Subgroups — C₁₃×#62793 #15749132

Order 3328.

7190 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3524	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3518	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3517	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3506	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3493	C₂	1	6	yes	maximal, complemented
8	C₁₃×#3487	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3483	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3482	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3480	C₂	1	8	yes	maximal, complemented
12	C₁₃×#3460	C₂	1	6	yes	maximal, complemented
13	C₁₃×#3444	C₂	1	6	yes	maximal, complemented
14	C₄×C₁₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	24	yes	complemented
19	Q₈²×C₁₃	C₂²	1	4	yes	complemented
20	C₁₃×#557	C₂²	1	8	yes	complemented
21	C₁₃×#557	C₂²	1	4	yes	complemented
22	C₁₃×#556	C₂²	1	24	yes	complemented
23	C₁₃×#556	C₂²	1	12	yes	complemented
24	C₁₃×#555	C₂²	1	12	yes	complemented
25	C₁₃×#555	C₂²	1	24	yes	complemented
26	C₁₃×#553	C₂²	1	24	yes	complemented
27	C₁₃×#553	C₂²	1	24	yes	complemented
28	C₁₃×#552	C₂²	1	24	yes	complemented
29	C₁₃×#550	C₂²	1	8	yes	—
30	C₁₃×#550	C₂²	1	8	yes	—
31	C₁₃×#550	C₂²	1	4	yes	complemented
32	C₁₃×#550	C₂²	1	12	yes	complemented
33	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
34	C₁₃×#548	C₂²	1	8	yes	—
35	C₁₃×#548	C₂²	1	8	yes	—
36	C₁₃×#548	C₂²	1	8	yes	complemented
37	C₁₃×#547	C₂²	1	12	yes	complemented
38	C₁₃×#544	C₂²	1	6	yes	—
39	C₁₃×#542	C₂²	1	24	yes	complemented
40	C₁₃×#540	C₂²	1	24	yes	complemented
41	C₁₃×#538	C₂²	1	24	yes	—
42	C₁₃×#537	C₂²	1	6	yes	—
43	C₁₃×#535	C₂²	1	12	yes	—
44	C₁₃×#533	C₂²	1	6	yes	—
45	C₁₃×#533	C₂²	1	6	yes	complemented
46	C₁₃×#533	C₂²	1	6	yes	complemented
47	C₁₃×#532	C₂²	1	6	yes	—
48	C₁₃×#532	C₂²	1	6	yes	complemented
49	C₁₃×#532	C₂²	1	6	yes	complemented
50	C₁₃×#532	C₂²	1	24	yes	complemented
51	C₁₃×#529	C₂²	1	4	yes	—
52	C₁₃×#529	C₂²	1	12	yes	—
53	C₁₃×#529	C₂²	1	12	yes	complemented
54	C₁₃×#529	C₂²	1	12	yes	complemented
55	C₁₃×#529	C₂²	1	12	yes	complemented
56	C₁₃×#529	C₂²	1	12	yes	complemented
57	C₁₃×#529	C₂²	1	24	yes	complemented
58	C₁₃×#525	C₂²	1	12	yes	—
59	C₁₃×#525	C₂²	1	12	yes	—
60	C₁₃×#525	C₂²	1	12	yes	—
61	C₁₃×#520	C₂²	1	12	yes	—
62	C₁₃×#520	C₂²	1	8	yes	complemented
63	C₁₃×#519	C₂²	1	2	yes	—
64	C₁₃×#519	C₂²	1	8	yes	complemented
65	C₄×C₁₃×#41	C₂²	1	4	yes	—
66	C₄×C₁₃×#41	C₂²	1	4	yes	—
67	C₄×C₁₃×#41	C₂²	1	4	yes	—
68	C₄×C₁₃×#41	C₂²	1	4	yes	—
69	C₄×C₁₃×#41	C₂²	1	12	yes	—
70	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
71	C₄×C₁₃×#41	C₂²	1	12	yes	complemented
72	C₄×C₁₃×#41	C₂²	1	12	yes	complemented
73	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
75	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
76	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
77	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
78	C₂×C₁₃×#117	C₂²	1	3	yes	—
79	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
80	C₁₃×2₋¹⁺⁴	—	2	16	no	—
81	C₂×C₁₃×#41	—	2	8	no	—
82	C₂×C₁₃×#41	C₂³	1	4	yes	—
83	C₂×C₁₃×#41	C₂³	1	4	yes	—
84	C₂×C₁₃×#41	C₂³	1	12	yes	—
85	C₂×C₁₃×#41	C₂³	1	8	yes	—
86	C₂×C₁₃×#41	C₂³	1	12	yes	—
87	C₂×C₁₃×#41	C₂³	1	12	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
98	C₁₃×#127	C₂³	1	6	yes	—
99	C₁₃×#127	C₂³	1	24	yes	—
100	C₁₃×#126	C₂³	1	8	yes	—
101	C₁₃×#126	C₂³	1	24	yes	—
102	C₁₃×#126	C₂³	1	48	yes	—
103	C₁₃×#125	C₂³	1	4	yes	—
104	C₁₃×#125	C₂³	1	12	yes	—
105	C₁₃×#125	C₂³	1	12	yes	—
106	C₁₃×#125	C₂³	1	24	yes	—
107	C₁₃×#124	C₂³	1	4	yes	—
108	C₁₃×#124	C₂³	1	12	yes	—
109	C₁₃×#124	C₂³	1	12	yes	—
110	C₁₃×#124	C₂³	1	24	yes	—
111	C₁₃×#124	C₂³	1	48	yes	—
112	C₁₃×#123	C₂³	1	8	yes	—
113	C₁₃×#123	C₂³	1	24	yes	—
114	C₁₃×#123	C₂³	1	24	yes	—
115	C₁₃×#123	C₂³	1	48	yes	—
116	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
118	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
119	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
123	C₁₃×#121	C₂³	1	4	yes	—
124	C₁₃×#121	C₂³	1	12	yes	—
125	C₁₃×#121	C₂³	1	12	yes	—
126	C₁₃×#121	C₂³	1	12	yes	—
127	C₁₃×#121	C₂³	1	12	yes	—
128	C₁₃×#121	C₂³	1	12	yes	—
129	C₁₃×#121	C₂³	1	24	yes	—
130	C₁₃×#121	C₂³	1	24	yes	—
131	C₁₃×#121	C₂³	1	24	yes	—
132	C₁₃×#121	C₂³	1	48	yes	—
133	C₁₃×#120	C₂³	1	24	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
137	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
139	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
140	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
141	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
142	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
144	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
145	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
147	C₄×D₄×C₁₃	C₂³	1	12	yes	—
148	C₄×D₄×C₁₃	C₂³	1	12	yes	—
149	C₄×D₄×C₁₃	C₂³	1	12	yes	—
150	C₄×D₄×C₁₃	C₂³	1	12	yes	—
151	C₄×D₄×C₁₃	C₂³	1	8	yes	—
152	C₄×D₄×C₁₃	C₂³	1	12	yes	—
153	C₄×D₄×C₁₃	C₂³	1	24	yes	—
154	C₄×D₄×C₁₃	C₂³	1	12	yes	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₄×D₄×C₁₃	C₂³	1	24	yes	—
157	C₄×D₄×C₁₃	C₂³	1	24	yes	—
158	C₄×D₄×C₁₃	C₂³	1	24	yes	—
159	C₄×D₄×C₁₃	C₂³	1	24	yes	—
160	C₄×D₄×C₁₃	C₂³	1	24	yes	—
161	C₄×D₄×C₁₃	C₂³	1	12	yes	—
162	C₄×D₄×C₁₃	C₂³	1	12	yes	—
163	C₄×D₄×C₁₃	C₂³	1	12	yes	—
164	C₁₃×#117	C₂³	1	12	yes	—
165	C₁₃×#117	C₂³	1	12	yes	—
166	C₁₃×#117	C₂³	1	12	yes	—
167	C₁₃×#117	C₂³	1	24	yes	—
168	C₁₃×#117	C₂³	1	8	yes	—
169	C₁₃×#117	C₂³	1	24	yes	—
170	C₁₃×#117	C₂³	1	12	yes	—
171	C₁₃×#117	C₂³	1	12	yes	—
172	C₁₃×#117	C₂³	1	24	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
186	#62793	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
188	C₁₃×#41	—	2	16	no	—
189	C₁₃×#41	—	2	16	no	—
190	C₁₃×#41	—	2	32	no	—
191	C₁₃×#41	—	2	48	no	—
192	C₁₃×#41	—	4	24	no	—
193	C₁₃×#41	—	4	24	no	—
194	C₂×Q₈×C₁₃	—	2	32	no	—
195	C₂×Q₈×C₁₃	#41	1	8	yes	complemented
196	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
197	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
198	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
199	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×D₄×C₁₃	—	2	12	no	—
201	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
203	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
204	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
206	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
207	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
208	C₂²×C₄×C₁₃	—	2	12	no	—
209	C₂²×C₄×C₁₃	—	4	6	no	—
210	C₂²×C₄×C₁₃	—	4	6	no	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
233	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
235	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
236	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
237	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
238	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
240	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
241	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
242	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
243	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
244	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
245	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
246	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
247	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
248	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
249	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
250	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₄²×C₁₃	C₂⁴	1	6	yes	—
253	C₄²×C₁₃	C₂⁴	1	6	yes	—
254	C₄²×C₁₃	C₂⁴	1	6	yes	—
255	C₄²×C₁₃	C₂⁴	1	6	yes	—
256	C₄²×C₁₃	C₂⁴	1	6	yes	—
257	C₄²×C₁₃	C₂⁴	1	24	yes	—
258	C₄²×C₁₃	C₂⁴	1	24	yes	—
259	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₄²×C₁₃	C₂⁴	1	6	yes	—
261	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₄²×C₁₃	C₂⁴	1	8	yes	—
263	#3524	C₂×C₁₃	1	8	yes	complemented
264	#3518	C₂×C₁₃	1	4	yes	complemented
265	#3517	C₂×C₁₃	1	4	yes	complemented
266	#3506	C₂×C₁₃	1	6	yes	complemented
267	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#3493	C₂×C₁₃	1	6	yes	complemented
270	#3487	C₂×C₁₃	1	2	yes	complemented
271	#3483	C₂×C₁₃	1	4	yes	complemented
272	#3482	C₂×C₁₃	1	4	yes	complemented
273	#3480	C₂×C₁₃	1	8	yes	complemented
274	#3460	C₂×C₁₃	1	6	yes	complemented
275	#3444	C₂×C₁₃	1	6	yes	complemented
276	C₄×2₋¹⁺⁴	C₂×C₁₃	1	2	yes	complemented
277	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	6	no	—
279	C₂³×C₁₃	—	4	3	no	—
280	C₂³×C₁₃	—	4	3	no	—
281	C₂³×C₁₃	C₂⁵	1	6	yes	—
282	C₂³×C₁₃	C₂⁵	1	8	yes	—
283	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
284	Q₈×C₁₃	—	2	24	no	—
285	Q₈×C₁₃	—	2	8	no	—
286	Q₈×C₁₃	—	4	12	no	—
287	Q₈×C₁₃	C₂×#41	1	16	yes	—
288	D₄×C₁₃	—	2	16	no	—
289	D₄×C₁₃	—	2	24	no	—
290	D₄×C₁₃	—	2	24	no	—
291	D₄×C₁₃	—	2	8	no	—
292	D₄×C₁₃	—	4	12	no	—
293	D₄×C₁₃	—	4	24	no	—
294	D₄×C₁₃	—	4	24	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	12	no	—
297	C₂×C₄×C₁₃	—	2	12	no	—
298	C₂×C₄×C₁₃	—	2	48	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	12	no	—
302	C₂×C₄×C₁₃	—	2	12	no	—
303	C₂×C₄×C₁₃	—	2	16	no	—
304	C₂×C₄×C₁₃	—	4	3	no	—
305	C₂×C₄×C₁₃	—	4	6	no	—
306	C₂×C₄×C₁₃	—	4	6	no	—
307	C₂×C₄×C₁₃	—	4	3	no	—
308	C₂×C₄×C₁₃	—	4	24	no	—
309	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
310	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
314	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
316	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
317	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
318	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
319	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
320	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
322	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
323	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
324	#559	C₂²×C₁₃	1	24	yes	complemented
325	Q₈²	C₂²×C₁₃	1	4	yes	complemented
326	#557	C₂²×C₁₃	1	8	yes	complemented
327	#557	C₂²×C₁₃	1	4	yes	complemented
328	#556	C₂²×C₁₃	1	24	yes	complemented
329	#556	C₂²×C₁₃	1	12	yes	complemented
330	#555	C₂²×C₁₃	1	24	yes	complemented
331	#555	C₂²×C₁₃	1	12	yes	complemented
332	#553	C₂²×C₁₃	1	24	yes	complemented
333	#553	C₂²×C₁₃	1	24	yes	complemented
334	#552	C₂²×C₁₃	1	24	yes	complemented
335	#550	C₂²×C₁₃	1	8	yes	—
336	#550	C₂²×C₁₃	1	8	yes	—
337	#550	C₂²×C₁₃	1	4	yes	complemented
338	#550	C₂²×C₁₃	1	12	yes	complemented
339	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
340	#548	C₂²×C₁₃	1	8	yes	—
341	#548	C₂²×C₁₃	1	8	yes	—
342	#548	C₂²×C₁₃	1	8	yes	complemented
343	#547	C₂²×C₁₃	1	12	yes	complemented
344	#544	C₂²×C₁₃	1	6	yes	—
345	#542	C₂²×C₁₃	1	24	yes	complemented
346	#540	C₂²×C₁₃	1	24	yes	complemented
347	#538	C₂²×C₁₃	1	24	yes	—
348	#537	C₂²×C₁₃	1	6	yes	—
349	#535	C₂²×C₁₃	1	12	yes	—
350	#533	C₂²×C₁₃	1	6	yes	—
351	#533	C₂²×C₁₃	1	6	yes	complemented
352	#533	C₂²×C₁₃	1	6	yes	complemented
353	#532	C₂²×C₁₃	1	6	yes	—
354	#532	C₂²×C₁₃	1	6	yes	complemented
355	#532	C₂²×C₁₃	1	6	yes	complemented
356	#532	C₂²×C₁₃	1	24	yes	complemented
357	#529	C₂²×C₁₃	1	4	yes	—
358	#529	C₂²×C₁₃	1	12	yes	—
359	#529	C₂²×C₁₃	1	12	yes	complemented
360	#529	C₂²×C₁₃	1	12	yes	complemented
361	#529	C₂²×C₁₃	1	12	yes	complemented
362	#529	C₂²×C₁₃	1	12	yes	complemented
363	#529	C₂²×C₁₃	1	24	yes	complemented
364	#525	C₂²×C₁₃	1	12	yes	—
365	#525	C₂²×C₁₃	1	12	yes	—
366	#525	C₂²×C₁₃	1	12	yes	—
367	#520	C₂²×C₁₃	1	12	yes	—
368	#520	C₂²×C₁₃	1	8	yes	complemented
369	#519	C₂²×C₁₃	1	2	yes	—
370	#519	C₂²×C₁₃	1	8	yes	complemented
371	C₄×#41	C₂²×C₁₃	1	4	yes	—
372	C₄×#41	C₂²×C₁₃	1	4	yes	—
373	C₄×#41	C₂²×C₁₃	1	4	yes	—
374	C₄×#41	C₂²×C₁₃	1	4	yes	—
375	C₄×#41	C₂²×C₁₃	1	12	yes	—
376	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
377	C₄×#41	C₂²×C₁₃	1	12	yes	complemented
378	C₄×#41	C₂²×C₁₃	1	12	yes	complemented
379	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
382	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
383	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
384	C₂×#117	C₂²×C₁₃	1	3	yes	—
385	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
386	C₂²×C₁₃	—	2	1	no	—
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	2	8	no	—
389	C₂²×C₁₃	—	2	6	no	—
390	C₂²×C₁₃	—	2	6	no	—
391	C₂²×C₁₃	—	2	6	no	—
392	C₂²×C₁₃	—	2	8	no	—
393	C₂²×C₁₃	—	2	8	no	—
394	C₂²×C₁₃	—	4	12	no	—
395	C₂²×C₁₃	C₂²×#41	1	2	yes	—
396	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
397	C₄×C₁₃	—	2	1	no	—
398	C₄×C₁₃	—	2	1	no	—
399	C₄×C₁₃	—	2	8	no	—
400	C₄×C₁₃	—	2	1	no	—
401	C₄×C₁₃	—	2	1	no	—
402	C₄×C₁₃	—	2	6	no	—
403	C₄×C₁₃	—	2	6	no	—
404	C₄×C₁₃	—	2	8	no	—
405	C₄×C₁₃	—	2	8	no	—
406	C₄×C₁₃	C₂²×#41	1	12	yes	—
407	C₄×C₁₃	#585	1	2	yes	—
408	C₄×C₁₃	#585	1	2	yes	—
409	2₋¹⁺⁴	—	2	16	no	—
410	C₂×#41	—	2	8	no	—
411	C₂×#41	C₂³×C₁₃	1	4	yes	—
412	C₂×#41	C₂³×C₁₃	1	4	yes	—
413	C₂×#41	C₂³×C₁₃	1	12	yes	—
414	C₂×#41	C₂³×C₁₃	1	8	yes	—
415	C₂×#41	C₂³×C₁₃	1	12	yes	—
416	C₂×#41	C₂³×C₁₃	1	12	yes	—
417	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
418	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
421	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
422	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
423	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
424	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
425	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
426	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
427	#127	C₂³×C₁₃	1	6	yes	—
428	#127	C₂³×C₁₃	1	24	yes	—
429	#126	C₂³×C₁₃	1	8	yes	—
430	#126	C₂³×C₁₃	1	24	yes	—
431	#126	C₂³×C₁₃	1	48	yes	—
432	#125	C₂³×C₁₃	1	4	yes	—
433	#125	C₂³×C₁₃	1	12	yes	—
434	#125	C₂³×C₁₃	1	12	yes	—
435	#125	C₂³×C₁₃	1	24	yes	—
436	#124	C₂³×C₁₃	1	4	yes	—
437	#124	C₂³×C₁₃	1	12	yes	—
438	#124	C₂³×C₁₃	1	12	yes	—
439	#124	C₂³×C₁₃	1	24	yes	—
440	#124	C₂³×C₁₃	1	48	yes	—
441	#123	C₂³×C₁₃	1	8	yes	—
442	#123	C₂³×C₁₃	1	24	yes	—
443	#123	C₂³×C₁₃	1	24	yes	—
444	#123	C₂³×C₁₃	1	48	yes	—
445	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
446	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
447	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
448	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
449	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
450	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
451	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
452	#121	C₂³×C₁₃	1	4	yes	—
453	#121	C₂³×C₁₃	1	12	yes	—
454	#121	C₂³×C₁₃	1	12	yes	—
455	#121	C₂³×C₁₃	1	12	yes	—
456	#121	C₂³×C₁₃	1	12	yes	—
457	#121	C₂³×C₁₃	1	12	yes	—
458	#121	C₂³×C₁₃	1	24	yes	—
459	#121	C₂³×C₁₃	1	24	yes	—
460	#121	C₂³×C₁₃	1	24	yes	—
461	#121	C₂³×C₁₃	1	48	yes	—
462	#120	C₂³×C₁₃	1	24	yes	—
463	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
464	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
465	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
466	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
467	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
468	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
469	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
470	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
471	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
472	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
473	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
474	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
475	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
476	C₄×D₄	C₂³×C₁₃	1	12	yes	—
477	C₄×D₄	C₂³×C₁₃	1	12	yes	—
478	C₄×D₄	C₂³×C₁₃	1	12	yes	—
479	C₄×D₄	C₂³×C₁₃	1	12	yes	—
480	C₄×D₄	C₂³×C₁₃	1	8	yes	—
481	C₄×D₄	C₂³×C₁₃	1	12	yes	—
482	C₄×D₄	C₂³×C₁₃	1	24	yes	—
483	C₄×D₄	C₂³×C₁₃	1	12	yes	—
484	C₄×D₄	C₂³×C₁₃	1	4	yes	—
485	C₄×D₄	C₂³×C₁₃	1	24	yes	—
486	C₄×D₄	C₂³×C₁₃	1	24	yes	—
487	C₄×D₄	C₂³×C₁₃	1	24	yes	—
488	C₄×D₄	C₂³×C₁₃	1	24	yes	—
489	C₄×D₄	C₂³×C₁₃	1	24	yes	—
490	C₄×D₄	C₂³×C₁₃	1	12	yes	—
491	C₄×D₄	C₂³×C₁₃	1	12	yes	—
492	C₄×D₄	C₂³×C₁₃	1	12	yes	—
493	#117	C₂³×C₁₃	1	12	yes	—
494	#117	C₂³×C₁₃	1	12	yes	—
495	#117	C₂³×C₁₃	1	12	yes	—
496	#117	C₂³×C₁₃	1	24	yes	—
497	#117	C₂³×C₁₃	1	8	yes	—
498	#117	C₂³×C₁₃	1	24	yes	—
499	#117	C₂³×C₁₃	1	12	yes	—
500	#117	C₂³×C₁₃	1	12	yes	—
501	#117	C₂³×C₁₃	1	24	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
506	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
507	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
508	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
509	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
510	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
511	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
512	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
513	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₁₃	—	2	2	no	—
516	C₂×C₁₃	—	4	8	no	—
517	C₂×C₁₃	—	4	6	no	—
518	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
519	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
520	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
521	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
522	#41	—	2	16	no	—
523	#41	—	2	16	no	—
524	#41	—	2	32	no	—
525	#41	—	2	48	no	—
526	#41	—	4	24	no	—
527	#41	—	4	24	no	—
528	C₂×Q₈	—	2	32	no	—
529	C₂×Q₈	C₁₃×#41	1	8	yes	complemented
530	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
531	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
532	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
533	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
534	C₂×D₄	—	2	12	no	—
535	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
536	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
537	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
538	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
539	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
540	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
541	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
542	C₂²×C₄	—	2	12	no	—
543	C₂²×C₄	—	4	6	no	—
544	C₂²×C₄	—	4	6	no	—
545	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
559	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
560	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
561	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
562	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
563	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
564	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
565	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
566	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
567	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
568	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
571	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
572	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
573	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
574	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
575	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
576	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
577	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
578	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
579	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
580	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
581	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
582	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
583	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
584	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₄²	C₂⁴×C₁₃	1	6	yes	—
586	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
587	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
589	C₄²	C₂⁴×C₁₃	1	6	yes	—
590	C₄²	C₂⁴×C₁₃	1	6	yes	—
591	C₄²	C₂⁴×C₁₃	1	8	yes	—
592	C₄²	C₂⁴×C₁₃	1	6	yes	—
593	C₄²	C₂⁴×C₁₃	1	6	yes	—
594	C₄²	C₂⁴×C₁₃	1	6	yes	—
595	C₄²	C₂⁴×C₁₃	1	24	yes	—
596	C₄²	C₂⁴×C₁₃	1	24	yes	—
597	C₁₃	#62793	1	1	yes	characteristic, direct product factor, Sylow
598	C₂³	—	2	6	no	—
599	C₂³	—	4	3	no	—
600	C₂³	—	4	3	no	—
601	C₂³	C₂⁵×C₁₃	1	6	yes	—
602	C₂³	C₂⁵×C₁₃	1	8	yes	—
603	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
604	Q₈	—	2	24	no	—
605	Q₈	—	2	8	no	—
606	Q₈	—	4	12	no	—
607	Q₈	C₂×C₁₃×#41	1	16	yes	—
608	D₄	—	2	16	no	—
609	D₄	—	2	24	no	—
610	D₄	—	2	24	no	—
611	D₄	—	2	8	no	—
612	D₄	—	4	12	no	—
613	D₄	—	4	24	no	—
614	D₄	—	4	24	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	12	no	—
617	C₂×C₄	—	2	12	no	—
618	C₂×C₄	—	2	48	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	12	no	—
622	C₂×C₄	—	2	12	no	—
623	C₂×C₄	—	2	16	no	—
624	C₂×C₄	—	4	3	no	—
625	C₂×C₄	—	4	6	no	—
626	C₂×C₄	—	4	6	no	—
627	C₂×C₄	—	4	3	no	—
628	C₂×C₄	—	4	24	no	—
629	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
630	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
631	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
632	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
634	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
636	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
637	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
638	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
639	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
640	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
641	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	6	no	—
646	C₂²	—	2	6	no	—
647	C₂²	—	2	6	no	—
648	C₂²	—	2	8	no	—
649	C₂²	—	2	8	no	—
650	C₂²	—	4	12	no	—
651	C₂²	C₂²×C₁₃×#41	1	2	yes	—
652	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	6	no	—
659	C₄	—	2	6	no	—
660	C₄	—	2	8	no	—
661	C₄	—	2	8	no	—
662	C₄	C₂²×C₁₃×#41	1	12	yes	—
663	C₄	C₁₃×#585	1	2	yes	—
664	C₄	C₁₃×#585	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	6	no	—
667	C₂	—	4	8	no	—
668	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
669	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
670	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3524	C₂	semidirect
2. C₁₃×#3518	C₂	semidirect
3. C₁₃×#3517	C₂	semidirect
4. C₁₃×#3506	C₂	semidirect
5. C₁₃×#3502	C₂	semidirect
6. C₁₃×#3497	C₂	semidirect
7. C₁₃×#3493	C₂	semidirect
8. C₁₃×#3487	C₂	semidirect
9. C₁₃×#3483	C₂	semidirect
10. C₁₃×#3482	C₂	semidirect
11. C₁₃×#3480	C₂	semidirect
12. C₁₃×#3460	C₂	semidirect
13. C₁₃×#3444	C₂	semidirect
14. C₄×C₁₃×2₋¹⁺⁴	C₂	semidirect
15. C₂×C₄×C₁₃×#41	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. Q₈²×C₁₃	C₂²	semidirect
20. C₁₃×#557	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#555	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#553	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
31. C₁₃×#550	C₂²	semidirect
32. C₁₃×#550	C₂²	semidirect
33. D₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
39. C₁₃×#542	C₂²	semidirect
40. C₁₃×#540	C₂²	semidirect
45. C₁₃×#533	C₂²	semidirect
46. C₁₃×#533	C₂²	semidirect
48. C₁₃×#532	C₂²	semidirect
49. C₁₃×#532	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
53. C₁₃×#529	C₂²	semidirect
54. C₁₃×#529	C₂²	semidirect
55. C₁₃×#529	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
57. C₁₃×#529	C₂²	semidirect
62. C₁₃×#520	C₂²	semidirect
64. C₁₃×#519	C₂²	semidirect
70. C₄×C₁₃×#41	C₂²	semidirect
71. C₄×C₁₃×#41	C₂²	semidirect
72. C₄×C₁₃×#41	C₂²	semidirect
75. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
186. #62793	C₁₃	direct (N × H)
195. C₂×Q₈×C₁₃	#41	semidirect
263. #3524	C₂×C₁₃	semidirect
264. #3518	C₂×C₁₃	semidirect
265. #3517	C₂×C₁₃	semidirect
266. #3506	C₂×C₁₃	semidirect
267. #3502	C₂×C₁₃	semidirect
268. #3497	C₂×C₁₃	semidirect
269. #3493	C₂×C₁₃	semidirect
270. #3487	C₂×C₁₃	semidirect
271. #3483	C₂×C₁₃	semidirect
272. #3482	C₂×C₁₃	semidirect
273. #3480	C₂×C₁₃	semidirect
274. #3460	C₂×C₁₃	semidirect
275. #3444	C₂×C₁₃	semidirect
276. C₄×2₋¹⁺⁴	C₂×C₁₃	semidirect
277. C₂×C₄×#41	C₂×C₁₃	semidirect
324. #559	C₂²×C₁₃	semidirect
325. Q₈²	C₂²×C₁₃	semidirect
326. #557	C₂²×C₁₃	semidirect
327. #557	C₂²×C₁₃	semidirect
328. #556	C₂²×C₁₃	semidirect
329. #556	C₂²×C₁₃	semidirect
330. #555	C₂²×C₁₃	semidirect
331. #555	C₂²×C₁₃	semidirect
332. #553	C₂²×C₁₃	semidirect
333. #553	C₂²×C₁₃	semidirect
334. #552	C₂²×C₁₃	semidirect
337. #550	C₂²×C₁₃	semidirect
338. #550	C₂²×C₁₃	semidirect
339. D₄×Q₈	C₂²×C₁₃	semidirect
342. #548	C₂²×C₁₃	semidirect
343. #547	C₂²×C₁₃	semidirect
345. #542	C₂²×C₁₃	semidirect
346. #540	C₂²×C₁₃	semidirect
351. #533	C₂²×C₁₃	semidirect
352. #533	C₂²×C₁₃	semidirect
354. #532	C₂²×C₁₃	semidirect
355. #532	C₂²×C₁₃	semidirect
356. #532	C₂²×C₁₃	semidirect
359. #529	C₂²×C₁₃	semidirect
360. #529	C₂²×C₁₃	semidirect
361. #529	C₂²×C₁₃	semidirect
362. #529	C₂²×C₁₃	semidirect
363. #529	C₂²×C₁₃	semidirect
368. #520	C₂²×C₁₃	semidirect
370. #519	C₂²×C₁₃	semidirect
376. C₄×#41	C₂²×C₁₃	semidirect
377. C₄×#41	C₂²×C₁₃	semidirect
378. C₄×#41	C₂²×C₁₃	semidirect
381. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
529. C₂×Q₈	C₁₃×#41	semidirect
597. C₁₃	#62793	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3524	2
C₁₃×#3518	2
C₁₃×#3517	2
C₁₃×#3506	2
C₁₃×#3502	2
C₁₃×#3497	2
C₁₃×#3493	2
C₁₃×#3487	2
C₁₃×#3483	2
C₁₃×#3482	2
C₁₃×#3480	2
C₁₃×#3460	2
C₁₃×#3444	2
C₄×C₁₃×2₋¹⁺⁴	2
C₂×C₄×C₁₃×#41	2
#62793	13

Subgroups — C13×#62793 #15749132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62793 #15749132