²×C₁₃	1	2	yes	—
380	#395	C₂²×C₁₃	1	2	yes	—
381	#394	C₂²×C₁₃	1	2	yes	—
382	#394	C₂²×C₁₃	1	2	yes	—
383	#393	C₂²×C₁₃	1	2	yes	—
384	#393	C₂²×C₁₃	1	2	yes	—
385	#392	C₂²×C₁₃	1	2	yes	—
386	#392	C₂²×C₁₃	1	2	yes	—
387	#390	C₂²×C₁₃	1	4	yes	—
388	#389	C₂²×C₁₃	1	4	yes	—
389	#388	C₂²×C₁₃	1	4	yes	—
390	#388	C₂²×C₁₃	1	4	yes	—
391	#388	C₂²×C₁₃	1	4	yes	—
392	#388	C₂²×C₁₃	1	4	yes	—
393	#387	C₂²×C₁₃	1	4	yes	—
394	#387	C₂²×C₁₃	1	4	yes	—
395	#386	C₂²×C₁₃	1	4	yes	—
396	#386	C₂²×C₁₃	1	4	yes	—
397	#386	C₂²×C₁₃	1	4	yes	—
398	#386	C₂²×C₁₃	1	4	yes	—
399	#385	C₂²×C₁₃	1	4	yes	—
400	#385	C₂²×C₁₃	1	4	yes	—
401	#380	C₂²×C₁₃	1	4	yes	—
402	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
405	#376	C₂²×C₁₃	1	2	yes	—
406	#376	C₂²×C₁₃	1	2	yes	—
407	#376	C₂²×C₁₃	1	1	yes	characteristic
408	#376	C₂²×C₁₃	1	1	yes	characteristic
409	#376	C₂²×C₁₃	1	2	yes	—
410	C₂×#95	C₂²×C₁₃	1	2	yes	—
411	C₂×#95	C₂²×C₁₃	1	2	yes	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	8	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	8	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	4	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	4	no	—
424	C₂²×C₁₃	—	4	4	no	—
425	C₂²×C₁₃	#525	1	4	yes	—
426	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
427	C₂²×C₁₃	C₂²×#41	1	2	yes	—
428	C₂²×C₁₃	C₂²×#41	1	2	yes	—
429	C₂²×C₁₃	#585	1	2	yes	—
430	C₄×C₁₃	—	2	2	no	—
431	C₄×C₁₃	—	2	2	no	—
432	C₄×C₁₃	—	2	4	no	—
433	C₄×C₁₃	—	2	2	no	—
434	C₄×C₁₃	—	2	2	no	—
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	8	no	—
437	C₄×C₁₃	—	4	2	no	—
438	C₄×C₁₃	—	4	2	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	—	4	4	no	—
443	C₄×C₁₃	#532	1	4	yes	—
444	C₂×#41	—	2	8	no	—
445	C₂×#41	—	2	4	no	—
446	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
450	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
451	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
452	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
455	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
457	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	#126	—	2	8	no	—
462	#125	—	2	4	no	—
463	#124	—	2	4	no	—
464	#123	—	2	8	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	#121	—	2	16	no	—
467	#121	—	2	4	no	—
468	C₄×Q₈	—	2	4	no	—
469	C₄×Q₈	—	2	4	no	—
470	C₄×Q₈	—	2	4	no	—
471	C₄×D₄	—	2	8	no	—
472	C₄×D₄	—	2	8	no	—
473	C₄×D₄	—	2	8	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	2	16	no	—
478	#117	—	2	4	no	—
479	#117	—	2	8	no	—
480	#117	—	2	8	no	—
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₄²	—	2	8	no	—
509	C₂×C₄²	—	2	8	no	—
510	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
511	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
512	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
517	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
522	#95	C₂³×C₁₃	1	4	yes	—
523	#95	C₂³×C₁₃	1	4	yes	—
524	#95	C₂³×C₁₃	1	2	yes	—
525	#95	C₂³×C₁₃	1	2	yes	—
526	#95	C₂³×C₁₃	1	2	yes	—
527	#95	C₂³×C₁₃	1	2	yes	—
528	#95	C₂³×C₁₃	1	4	yes	—
529	#95	C₂³×C₁₃	1	4	yes	—
530	#95	C₂³×C₁₃	1	4	yes	—
531	#95	C₂³×C₁₃	1	4	yes	—
532	#95	C₂³×C₁₃	1	4	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	C₂×C₁₃	—	2	4	no	—
535	C₂×C₁₃	—	4	4	no	—
536	C₂×C₁₃	—	8	2	no	—
537	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
538	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
539	C₂×C₁₃	#3449	1	1	yes	characteristic
540	C₂×C₁₃	#3475	1	4	yes	—
541	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
542	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
543	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
544	#41	—	2	32	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×Q₈	—	4	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	C₁₃×#41	1	8	yes	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	8	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	2	8	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
577	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	8	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	8	no	—
625	C₄²	—	2	4	no	—
626	C₄²	C₂×D₄×C₁₃	1	4	yes	—
627	C₄²	C₂×D₄×C₁₃	1	4	yes	—
628	C₄²	C₂×D₄×C₁₃	1	4	yes	—
629	C₄²	C₂×D₄×C₁₃	1	4	yes	—
630	C₄²	C₁₃×#41	1	8	yes	complemented
631	C₁₃	#34876	1	1	yes	characteristic, direct product factor, Sylow
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
644	C₂³	C₂×C₁₃×#41	1	4	yes	—
645	C₂³	C₂×C₁₃×#41	1	4	yes	—
646	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
647	Q₈	—	2	8	no	—
648	Q₈	—	4	4	no	—
649	D₄	—	2	8	no	—
650	D₄	—	2	16	no	—
651	D₄	—	4	16	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	8	no	—
654	C₂×C₄	—	2	16	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	8	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	4	16	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
687	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
691	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
692	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
693	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	8	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	8	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	C₁₃×#525	1	4	yes	—
708	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
709	C₂²	C₂²×C₁₃×#41	1	2	yes	—
710	C₂²	C₂²×C₁₃×#41	1	2	yes	—
711	C₂²	C₁₃×#585	1	2	yes	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	8	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	4	no	—
725	C₄	C₁₃×#532	1	4	yes	—
726	C₂	—	2	4	no	—
727	C₂	—	4	4	no	—
728	C₂	—	8	2	no	—
729	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
730	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
731	C₂	C₁₃×#3449	1	1	yes	characteristic
732	C₂	C₁₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2611	C₂	semidirect
4. C₁₃×#2610	C₂	semidirect
5. C₁₃×#2604	C₂	semidirect
6. C₁₃×#2603	C₂	semidirect
7. C₁₃×#2564	C₂	semidirect
8. C₁₃×#2543	C₂	semidirect
9. C₁₃×#2498	C₂	semidirect
10. C₁₃×#2430	C₂	semidirect
11. C₁₃×#2399	C₂	semidirect
12. C₁₃×#2398	C₂	semidirect
13. C₁₃×#2398	C₂	semidirect
14. C₁₃×#2397	C₂	semidirect
15. C₄×C₁₃×#121	C₂	semidirect
16. C₁₃×#2290	C₂	semidirect
17. C₂×C₁₃×#376	C₂	semidirect
151. C₂×C₄²×C₁₃	D₄	semidirect
175. #34876	C₁₃	direct (N × H)
265. C₄²×C₁₃	#41	semidirect
266. C₂×#529	C₂×C₁₃	semidirect
267. C₂×C₄×#41	C₂×C₁₃	semidirect
268. #2611	C₂×C₁₃	semidirect
269. #2610	C₂×C₁₃	semidirect
270. #2604	C₂×C₁₃	semidirect
271. #2603	C₂×C₁₃	semidirect
272. #2564	C₂×C₁₃	semidirect
273. #2543	C₂×C₁₃	semidirect
274. #2498	C₂×C₁₃	semidirect
275. #2430	C₂×C₁₃	semidirect
276. #2399	C₂×C₁₃	semidirect
277. #2398	C₂×C₁₃	semidirect
278. #2398	C₂×C₁₃	semidirect
279. #2397	C₂×C₁₃	semidirect
280. C₄×#121	C₂×C₁₃	semidirect
281. #2290	C₂×C₁₃	semidirect
282. C₂×#376	C₂×C₁₃	semidirect
510. C₂×C₄²	D₄×C₁₃	semidirect
630. C₄²	C₁₃×#41	semidirect
631. C₁₃	#34876	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×#529	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2611	2
C₁₃×#2610	2
C₁₃×#2604	2
C₁₃×#2603	2
C₁₃×#2564	2
C₁₃×#2543	2
C₁₃×#2498	2
C₁₃×#2430	2
C₁₃×#2399	2
C₁₃×#2398	2
C₁₃×#2397	2
C₄×C₁₃×#121	2
C₁₃×#2290	2
C₂×C₁₃×#376	2
#34876	13

Subgroups — C13×#34876 #15721215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34876 #15721215