Subgroups — C₁₃×#22052 #15708391

Order 3328.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₁₃×#450	C₄	1	8	yes	complemented
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#390	—	2	1	no	—
40	C₁₃×#390	—	2	1	no	—
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#389	—	2	1	no	—
46	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#387	—	2	1	no	—
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#379	—	2	1	no	—
52	C₁₃×#379	—	2	1	no	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₂⁵×C₁₃	—	2	1	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	4	1	no	—
65	C₂²×D₄×C₁₃	—	4	1	no	—
66	C₂²×D₄×C₁₃	—	4	1	no	—
67	C₂²×D₄×C₁₃	—	4	1	no	—
68	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×SD₁₆	—	4	1	no	—
73	C₂×C₁₃×SD₁₆	—	4	1	no	—
74	C₂×C₁₃×SD₁₆	—	4	1	no	—
75	C₂×C₁₃×SD₁₆	—	4	1	no	—
76	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
77	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₁₃	—	4	1	no	—
85	C₄×Q₈×C₁₃	—	4	1	no	—
86	C₁₃×#117	—	4	1	no	—
87	C₁₃×#117	—	4	1	no	—
88	C₁₃×#117	—	4	1	no	—
89	C₁₃×#117	—	4	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	—	2	1	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	—	4	1	no	—
119	C₁₃×#106	—	4	1	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#102	—	4	1	no	—
123	C₁₃×#102	—	4	1	no	—
124	C₁₃×#102	—	4	1	no	—
125	C₁₃×#102	—	4	1	no	—
126	C₁₃×#102	C₂×C₄	1	4	yes	—
127	C₁₃×#102	C₂×C₄	1	4	yes	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
130	C₁₃×#97	—	4	1	no	—
131	C₄×C₈×C₁₃	—	4	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	#22052	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	1	no	—
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	—	2	4	no	—
141	C₂⁴×C₁₃	—	4	2	no	—
142	C₂⁴×C₁₃	—	4	2	no	—
143	C₂⁴×C₁₃	—	8	1	no	—
144	C₂⁴×C₁₃	—	8	1	no	—
145	C₂⁴×C₁₃	—	8	1	no	—
146	C₂⁴×C₁₃	—	8	1	no	—
147	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	—	4	4	no	—
171	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
172	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	#41	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×SD₁₆	—	4	4	no	—
192	C₁₃×SD₁₆	—	4	4	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
204	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	4	1	no	—
216	C₁₃×C₄⋊C₄	—	4	1	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₄⋊C₄	—	8	1	no	—
219	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	4	1	no	—
222	C₁₃×C₂²⋊C₄	—	4	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	2	no	—
224	C₁₃×C₂²⋊C₄	—	8	1	no	—
225	C₁₃×C₂²⋊C₄	—	8	1	no	—
226	C₁₃×C₂²⋊C₄	—	8	1	no	—
227	C₁₃×C₂²⋊C₄	—	8	1	no	—
228	C₁₃×C₂²⋊C₄	—	8	1	no	—
229	C₁₃×C₂²⋊C₄	—	8	1	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₁₃×C₂²⋊C₄	—	8	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	2	1	no	—
237	C₄²×C₁₃	—	4	2	no	—
238	C₄²×C₁₃	—	4	2	no	—
239	C₄²×C₁₃	—	8	1	no	—
240	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
241	#2323	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2309	C₂×C₁₃	1	1	yes	characteristic
243	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1786	C₂×C₁₃	1	1	yes	characteristic
254	#1750	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	4	8	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	8	4	no	—
277	C₂³×C₁₃	—	8	4	no	—
278	C₂³×C₁₃	—	8	4	no	—
279	C₂³×C₁₃	—	8	4	no	—
280	C₂³×C₁₃	—	8	4	no	—
281	C₂³×C₁₃	—	8	4	no	—
282	C₂³×C₁₃	C₄×D₄	1	2	yes	—
283	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₁₃	—	2	2	no	—
285	Q₈×C₁₃	—	2	2	no	—
286	Q₈×C₁₃	—	4	1	no	—
287	Q₈×C₁₃	—	4	1	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	2	no	—
291	D₄×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	4	8	no	—
293	D₄×C₁₃	—	4	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
334	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₁₃	—	2	2	no	—
341	C₈×C₁₃	—	2	2	no	—
342	C₈×C₁₃	—	4	1	no	—
343	C₈×C₁₃	—	4	1	no	—
344	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
349	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
351	#450	C₄×C₁₃	1	8	yes	complemented
352	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
354	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
355	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
365	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
366	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	#390	—	2	1	no	—
368	#390	—	2	1	no	—
369	#390	C₂²×C₁₃	1	1	yes	characteristic
370	#390	C₂²×C₁₃	1	1	yes	characteristic
371	#390	C₂²×C₁₃	1	1	yes	characteristic
372	#390	C₂²×C₁₃	1	1	yes	characteristic
373	#389	—	2	1	no	—
374	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#387	—	2	1	no	—
378	#380	C₂²×C₁₃	1	1	yes	characteristic
379	#379	—	2	1	no	—
380	#379	—	2	1	no	—
381	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	4	1	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	2	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	2	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	8	16	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	—	8	1	no	—
406	C₂²×C₁₃	—	8	1	no	—
407	C₂²×C₁₃	—	8	1	no	—
408	C₂²×C₁₃	—	8	1	no	—
409	C₂²×C₁₃	—	8	1	no	—
410	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂²×C₁₃	#534	1	1	yes	characteristic
412	C₂²×C₁₃	#535	1	1	yes	characteristic
413	C₂²×C₁₃	#576	1	1	yes	characteristic
414	C₂²×C₁₃	#577	1	1	yes	characteristic
415	C₂²×C₁₃	#577	1	1	yes	characteristic
416	C₂²×C₁₃	#577	1	1	yes	characteristic
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	4	1	no	—
421	C₄×C₁₃	—	4	1	no	—
422	C₄×C₁₃	—	4	1	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	8	1	no	—
425	C₄×C₁₃	—	8	1	no	—
426	C₄×C₁₃	—	8	1	no	—
427	C₄×C₁₃	—	8	1	no	—
428	C₄×C₁₃	#518	1	1	yes	characteristic
429	C₄×C₁₃	#518	1	1	yes	characteristic
430	C₄×C₁₃	#538	1	1	yes	characteristic
431	C₄×C₁₃	#538	1	1	yes	characteristic
432	C₂⁵	—	2	1	no	—
433	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	—	2	2	no	—
436	C₂²×D₄	—	4	1	no	—
437	C₂²×D₄	—	4	1	no	—
438	C₂²×D₄	—	4	1	no	—
439	C₂²×D₄	—	4	1	no	—
440	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
441	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×SD₁₆	—	4	1	no	—
445	C₂×SD₁₆	—	4	1	no	—
446	C₂×SD₁₆	—	4	1	no	—
447	C₂×SD₁₆	—	4	1	no	—
448	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
449	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
450	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
456	C₄×Q₈	—	4	1	no	—
457	C₄×Q₈	—	4	1	no	—
458	#117	—	4	1	no	—
459	#117	—	4	1	no	—
460	#117	—	4	1	no	—
461	#117	—	4	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
490	#107	—	4	1	no	—
491	#106	—	4	1	no	—
492	#103	—	4	1	no	—
493	#103	—	4	1	no	—
494	#102	—	4	1	no	—
495	#102	—	4	1	no	—
496	#102	—	4	1	no	—
497	#102	—	4	1	no	—
498	#102	C₂×C₄×C₁₃	1	4	yes	—
499	#102	C₂×C₄×C₁₃	1	4	yes	—
500	C₂²⋊C₈	—	2	2	no	—
501	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
502	#97	—	4	1	no	—
503	C₄×C₈	—	4	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	C₂×C₁₃	—	4	2	no	—
510	C₂×C₁₃	—	8	2	no	—
511	C₂×C₁₃	—	8	2	no	—
512	C₂×C₁₃	#2321	1	1	yes	characteristic
513	C₂×C₁₃	#2946	1	1	yes	characteristic
514	C₂×C₁₃	#2949	1	1	yes	characteristic
515	C₂×C₁₃	#3198	1	1	yes	characteristic
516	C₂×C₁₃	#3200	1	1	yes	characteristic
517	C₂×C₁₃	#3222	1	1	yes	characteristic
518	C₂×C₁₃	#3224	1	1	yes	characteristic
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	—	8	1	no	—
525	C₂⁴	—	8	1	no	—
526	C₂⁴	—	8	1	no	—
527	C₂⁴	—	8	1	no	—
528	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
553	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
570	C₂²×C₄	C₁₃×#41	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	SD₁₆	—	4	4	no	—
573	SD₁₆	—	4	4	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
585	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	—	4	1	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	—	8	1	no	—
600	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	8	1	no	—
606	C₂²⋊C₄	—	8	1	no	—
607	C₂²⋊C₄	—	8	1	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₂²⋊C₄	—	8	1	no	—
610	C₂²⋊C₄	—	8	1	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₂²⋊C₄	—	8	1	no	—
613	C₂²⋊C₄	—	8	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	4	2	no	—
619	C₄²	—	4	2	no	—
620	C₄²	—	8	1	no	—
621	C₁₃	#22052	1	1	yes	characteristic, direct product factor, Sylow
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	8	4	no	—
644	C₂³	—	8	4	no	—
645	C₂³	—	8	4	no	—
646	C₂³	—	8	4	no	—
647	C₂³	—	8	4	no	—
648	C₂³	—	8	4	no	—
649	C₂³	C₄×D₄×C₁₃	1	2	yes	—
650	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	4	8	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	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	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
701	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
702	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
703	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	8	16	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
734	C₂²	C₁₃×#534	1	1	yes	characteristic
735	C₂²	C₁₃×#535	1	1	yes	characteristic
736	C₂²	C₁₃×#576	1	1	yes	characteristic
737	C₂²	C₁₃×#577	1	1	yes	characteristic
738	C₂²	C₁₃×#577	1	1	yes	characteristic
739	C₂²	C₁₃×#577	1	1	yes	characteristic
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	2	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	—	8	1	no	—
750	C₄	—	8	1	no	—
751	C₄	C₁₃×#518	1	1	yes	characteristic
752	C₄	C₁₃×#518	1	1	yes	characteristic
753	C₄	C₁₃×#538	1	1	yes	characteristic
754	C₄	C₁₃×#538	1	1	yes	characteristic
755	C₂	—	4	2	no	—
756	C₂	—	8	2	no	—
757	C₂	—	8	2	no	—
758	C₂	C₁₃×#2321	1	1	yes	characteristic
759	C₂	C₁₃×#2946	1	1	yes	characteristic
760	C₂	C₁₃×#2949	1	1	yes	characteristic
761	C₂	C₁₃×#3198	1	1	yes	characteristic
762	C₂	C₁₃×#3200	1	1	yes	characteristic
763	C₂	C₁₃×#3222	1	1	yes	characteristic
764	C₂	C₁₃×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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×#2323	C₂	semidirect
4. C₁₃×#1973	C₂	semidirect
5. C₁₃×#1968	C₂	semidirect
6. C₁₃×#1936	C₂	semidirect
7. C₁₃×#1934	C₂	semidirect
8. C₁₃×#1926	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
10. C₁₃×#1880	C₂	semidirect
11. C₁₃×#1880	C₂	semidirect
12. C₁₃×#1873	C₂	semidirect
13. C₁₃×#1854	C₂	semidirect
15. C₁₃×#1750	C₂	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
23. C₁₃×#450	C₄	semidirect
24. C₂×C₁₃×#107	C₂²	semidirect
25. C₂×C₁₃×#106	C₂²	semidirect
26. C₂×C₁₃×#103	C₂²	semidirect
27. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#97	C₂²	semidirect
37. C₂×C₄×C₈×C₁₃	C₂²	semidirect
38. C₁₃×#391	C₂²	semidirect
46. C₁₃×#389	C₂²	semidirect
53. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
54. C₁₃×#340	C₂²	semidirect
55. C₁₃×#340	C₂²	semidirect
56. C₁₃×#340	C₂²	semidirect
57. C₁₃×#340	C₂²	semidirect
58. C₁₃×#336	C₂²	semidirect
59. C₁₃×#336	C₂²	semidirect
137. #22052	C₁₃	direct (N × H)
241. #2323	C₂×C₁₃	semidirect
243. #1973	C₂×C₁₃	semidirect
244. #1968	C₂×C₁₃	semidirect
245. #1936	C₂×C₁₃	semidirect
246. #1934	C₂×C₁₃	semidirect
247. #1926	C₂×C₁₃	semidirect
248. #1925	C₂×C₁₃	semidirect
249. #1880	C₂×C₁₃	semidirect
250. #1880	C₂×C₁₃	semidirect
251. #1873	C₂×C₁₃	semidirect
252. #1854	C₂×C₁₃	semidirect
254. #1750	C₂×C₁₃	semidirect
348. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
351. #450	C₄×C₁₃	semidirect
352. C₂×#107	C₂²×C₁₃	semidirect
353. C₂×#106	C₂²×C₁₃	semidirect
354. C₂×#103	C₂²×C₁₃	semidirect
355. C₂×#103	C₂²×C₁₃	semidirect
364. C₂×#97	C₂²×C₁₃	semidirect
365. C₂×C₄×C₈	C₂²×C₁₃	semidirect
366. #391	C₂²×C₁₃	semidirect
374. #389	C₂²×C₁₃	semidirect
381. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
382. #340	C₂²×C₁₃	semidirect
383. #340	C₂²×C₁₃	semidirect
384. #340	C₂²×C₁₃	semidirect
385. #340	C₂²×C₁₃	semidirect
386. #336	C₂²×C₁₃	semidirect
387. #336	C₂²×C₁₃	semidirect
621. C₁₃	#22052	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×#450	2
C₁₃×#2323	2
C₁₃×#2309	2
C₁₃×#1973	2
C₁₃×#1968	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1925	2
C₁₃×#1880	2
C₁₃×#1873	2
C₁₃×#1854	2
C₁₃×#1786	2
C₁₃×#1750	2
#22052	13

Subgroups — C13×#22052 #15708391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22052 #15708391