Subgroups — C₁₃×#24575 #15710914

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1822	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₁₃×#482	—	2	1	no	—
25	C₁₃×#482	—	2	1	no	—
26	C₁₃×#482	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#449	—	2	1	no	—
29	C₁₃×#449	—	2	1	no	—
30	C₁₃×#448	—	2	1	no	—
31	C₁₃×#447	—	2	1	no	—
32	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#419	—	2	1	no	—
37	C₁₃×#418	—	2	1	no	—
38	C₁₃×#417	C₂²	1	1	yes	characteristic
39	C₁₃×#417	C₂²	1	1	yes	characteristic
40	C₁₃×#417	C₂²	1	1	yes	characteristic
41	C₁₃×#417	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₁₃×#417	C₂²	1	1	yes	characteristic
44	C₁₃×#416	—	2	1	no	—
45	C₁₃×#416	—	2	1	no	—
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#408	—	2	1	no	—
51	C₁₃×#408	—	2	1	no	—
52	C₁₃×#408	C₂²	1	1	yes	characteristic
53	C₁₃×#408	C₂²	1	1	yes	characteristic
54	C₁₃×#407	—	2	1	no	—
55	C₁₃×#407	C₂²	1	1	yes	characteristic
56	C₁₃×#407	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
58	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂×C₁₃×#41	—	4	1	no	—
73	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
74	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
85	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
87	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
88	C₂×C₁₃×SD₁₆	—	2	1	no	—
89	C₂×C₁₃×SD₁₆	—	2	1	no	—
90	C₂×C₁₃×D₈	—	2	1	no	—
91	C₂×C₁₃×D₈	—	2	1	no	—
92	C₁₃×#131	—	2	2	no	—
93	C₁₃×#131	—	2	2	no	—
94	C₁₃×#131	—	4	1	no	—
95	C₁₃×#131	—	4	1	no	—
96	C₂×C₁₃×M₁₆	—	2	1	no	—
97	C₂×C₁₃×M₁₆	—	2	1	no	—
98	C₂×C₁₃×M₁₆	—	2	1	no	—
99	C₂×C₁₃×M₁₆	—	4	1	no	—
100	C₂×C₁₃×M₁₆	—	4	1	no	—
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	—	2	1	no	—
108	C₂²×C₈×C₁₃	—	2	1	no	—
109	C₂²×C₈×C₁₃	—	2	1	no	—
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#121	—	2	1	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	1	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#117	—	2	1	no	—
117	C₁₃×#117	—	2	1	no	—
118	C₁₃×#117	—	2	1	no	—
119	C₁₃×#117	—	2	1	no	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₁₃×#108	—	4	1	no	—
127	C₁₃×#108	—	4	1	no	—
128	C₁₃×#107	—	2	1	no	—
129	C₁₃×#107	—	2	1	no	—
130	C₁₃×#106	—	2	1	no	—
131	C₁₃×#106	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#102	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#100	—	4	1	no	—
149	C₁₃×#100	—	4	1	no	—
150	C₁₃×C₂²⋊C₈	—	2	1	no	—
151	C₁₃×C₂²⋊C₈	—	2	1	no	—
152	C₁₃×C₂²⋊C₈	—	2	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×C₂²⋊C₈	—	2	1	no	—
155	C₁₃×C₂²⋊C₈	—	2	1	no	—
156	C₁₃×C₂²⋊C₈	—	2	1	no	—
157	C₁₃×C₂²⋊C₈	—	2	1	no	—
158	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
159	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
161	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
162	#24575	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	#41	1	1	yes	characteristic
166	C₁₃×#41	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₁₃×#41	—	2	2	no	—
169	C₁₃×#41	—	2	2	no	—
170	C₁₃×#41	—	2	1	no	—
171	C₁₃×#41	—	2	1	no	—
172	C₁₃×#41	—	2	1	no	—
173	C₁₃×#41	—	2	1	no	—
174	C₁₃×#41	—	4	2	no	—
175	C₁₃×#41	—	4	2	no	—
176	C₁₃×#41	—	4	1	no	—
177	C₁₃×#41	—	4	1	no	—
178	C₁₃×#41	—	4	2	no	—
179	C₁₃×#41	—	4	2	no	—
180	C₁₃×#41	#41	1	2	yes	—
181	C₁₃×#41	#41	1	2	yes	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	2	no	—
184	C₂×Q₈×C₁₃	—	4	1	no	—
185	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	4	1	no	—
200	C₂×D₄×C₁₃	—	4	2	no	—
201	C₂×D₄×C₁₃	—	4	2	no	—
202	C₂×D₄×C₁₃	—	4	1	no	—
203	C₂×D₄×C₁₃	—	4	1	no	—
204	C₂×D₄×C₁₃	—	8	2	no	—
205	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	4	2	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×SD₁₆	—	4	2	no	—
228	C₁₃×SD₁₆	—	4	2	no	—
229	C₁₃×D₈	—	4	2	no	—
230	C₁₃×D₈	—	4	2	no	—
231	C₁₃×M₁₆	—	2	1	no	—
232	C₁₃×M₁₆	—	2	1	no	—
233	C₁₃×M₁₆	—	2	1	no	—
234	C₁₃×M₁₆	—	2	1	no	—
235	C₁₃×M₁₆	—	2	1	no	—
236	C₁₃×M₁₆	—	2	1	no	—
237	C₁₃×M₁₆	—	2	1	no	—
238	C₁₃×M₁₆	—	2	1	no	—
239	C₁₃×M₁₆	—	2	1	no	—
240	C₁₃×M₁₆	—	2	1	no	—
241	C₁₃×M₁₆	—	2	1	no	—
242	C₁₃×M₁₆	—	2	1	no	—
243	C₁₃×M₁₆	—	4	2	no	—
244	C₁₃×M₁₆	—	4	2	no	—
245	C₁₃×M₁₆	—	4	2	no	—
246	C₂×C₈×C₁₃	—	2	1	no	—
247	C₂×C₈×C₁₃	—	2	1	no	—
248	C₂×C₈×C₁₃	—	2	1	no	—
249	C₂×C₈×C₁₃	—	2	1	no	—
250	C₂×C₈×C₁₃	—	2	1	no	—
251	C₂×C₈×C₁₃	—	2	1	no	—
252	C₂×C₈×C₁₃	—	2	1	no	—
253	C₂×C₈×C₁₃	—	2	1	no	—
254	C₂×C₈×C₁₃	—	2	1	no	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	—	4	2	no	—
257	C₂×C₈×C₁₃	—	4	2	no	—
258	C₂×C₈×C₁₃	—	4	2	no	—
259	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₂²⋊C₄	—	4	1	no	—
270	C₁₃×C₂²⋊C₄	—	4	1	no	—
271	C₁₃×C₂²⋊C₄	—	4	1	no	—
272	C₁₃×C₂²⋊C₄	—	4	1	no	—
273	C₄²×C₁₃	—	4	1	no	—
274	C₄²×C₁₃	—	4	1	no	—
275	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#3006	C₂×C₁₃	1	1	yes	characteristic
277	#2896	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2079	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2078	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1822	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	—	4	1	no	—
296	C₂³×C₁₃	—	4	2	no	—
297	C₂³×C₁₃	—	4	2	no	—
298	C₂³×C₁₃	—	4	1	no	—
299	C₂³×C₁₃	—	4	1	no	—
300	C₂³×C₁₃	—	4	1	no	—
301	C₂³×C₁₃	—	8	1	no	—
302	C₂³×C₁₃	—	8	1	no	—
303	C₂³×C₁₃	—	8	1	no	—
304	C₂³×C₁₃	#121	1	1	yes	characteristic
305	C₂³×C₁₃	#121	1	1	yes	characteristic
306	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
307	Q₈×C₁₃	—	2	1	no	—
308	Q₈×C₁₃	—	2	1	no	—
309	Q₈×C₁₃	—	2	1	no	—
310	Q₈×C₁₃	—	4	2	no	—
311	Q₈×C₁₃	#123	1	2	yes	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	2	no	—
314	D₄×C₁₃	—	2	1	no	—
315	D₄×C₁₃	—	2	1	no	—
316	D₄×C₁₃	—	2	1	no	—
317	D₄×C₁₃	—	4	2	no	—
318	D₄×C₁₃	—	4	2	no	—
319	D₄×C₁₃	—	4	2	no	—
320	D₄×C₁₃	—	4	1	no	—
321	D₄×C₁₃	—	4	1	no	—
322	D₄×C₁₃	—	4	1	no	—
323	D₄×C₁₃	—	4	1	no	—
324	D₄×C₁₃	—	4	1	no	—
325	D₄×C₁₃	—	4	1	no	—
326	D₄×C₁₃	—	8	2	no	—
327	D₄×C₁₃	—	8	2	no	—
328	D₄×C₁₃	#123	1	2	yes	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	4	2	no	—
344	C₂×C₄×C₁₃	—	4	2	no	—
345	C₂×C₄×C₁₃	—	4	2	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	8	1	no	—
352	C₂×C₄×C₁₃	—	8	1	no	—
353	C₂×C₄×C₁₃	—	8	1	no	—
354	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
355	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₈×C₁₃	—	2	1	no	—
363	C₈×C₁₃	—	2	1	no	—
364	C₈×C₁₃	—	2	1	no	—
365	C₈×C₁₃	—	2	1	no	—
366	C₈×C₁₃	—	4	1	no	—
367	C₈×C₁₃	—	4	1	no	—
368	C₈×C₁₃	—	4	1	no	—
369	C₈×C₁₃	—	4	1	no	—
370	C₈×C₁₃	—	4	1	no	—
371	C₈×C₁₃	—	4	1	no	—
372	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
380	#482	—	2	1	no	—
381	#482	—	2	1	no	—
382	#482	—	2	1	no	—
383	#482	—	2	1	no	—
384	#449	—	2	1	no	—
385	#449	—	2	1	no	—
386	#448	—	2	1	no	—
387	#447	—	2	1	no	—
388	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	#419	—	2	1	no	—
393	#418	—	2	1	no	—
394	#417	C₂²×C₁₃	1	1	yes	characteristic
395	#417	C₂²×C₁₃	1	1	yes	characteristic
396	#417	C₂²×C₁₃	1	1	yes	characteristic
397	#417	C₂²×C₁₃	1	1	yes	characteristic
398	#417	C₂²×C₁₃	1	1	yes	characteristic
399	#417	C₂²×C₁₃	1	1	yes	characteristic
400	#416	—	2	1	no	—
401	#416	—	2	1	no	—
402	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	#408	—	2	1	no	—
407	#408	—	2	1	no	—
408	#408	C₂²×C₁₃	1	1	yes	characteristic
409	#408	C₂²×C₁₃	1	1	yes	characteristic
410	#407	—	2	1	no	—
411	#407	C₂²×C₁₃	1	1	yes	characteristic
412	#407	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₈	—	2	1	no	—
414	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
415	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂²×C₁₃	—	2	1	no	—
424	C₂²×C₁₃	—	2	1	no	—
425	C₂²×C₁₃	—	2	1	no	—
426	C₂²×C₁₃	—	2	1	no	—
427	C₂²×C₁₃	—	2	2	no	—
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	2	1	no	—
431	C₂²×C₁₃	—	2	1	no	—
432	C₂²×C₁₃	—	4	1	no	—
433	C₂²×C₁₃	—	4	1	no	—
434	C₂²×C₁₃	—	4	1	no	—
435	C₂²×C₁₃	—	4	1	no	—
436	C₂²×C₁₃	—	4	1	no	—
437	C₂²×C₁₃	—	8	1	no	—
438	C₂²×C₁₃	—	8	1	no	—
439	C₂²×C₁₃	—	8	4	no	—
440	C₂²×C₁₃	—	8	1	no	—
441	C₂²×C₁₃	—	8	1	no	—
442	C₂²×C₁₃	—	8	1	no	—
443	C₂²×C₁₃	—	16	1	no	—
444	C₂²×C₁₃	—	16	1	no	—
445	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
446	C₂²×C₁₃	#551	1	1	yes	characteristic
447	C₂²×C₁₃	#551	1	1	yes	characteristic
448	C₄×C₁₃	—	2	1	no	—
449	C₄×C₁₃	—	2	1	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	4	1	no	—
452	C₄×C₁₃	—	8	1	no	—
453	C₄×C₁₃	—	8	1	no	—
454	C₄×C₁₃	—	8	1	no	—
455	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
456	C₄×C₁₃	#534	1	1	yes	characteristic
457	C₄×C₁₃	#546	1	1	yes	characteristic
458	C₄×C₁₃	#546	1	1	yes	characteristic
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	4	1	no	—
464	C₂×#41	—	4	1	no	—
465	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
466	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
467	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	AGL(1,ℤ/8)	—	2	2	no	—
477	AGL(1,ℤ/8)	—	2	2	no	—
478	AGL(1,ℤ/8)	—	4	1	no	—
479	AGL(1,ℤ/8)	—	4	1	no	—
480	C₂×SD₁₆	—	2	1	no	—
481	C₂×SD₁₆	—	2	1	no	—
482	C₂×D₈	—	2	1	no	—
483	C₂×D₈	—	2	1	no	—
484	#131	—	2	2	no	—
485	#131	—	2	2	no	—
486	#131	—	4	1	no	—
487	#131	—	4	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	4	1	no	—
492	C₂×M₁₆	—	4	1	no	—
493	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×C₈	—	2	1	no	—
500	C₂²×C₈	—	2	1	no	—
501	C₂²×C₈	—	2	1	no	—
502	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#117	—	2	1	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	#108	—	4	1	no	—
519	#108	—	4	1	no	—
520	#107	—	2	1	no	—
521	#107	—	2	1	no	—
522	#106	—	2	1	no	—
523	#106	—	2	1	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#103	—	2	1	no	—
527	#103	—	2	1	no	—
528	#103	—	2	1	no	—
529	#103	—	2	1	no	—
530	#102	—	2	1	no	—
531	#102	—	2	1	no	—
532	#102	—	2	1	no	—
533	#102	—	2	1	no	—
534	#102	—	2	1	no	—
535	#102	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	#102	—	2	1	no	—
540	#100	—	4	1	no	—
541	#100	—	4	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₂²⋊C₈	—	2	1	no	—
545	C₂²⋊C₈	—	2	1	no	—
546	C₂²⋊C₈	—	2	1	no	—
547	C₂²⋊C₈	—	2	1	no	—
548	C₂²⋊C₈	—	2	1	no	—
549	C₂²⋊C₈	—	2	1	no	—
550	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
551	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
552	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
553	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₁₃	—	2	1	no	—
555	C₂×C₁₃	—	2	1	no	—
556	C₂×C₁₃	—	4	1	no	—
557	C₂×C₁₃	—	4	1	no	—
558	C₂×C₁₃	—	4	2	no	—
559	C₂×C₁₃	—	8	1	no	—
560	C₂×C₁₃	—	16	1	no	—
561	C₂×C₁₃	#2412	1	1	yes	characteristic
562	C₂×C₁₃	#3067	1	1	yes	characteristic
563	C₂×C₁₃	#3068	1	1	yes	characteristic
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	C₁₃×#41	1	1	yes	characteristic
567	#41	—	2	1	no	—
568	#41	—	2	1	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	2	1	no	—
572	#41	—	2	1	no	—
573	#41	—	2	1	no	—
574	#41	—	2	1	no	—
575	#41	—	4	2	no	—
576	#41	—	4	2	no	—
577	#41	—	4	1	no	—
578	#41	—	4	1	no	—
579	#41	—	4	2	no	—
580	#41	—	4	2	no	—
581	#41	C₁₃×#41	1	2	yes	—
582	#41	C₁₃×#41	1	2	yes	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	4	1	no	—
586	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	4	1	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	8	2	no	—
606	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
628	SD₁₆	—	4	2	no	—
629	SD₁₆	—	4	2	no	—
630	D₈	—	4	2	no	—
631	D₈	—	4	2	no	—
632	M₁₆	—	2	1	no	—
633	M₁₆	—	2	1	no	—
634	M₁₆	—	2	1	no	—
635	M₁₆	—	2	1	no	—
636	M₁₆	—	2	1	no	—
637	M₁₆	—	2	1	no	—
638	M₁₆	—	2	1	no	—
639	M₁₆	—	2	1	no	—
640	M₁₆	—	2	1	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	1	no	—
643	M₁₆	—	2	1	no	—
644	M₁₆	—	4	2	no	—
645	M₁₆	—	4	2	no	—
646	M₁₆	—	4	2	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	4	2	no	—
658	C₂×C₈	—	4	2	no	—
659	C₂×C₈	—	4	2	no	—
660	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	4	1	no	—
671	C₂²⋊C₄	—	4	1	no	—
672	C₂²⋊C₄	—	4	1	no	—
673	C₂²⋊C₄	—	4	1	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	1	no	—
676	C₁₃	#24575	1	1	yes	characteristic, direct product factor, Sylow
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	8	1	no	—
689	C₂³	—	8	1	no	—
690	C₂³	—	8	1	no	—
691	C₂³	C₁₃×#121	1	1	yes	characteristic
692	C₂³	C₁₃×#121	1	1	yes	characteristic
693	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
694	Q₈	—	2	1	no	—
695	Q₈	—	2	1	no	—
696	Q₈	—	2	1	no	—
697	Q₈	—	4	2	no	—
698	Q₈	C₁₃×#123	1	2	yes	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	1	no	—
702	D₄	—	2	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	1	no	—
708	D₄	—	4	1	no	—
709	D₄	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	D₄	—	8	2	no	—
714	D₄	—	8	2	no	—
715	D₄	C₁₃×#123	1	2	yes	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
742	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
746	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
747	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₈	—	2	1	no	—
750	C₈	—	2	1	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	—	4	1	no	—
754	C₈	—	4	1	no	—
755	C₈	—	4	1	no	—
756	C₈	—	4	1	no	—
757	C₈	—	4	1	no	—
758	C₈	—	4	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	4	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	16	1	no	—
780	C₂²	—	16	1	no	—
781	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
782	C₂²	C₁₃×#551	1	1	yes	characteristic
783	C₂²	C₁₃×#551	1	1	yes	characteristic
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	8	1	no	—
789	C₄	—	8	1	no	—
790	C₄	—	8	1	no	—
791	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
792	C₄	C₁₃×#534	1	1	yes	characteristic
793	C₄	C₁₃×#546	1	1	yes	characteristic
794	C₄	C₁₃×#546	1	1	yes	characteristic
795	C₂	—	2	1	no	—
796	C₂	—	2	1	no	—
797	C₂	—	4	1	no	—
798	C₂	—	4	1	no	—
799	C₂	—	4	2	no	—
800	C₂	—	8	1	no	—
801	C₂	—	16	1	no	—
802	C₂	C₁₃×#2412	1	1	yes	characteristic
803	C₂	C₁₃×#3067	1	1	yes	characteristic
804	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3006	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#482	C₂	semidirect
3. C₁₃×#2896	C₂	semidirect
4. C₁₃×#2880	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2078	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#1907	C₂	semidirect
10. C₁₃×#1907	C₂	semidirect
11. C₁₃×#1900	C₂	semidirect
12. C₁₃×#1855	C₂	semidirect
13. C₁₃×#1822	C₂	semidirect
14. C₁₃×#1816	C₂	semidirect
15. C₁₃×#1815	C₂	semidirect
32. C₂×C₁₃×#108	C₂²	semidirect
33. C₂×C₁₃×#108	C₂²	semidirect
34. C₂×C₁₃×#107	C₂²	semidirect
35. C₂×C₁₃×#106	C₂²	semidirect
46. C₂×C₁₃×#102	C₂²	semidirect
47. C₂×C₁₃×#102	C₂²	semidirect
48. C₂×C₁₃×#100	C₂²	semidirect
49. C₂×C₁₃×#100	C₂²	semidirect
59. C₁₃×#343	C₂²	semidirect
60. C₁₃×#343	C₂²	semidirect
61. C₁₃×#343	C₂²	semidirect
62. C₁₃×#343	C₂²	semidirect
63. C₁₃×#343	C₂²	semidirect
64. C₁₃×#343	C₂²	semidirect
65. C₁₃×#341	C₂²	semidirect
66. C₁₃×#341	C₂²	semidirect
162. #24575	C₁₃	direct (N × H)
275. C₂×#482	C₂×C₁₃	semidirect
277. #2896	C₂×C₁₃	semidirect
278. #2880	C₂×C₁₃	semidirect
279. #2079	C₂×C₁₃	semidirect
280. #2078	C₂×C₁₃	semidirect
281. #2051	C₂×C₁₃	semidirect
282. #2051	C₂×C₁₃	semidirect
283. #1907	C₂×C₁₃	semidirect
284. #1907	C₂×C₁₃	semidirect
285. #1900	C₂×C₁₃	semidirect
286. #1855	C₂×C₁₃	semidirect
287. #1822	C₂×C₁₃	semidirect
288. #1816	C₂×C₁₃	semidirect
289. #1815	C₂×C₁₃	semidirect
388. C₂×#108	C₂²×C₁₃	semidirect
389. C₂×#108	C₂²×C₁₃	semidirect
390. C₂×#107	C₂²×C₁₃	semidirect
391. C₂×#106	C₂²×C₁₃	semidirect
402. C₂×#102	C₂²×C₁₃	semidirect
403. C₂×#102	C₂²×C₁₃	semidirect
404. C₂×#100	C₂²×C₁₃	semidirect
405. C₂×#100	C₂²×C₁₃	semidirect
415. #343	C₂²×C₁₃	semidirect
416. #343	C₂²×C₁₃	semidirect
417. #343	C₂²×C₁₃	semidirect
418. #343	C₂²×C₁₃	semidirect
419. #343	C₂²×C₁₃	semidirect
420. #343	C₂²×C₁₃	semidirect
421. #341	C₂²×C₁₃	semidirect
422. #341	C₂²×C₁₃	semidirect
676. C₁₃	#24575	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×#482	2
C₁₃×#3006	2
C₁₃×#2896	2
C₁₃×#2880	2
C₁₃×#2079	2
C₁₃×#2078	2
C₁₃×#2051	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1822	2
C₁₃×#1816	2
C₁₃×#1815	2
#24575	13

Subgroups — C13×#24575 #15710914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24575 #15710914