Subgroups — C₁₃×#35050 #15721389

Order 3328.

4146 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2617	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2561	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2539	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2534	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2482	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2411	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2404	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2321	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#525	—	2	8	no	—
20	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#120	C₂²	1	4	yes	—
27	C₂×C₁₃×#120	C₂²	1	2	yes	—
28	C₂×C₁₃×#120	C₂²	1	4	yes	—
29	C₂×C₁₃×#120	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
34	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₁₃×#399	C₂²	1	4	yes	complemented
42	C₁₃×#397	C₂²	1	4	yes	complemented
43	C₁₃×#396	C₂²	1	8	yes	complemented
44	C₁₃×#394	C₂²	1	8	yes	complemented
45	C₁₃×#393	C₂²	1	4	yes	complemented
46	C₁₃×#392	C₂²	1	4	yes	complemented
47	C₁₃×#390	C₂²	1	8	yes	complemented
48	C₁₃×#388	C₂²	1	8	yes	complemented
49	C₁₃×#388	C₂²	1	8	yes	complemented
50	C₁₃×#386	C₂²	1	8	yes	complemented
51	C₁₃×#386	C₂²	1	4	yes	complemented
52	C₁₃×#386	C₂²	1	4	yes	complemented
53	C₁₃×#385	C₂²	1	4	yes	complemented
54	C₁₃×#385	C₂²	1	4	yes	complemented
55	C₁₃×#381	C₂²	1	4	yes	complemented
56	C₁₃×#381	C₂²	1	2	yes	complemented
57	C₁₃×#380	C₂²	1	2	yes	complemented
58	C₁₃×#380	C₂²	1	2	yes	complemented
59	C₁₃×#379	C₂²	1	4	yes	—
60	C₁₃×#379	C₂²	1	2	yes	—
61	C₁₃×#379	C₂²	1	4	yes	—
62	C₁₃×#379	C₂²	1	4	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₃	—	2	4	no	—
66	C₂⁵×C₁₃	—	2	8	no	—
67	C₂⁵×C₁₃	—	4	4	no	—
68	C₂⁵×C₁₃	—	4	4	no	—
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂⁵×C₁₃	C₂³	1	2	yes	—
71	C₂⁵×C₁₃	C₂³	1	2	yes	—
72	C₂⁵×C₁₃	C₂³	1	2	yes	—
73	C₂×C₁₃×#41	—	2	4	no	—
74	C₂×C₁₃×#41	—	4	4	no	—
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
81	C₂³×C₄×C₁₃	—	2	4	no	—
82	C₂³×C₄×C₁₃	—	4	4	no	—
83	C₂³×C₄×C₁₃	—	4	4	no	—
84	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×#123	—	4	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#120	—	2	8	no	—
102	C₁₃×#120	—	2	16	no	—
103	C₁₃×#120	—	4	8	no	—
104	C₁₃×#120	—	4	8	no	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	4	4	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
115	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	complemented
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
139	C₁₃×#95	C₂³	1	4	yes	complemented
140	C₁₃×#95	C₂³	1	4	yes	complemented
141	C₁₃×#95	C₂³	1	8	yes	complemented
142	C₁₃×#95	C₂³	1	8	yes	complemented
143	#35050	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂⁴×C₁₃	—	2	4	no	—
145	C₂⁴×C₁₃	—	2	4	no	—
146	C₂⁴×C₁₃	—	2	4	no	—
147	C₂⁴×C₁₃	—	2	32	no	—
148	C₂⁴×C₁₃	—	2	4	no	—
149	C₂⁴×C₁₃	—	2	4	no	—
150	C₂⁴×C₁₃	—	2	4	no	—
151	C₂⁴×C₁₃	—	2	8	no	—
152	C₂⁴×C₁₃	—	2	8	no	—
153	C₂⁴×C₁₃	—	2	4	no	—
154	C₂⁴×C₁₃	—	2	8	no	—
155	C₂⁴×C₁₃	—	2	8	no	—
156	C₂⁴×C₁₃	—	4	4	no	—
157	C₂⁴×C₁₃	—	4	4	no	—
158	C₂⁴×C₁₃	—	4	4	no	—
159	C₂⁴×C₁₃	—	4	4	no	—
160	C₂⁴×C₁₃	—	4	64	no	—
161	C₂⁴×C₁₃	—	4	16	no	—
162	C₂⁴×C₁₃	—	4	16	no	—
163	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
164	C₂⁴×C₁₃	#41	1	8	yes	complemented
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×#41	—	4	16	no	—
171	C₂×Q₈×C₁₃	—	2	2	no	—
172	C₂×Q₈×C₁₃	—	4	2	no	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	4	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	8	no	—
177	C₂×D₄×C₁₃	—	2	8	no	—
178	C₂×D₄×C₁₃	—	2	8	no	—
179	C₂×D₄×C₁₃	—	2	16	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	4	2	no	—
182	C₂×D₄×C₁₃	—	4	8	no	—
183	C₂×D₄×C₁₃	—	4	8	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	8	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	4	16	no	—
192	C₂²×C₄×C₁₃	—	4	2	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	4	2	no	—
195	C₂²×C₄×C₁₃	—	4	2	no	—
196	C₂²×C₄×C₁₃	—	4	4	no	—
197	C₂²×C₄×C₁₃	—	4	4	no	—
198	C₂²×C₄×C₁₃	—	4	4	no	—
199	C₂²×C₄×C₁₃	—	4	16	no	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	4	4	no	—
220	C₁₃×C₄⋊C₄	—	4	8	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	4	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	16	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	8	no	—
227	C₁₃×C₂²⋊C₄	—	2	8	no	—
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	—	2	8	no	—
231	C₁₃×C₂²⋊C₄	—	2	8	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	4	8	no	—
235	C₁₃×C₂²⋊C₄	—	4	8	no	—
236	C₁₃×C₂²⋊C₄	—	4	8	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	—	4	4	no	—
239	C₂×#525	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2849	C₂×C₁₃	1	2	yes	complemented
242	#2846	C₂×C₁₃	1	2	yes	complemented
243	#2626	C₂×C₁₃	1	2	yes	complemented
244	#2617	C₂×C₁₃	1	2	yes	complemented
245	#2561	C₂×C₁₃	1	2	yes	complemented
246	#2539	C₂×C₁₃	1	2	yes	complemented
247	#2534	C₂×C₁₃	1	4	yes	complemented
248	#2482	C₂×C₁₃	1	2	yes	complemented
249	#2411	C₂×C₁₃	1	4	yes	complemented
250	#2404	C₂×C₁₃	1	2	yes	complemented
251	#2321	C₂×C₁₃	1	4	yes	complemented
252	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂³×C₁₃	—	2	32	no	—
254	C₂³×C₁₃	—	2	8	no	—
255	C₂³×C₁₃	—	2	8	no	—
256	C₂³×C₁₃	—	2	8	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	16	no	—
264	C₂³×C₁₃	—	2	16	no	—
265	C₂³×C₁₃	—	2	16	no	—
266	C₂³×C₁₃	—	2	4	no	—
267	C₂³×C₁₃	—	2	4	no	—
268	C₂³×C₁₃	—	2	8	no	—
269	C₂³×C₁₃	—	2	8	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	2	4	no	—
272	C₂³×C₁₃	—	2	4	no	—
273	C₂³×C₁₃	—	2	4	no	—
274	C₂³×C₁₃	—	4	16	no	—
275	C₂³×C₁₃	—	4	32	no	—
276	C₂³×C₁₃	—	4	32	no	—
277	C₂³×C₁₃	—	4	128	no	—
278	C₂³×C₁₃	—	4	8	no	—
279	C₂³×C₁₃	—	4	8	no	—
280	C₂³×C₁₃	—	4	8	no	—
281	C₂³×C₁₃	—	4	8	no	—
282	C₂³×C₁₃	—	4	16	no	—
283	C₂³×C₁₃	—	4	8	no	—
284	C₂³×C₁₃	—	4	8	no	—
285	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂³×C₁₃	C₂×#41	1	8	yes	—
289	C₂³×C₁₃	C₂×#41	1	4	yes	—
290	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
291	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
292	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
293	Q₈×C₁₃	—	4	4	no	—
294	D₄×C₁₃	—	4	4	no	—
295	D₄×C₁₃	—	4	8	no	—
296	D₄×C₁₃	—	4	8	no	—
297	D₄×C₁₃	—	4	8	no	—
298	D₄×C₁₃	—	8	16	no	—
299	C₂×C₄×C₁₃	—	2	8	no	—
300	C₂×C₄×C₁₃	—	2	8	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	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	8	no	—
311	C₂×C₄×C₁₃	—	2	8	no	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	2	8	no	—
316	C₂×C₄×C₁₃	—	4	4	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	4	no	—
320	C₂×C₄×C₁₃	—	4	8	no	—
321	C₂×C₄×C₁₃	—	4	8	no	—
322	C₂×C₄×C₁₃	—	4	8	no	—
323	C₂×C₄×C₁₃	—	4	8	no	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
332	#525	—	2	8	no	—
333	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
334	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
335	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#120	C₂²×C₁₃	1	4	yes	—
340	C₂×#120	C₂²×C₁₃	1	2	yes	—
341	C₂×#120	C₂²×C₁₃	1	4	yes	—
342	C₂×#120	C₂²×C₁₃	1	4	yes	—
343	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
344	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
345	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
346	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
347	C₂²×C₂²⋊C₄	—	2	8	no	—
348	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
351	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
354	#399	C₂²×C₁₃	1	4	yes	complemented
355	#397	C₂²×C₁₃	1	4	yes	complemented
356	#396	C₂²×C₁₃	1	8	yes	complemented
357	#394	C₂²×C₁₃	1	8	yes	complemented
358	#393	C₂²×C₁₃	1	4	yes	complemented
359	#392	C₂²×C₁₃	1	4	yes	complemented
360	#390	C₂²×C₁₃	1	8	yes	complemented
361	#388	C₂²×C₁₃	1	8	yes	complemented
362	#388	C₂²×C₁₃	1	8	yes	complemented
363	#386	C₂²×C₁₃	1	8	yes	complemented
364	#386	C₂²×C₁₃	1	4	yes	complemented
365	#386	C₂²×C₁₃	1	4	yes	complemented
366	#385	C₂²×C₁₃	1	4	yes	complemented
367	#385	C₂²×C₁₃	1	4	yes	complemented
368	#381	C₂²×C₁₃	1	4	yes	complemented
369	#381	C₂²×C₁₃	1	2	yes	complemented
370	#380	C₂²×C₁₃	1	2	yes	complemented
371	#380	C₂²×C₁₃	1	2	yes	complemented
372	#379	C₂²×C₁₃	1	4	yes	—
373	#379	C₂²×C₁₃	1	4	yes	—
374	#379	C₂²×C₁₃	1	2	yes	—
375	#379	C₂²×C₁₃	1	4	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
377	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
378	C₂²×C₁₃	—	2	32	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	2	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	8	no	—
386	C₂²×C₁₃	—	2	8	no	—
387	C₂²×C₁₃	—	2	8	no	—
388	C₂²×C₁₃	—	2	8	no	—
389	C₂²×C₁₃	—	2	16	no	—
390	C₂²×C₁₃	—	4	32	no	—
391	C₂²×C₁₃	—	4	32	no	—
392	C₂²×C₁₃	—	4	32	no	—
393	C₂²×C₁₃	—	4	4	no	—
394	C₂²×C₁₃	—	4	4	no	—
395	C₂²×C₁₃	—	4	8	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	2	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	8	no	—
400	C₂²×C₁₃	#525	1	4	yes	—
401	C₂²×C₁₃	#534	1	4	yes	—
402	C₂²×C₁₃	#535	1	4	yes	—
403	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
404	C₂²×C₁₃	C₂²×#41	1	2	yes	—
405	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	2	2	no	—
410	C₄×C₁₃	—	2	2	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	4	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	—	4	8	no	—
416	C₂⁵	—	2	4	no	—
417	C₂⁵	—	2	8	no	—
418	C₂⁵	—	4	4	no	—
419	C₂⁵	—	4	4	no	—
420	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
421	C₂⁵	C₂³×C₁₃	1	2	yes	—
422	C₂⁵	C₂³×C₁₃	1	2	yes	—
423	C₂⁵	C₂³×C₁₃	1	2	yes	—
424	C₂×#41	—	2	4	no	—
425	C₂×#41	—	4	4	no	—
426	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
427	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
428	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
430	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
431	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	4	4	no	—
434	C₂³×C₄	—	4	4	no	—
435	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
436	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
437	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
440	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
441	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
446	#123	—	2	8	no	—
447	#123	—	4	8	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	—	2	4	no	—
450	#121	—	2	4	no	—
451	#121	—	2	4	no	—
452	#120	—	2	8	no	—
453	#120	—	2	16	no	—
454	#120	—	4	8	no	—
455	#120	—	4	8	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	8	no	—
458	#117	—	2	4	no	—
459	#117	—	4	4	no	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
466	C₂×C₂²⋊C₄	—	2	8	no	—
467	C₂×C₂²⋊C₄	—	2	8	no	—
468	C₂×C₂²⋊C₄	—	2	8	no	—
469	C₂×C₂²⋊C₄	—	2	8	no	—
470	C₂×C₂²⋊C₄	—	2	8	no	—
471	C₂×C₂²⋊C₄	—	2	8	no	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
486	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
487	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
488	C₂×C₄²	C₂³×C₁₃	1	2	yes	complemented
489	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
490	#95	C₂³×C₁₃	1	4	yes	complemented
491	#95	C₂³×C₁₃	1	4	yes	complemented
492	#95	C₂³×C₁₃	1	8	yes	complemented
493	#95	C₂³×C₁₃	1	8	yes	complemented
494	C₂×C₁₃	—	2	4	no	—
495	C₂×C₁₃	—	2	4	no	—
496	C₂×C₁₃	—	2	4	no	—
497	C₂×C₁₃	—	4	8	no	—
498	C₂×C₁₃	—	8	2	no	—
499	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
500	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
501	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
502	C₂×C₁₃	#3490	1	4	yes	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	—	2	32	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	2	4	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	8	no	—
511	C₂⁴	—	2	8	no	—
512	C₂⁴	—	2	4	no	—
513	C₂⁴	—	2	8	no	—
514	C₂⁴	—	2	8	no	—
515	C₂⁴	—	4	4	no	—
516	C₂⁴	—	4	4	no	—
517	C₂⁴	—	4	4	no	—
518	C₂⁴	—	4	4	no	—
519	C₂⁴	—	4	64	no	—
520	C₂⁴	—	4	16	no	—
521	C₂⁴	—	4	16	no	—
522	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
523	C₂⁴	C₁₃×#41	1	8	yes	complemented
524	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
525	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
526	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
529	#41	—	4	16	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	8	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	16	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	8	no	—
542	C₂×D₄	—	4	8	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	4	16	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	4	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	16	no	—
559	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
560	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
561	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
562	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
563	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
567	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	—	4	8	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	16	no	—
584	C₂²⋊C₄	—	2	8	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	4	8	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₂²⋊C₄	—	4	8	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	4	4	no	—
598	C₁₃	#35050	1	1	yes	characteristic, direct product factor, Sylow
599	C₂³	—	2	32	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	16	no	—
610	C₂³	—	2	16	no	—
611	C₂³	—	2	16	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	16	no	—
621	C₂³	—	4	32	no	—
622	C₂³	—	4	32	no	—
623	C₂³	—	4	128	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	8	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	16	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	8	no	—
631	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
632	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
633	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
634	C₂³	C₂×C₁₃×#41	1	8	yes	—
635	C₂³	C₂×C₁₃×#41	1	4	yes	—
636	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
637	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
638	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
639	Q₈	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	8	16	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
672	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
673	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
674	C₂²	—	2	32	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	2	8	no	—
683	C₂²	—	2	8	no	—
684	C₂²	—	2	8	no	—
685	C₂²	—	2	16	no	—
686	C₂²	—	4	32	no	—
687	C₂²	—	4	32	no	—
688	C₂²	—	4	32	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	8	no	—
696	C₂²	C₁₃×#525	1	4	yes	—
697	C₂²	C₁₃×#534	1	4	yes	—
698	C₂²	C₁₃×#535	1	4	yes	—
699	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
700	C₂²	C₂²×C₁₃×#41	1	2	yes	—
701	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
702	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	8	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	8	no	—
716	C₂	—	8	2	no	—
717	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
718	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
719	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
720	C₂	C₁₃×#3490	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#525	C₂	semidirect
2. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
3. C₁₃×#2849	C₂	semidirect
4. C₁₃×#2846	C₂	semidirect
5. C₁₃×#2626	C₂	semidirect
6. C₁₃×#2617	C₂	semidirect
7. C₁₃×#2561	C₂	semidirect
8. C₁₃×#2539	C₂	semidirect
9. C₁₃×#2534	C₂	semidirect
10. C₁₃×#2482	C₂	semidirect
11. C₁₃×#2411	C₂	semidirect
12. C₁₃×#2404	C₂	semidirect
13. C₁₃×#2321	C₂	semidirect
14. C₁₃×#2280	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂×C₁₃×#123	C₂²	semidirect
21. C₂×C₁₃×#123	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₁₃×#117	C₂²	semidirect
33. C₂×C₁₃×#117	C₂²	semidirect
41. C₁₃×#399	C₂²	semidirect
42. C₁₃×#397	C₂²	semidirect
43. C₁₃×#396	C₂²	semidirect
44. C₁₃×#394	C₂²	semidirect
45. C₁₃×#393	C₂²	semidirect
46. C₁₃×#392	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#388	C₂²	semidirect
49. C₁₃×#388	C₂²	semidirect
50. C₁₃×#386	C₂²	semidirect
51. C₁₃×#386	C₂²	semidirect
52. C₁₃×#386	C₂²	semidirect
53. C₁₃×#385	C₂²	semidirect
54. C₁₃×#385	C₂²	semidirect
55. C₁₃×#381	C₂²	semidirect
56. C₁₃×#381	C₂²	semidirect
57. C₁₃×#380	C₂²	semidirect
58. C₁₃×#380	C₂²	semidirect
63. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
64. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
75. C₂²×Q₈×C₁₃	C₂³	semidirect
80. C₂²×D₄×C₁₃	C₂³	semidirect
84. C₂³×C₄×C₁₃	D₄	semidirect
94. C₂³×C₄×C₁₃	C₂³	semidirect
109. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
110. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
111. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
112. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
113. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
114. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
134. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
135. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
136. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
137. C₂×C₄²×C₁₃	C₂³	semidirect
138. C₂×C₄²×C₁₃	C₂³	semidirect
139. C₁₃×#95	C₂³	semidirect
140. C₁₃×#95	C₂³	semidirect
141. C₁₃×#95	C₂³	semidirect
142. C₁₃×#95	C₂³	semidirect
143. #35050	C₁₃	direct (N × H)
164. C₂⁴×C₁₃	#41	semidirect
239. C₂×#525	C₂×C₁₃	semidirect
240. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
241. #2849	C₂×C₁₃	semidirect
242. #2846	C₂×C₁₃	semidirect
243. #2626	C₂×C₁₃	semidirect
244. #2617	C₂×C₁₃	semidirect
245. #2561	C₂×C₁₃	semidirect
246. #2539	C₂×C₁₃	semidirect
247. #2534	C₂×C₁₃	semidirect
248. #2482	C₂×C₁₃	semidirect
249. #2411	C₂×C₁₃	semidirect
250. #2404	C₂×C₁₃	semidirect
251. #2321	C₂×C₁₃	semidirect
252. #2280	C₂×C₁₃	semidirect
329. C₂²×#41	C₂²×C₁₃	semidirect
333. C₂×#123	C₂²×C₁₃	semidirect
334. C₂×#123	C₂²×C₁₃	semidirect
335. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
336. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
337. C₂×#121	C₂²×C₁₃	semidirect
338. C₂×#121	C₂²×C₁₃	semidirect
343. C₂×C₄×D₄	C₂²×C₁₃	semidirect
344. C₂×C₄×D₄	C₂²×C₁₃	semidirect
345. C₂×#117	C₂²×C₁₃	semidirect
346. C₂×#117	C₂²×C₁₃	semidirect
354. #399	C₂²×C₁₃	semidirect
355. #397	C₂²×C₁₃	semidirect
356. #396	C₂²×C₁₃	semidirect
357. #394	C₂²×C₁₃	semidirect
358. #393	C₂²×C₁₃	semidirect
359. #392	C₂²×C₁₃	semidirect
360. #390	C₂²×C₁₃	semidirect
361. #388	C₂²×C₁₃	semidirect
362. #388	C₂²×C₁₃	semidirect
363. #386	C₂²×C₁₃	semidirect
364. #386	C₂²×C₁₃	semidirect
365. #386	C₂²×C₁₃	semidirect
366. #385	C₂²×C₁₃	semidirect
367. #385	C₂²×C₁₃	semidirect
368. #381	C₂²×C₁₃	semidirect
369. #381	C₂²×C₁₃	semidirect
370. #380	C₂²×C₁₃	semidirect
371. #380	C₂²×C₁₃	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
377. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
426. C₂²×Q₈	C₂³×C₁₃	semidirect
431. C₂²×D₄	C₂³×C₁₃	semidirect
435. C₂³×C₄	D₄×C₁₃	semidirect
445. C₂³×C₄	C₂³×C₁₃	semidirect
460. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
461. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
462. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
463. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
464. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
465. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
485. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
486. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
487. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
488. C₂×C₄²	C₂³×C₁₃	semidirect
489. C₂×C₄²	C₂³×C₁₃	semidirect
490. #95	C₂³×C₁₃	semidirect
491. #95	C₂³×C₁₃	semidirect
492. #95	C₂³×C₁₃	semidirect
493. #95	C₂³×C₁₃	semidirect
523. C₂⁴	C₁₃×#41	semidirect
598. C₁₃	#35050	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×#525	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2849	2
C₁₃×#2846	2
C₁₃×#2626	2
C₁₃×#2617	2
C₁₃×#2561	2
C₁₃×#2539	2
C₁₃×#2534	2
C₁₃×#2482	2
C₁₃×#2411	2
C₁₃×#2404	2
C₁₃×#2321	2
C₁₃×#2280	2
#35050	13

Subgroups — C13×#35050 #15721389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35050 #15721389