Subgroups — C₁₃×#34198 #15720537

Order 3328.

4982 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2358	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2342	C₂	1	4	yes	maximal, complemented
6	D₄×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2321	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2273	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
17	C₂×C₁₃×#120	C₄	1	16	yes	complemented
18	C₂×C₁₃×#120	C₂²	1	2	yes	—
19	C₂×C₁₃×#120	C₂²	1	2	yes	—
20	C₂×C₁₃×#120	C₂²	1	4	yes	—
21	C₁₃×#518	—	2	8	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
25	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
38	C₁₃×#390	C₂²	1	8	yes	complemented
39	C₁₃×#388	C₂²	1	8	yes	complemented
40	C₁₃×#388	C₂²	1	8	yes	complemented
41	C₁₃×#386	C₂²	1	8	yes	complemented
42	C₁₃×#386	C₂²	1	4	yes	complemented
43	C₁₃×#386	C₂²	1	8	yes	complemented
44	C₁₃×#386	C₂²	1	4	yes	complemented
45	C₁₃×#385	C₂²	1	4	yes	complemented
46	C₁₃×#385	C₂²	1	8	yes	complemented
47	C₁₃×#385	C₂²	1	4	yes	complemented
48	C₁₃×#381	C₂²	1	2	yes	complemented
49	C₁₃×#380	C₂²	1	4	yes	complemented
50	C₁₃×#379	C₂²	1	4	yes	—
51	C₁₃×#379	C₂²	1	2	yes	complemented
52	C₁₃×#379	C₂²	1	2	yes	complemented
53	C₁₃×#379	C₂²	1	2	yes	complemented
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
58	C₂⁵×C₁₃	—	2	4	no	—
59	C₂⁵×C₁₃	—	2	4	no	—
60	C₂⁵×C₁₃	—	4	8	no	—
61	C₂⁵×C₁₃	C₂×C₄	1	8	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂⁵×C₁₃	C₂³	1	2	yes	—
64	C₂⁵×C₁₃	C₂³	1	2	yes	—
65	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
66	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
67	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	—	2	4	no	—
70	C₂²×D₄×C₁₃	—	4	8	no	—
71	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
72	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	—	2	8	no	—
78	C₂³×C₄×C₁₃	—	4	8	no	—
79	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
87	C₁₃×#120	C₂×C₄	1	16	yes	complemented
88	C₁₃×#120	C₂×C₄	1	32	yes	complemented
89	C₁₃×#120	C₂×C₄	1	16	yes	complemented
90	C₄×D₄×C₁₃	—	2	16	no	—
91	C₄×D₄×C₁₃	—	2	16	no	—
92	C₄×D₄×C₁₃	—	4	16	no	—
93	C₁₃×#117	—	2	8	no	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
96	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
104	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
106	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
125	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
126	C₁₃×#95	C₂³	1	8	yes	complemented
127	C₁₃×#95	C₂³	1	8	yes	complemented
128	C₁₃×#95	C₂³	1	8	yes	complemented
129	#34198	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	8	no	—
133	C₂⁴×C₁₃	—	2	32	no	—
134	C₂⁴×C₁₃	—	2	4	no	—
135	C₂⁴×C₁₃	—	2	4	no	—
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	—	2	4	no	—
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	2	2	no	—
140	C₂⁴×C₁₃	—	2	8	no	—
141	C₂⁴×C₁₃	—	2	8	no	—
142	C₂⁴×C₁₃	—	2	2	no	—
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₂⁴×C₁₃	—	4	32	no	—
145	C₂⁴×C₁₃	—	4	4	no	—
146	C₂⁴×C₁₃	—	4	4	no	—
147	C₂⁴×C₁₃	—	4	4	no	—
148	C₂⁴×C₁₃	—	4	4	no	—
149	C₂⁴×C₁₃	—	4	4	no	—
150	C₂⁴×C₁₃	—	4	32	no	—
151	C₂⁴×C₁₃	—	4	32	no	—
152	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
154	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
155	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
156	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
157	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	complemented
158	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
159	C₂⁴×C₁₃	#41	1	4	yes	—
160	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
161	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
162	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂×D₄×C₁₃	—	2	32	no	—
167	C₂×D₄×C₁₃	—	2	4	no	—
168	C₂×D₄×C₁₃	—	2	4	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	16	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	32	no	—
174	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
176	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	complemented
177	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	complemented
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	16	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	16	no	—
185	C₂²×C₄×C₁₃	—	2	8	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	—	4	8	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	—	4	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	—	4	4	no	—
192	C₂²×C₄×C₁₃	—	4	8	no	—
193	C₂²×C₄×C₁₃	—	4	32	no	—
194	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	complemented
195	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
196	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
197	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
203	C₁₃×C₄⋊C₄	—	2	8	no	—
204	C₁₃×C₄⋊C₄	—	4	8	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	16	no	—
212	C₁₃×C₂²⋊C₄	—	2	16	no	—
213	C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₁₃×C₂²⋊C₄	—	4	8	no	—
215	C₁₃×C₂²⋊C₄	—	4	8	no	—
216	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
217	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
218	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
219	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
220	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
221	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
222	C₄²×C₁₃	—	2	8	no	—
223	C₄²×C₁₃	—	4	8	no	—
224	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic
225	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2358	C₂×C₁₃	1	8	yes	complemented
228	#2342	C₂×C₁₃	1	4	yes	complemented
229	D₄×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
230	#2321	C₂×C₁₃	1	4	yes	complemented
231	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2308	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₄×#120	C₂×C₁₃	1	4	yes	complemented
234	C₂×#379	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2273	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	16	no	—
237	C₂³×C₁₃	—	2	16	no	—
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	16	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	4	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	2	4	no	—
246	C₂³×C₁₃	—	2	16	no	—
247	C₂³×C₁₃	—	2	16	no	—
248	C₂³×C₁₃	—	2	8	no	—
249	C₂³×C₁₃	—	2	16	no	—
250	C₂³×C₁₃	—	2	16	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	4	no	—
256	C₂³×C₁₃	—	2	8	no	—
257	C₂³×C₁₃	—	2	4	no	—
258	C₂³×C₁₃	—	2	8	no	—
259	C₂³×C₁₃	—	4	8	no	—
260	C₂³×C₁₃	—	4	8	no	—
261	C₂³×C₁₃	—	4	8	no	—
262	C₂³×C₁₃	—	4	8	no	—
263	C₂³×C₁₃	—	4	8	no	—
264	C₂³×C₁₃	—	4	8	no	—
265	C₂³×C₁₃	—	4	8	no	—
266	C₂³×C₁₃	—	4	16	no	—
267	C₂³×C₁₃	—	4	16	no	—
268	C₂³×C₁₃	—	4	16	no	—
269	C₂³×C₁₃	—	4	16	no	—
270	C₂³×C₁₃	—	4	128	no	—
271	C₂³×C₁₃	—	4	8	no	—
272	C₂³×C₁₃	—	4	8	no	—
273	C₂³×C₁₃	—	8	4	no	—
274	C₂³×C₁₃	—	8	4	no	—
275	C₂³×C₁₃	C₄×D₄	1	16	yes	complemented
276	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
277	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
278	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
279	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
280	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂³×C₁₃	C₂×#41	1	2	yes	—
286	C₂³×C₁₃	C₂×#41	1	2	yes	—
287	C₂³×C₁₃	C₂×#41	1	2	yes	—
288	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
289	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
290	D₄×C₁₃	—	2	16	no	—
291	D₄×C₁₃	—	2	16	no	—
292	D₄×C₁₃	—	2	32	no	—
293	D₄×C₁₃	—	4	16	no	—
294	C₂×C₄×C₁₃	—	2	8	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	8	no	—
298	C₂×C₄×C₁₃	—	2	8	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	8	no	—
303	C₂×C₄×C₁₃	—	2	8	no	—
304	C₂×C₄×C₁₃	—	2	8	no	—
305	C₂×C₄×C₁₃	—	4	8	no	—
306	C₂×C₄×C₁₃	—	4	8	no	—
307	C₂×C₄×C₁₃	—	4	32	no	—
308	C₂×C₄×C₁₃	—	4	8	no	—
309	C₂×C₄×C₁₃	—	8	8	no	—
310	C₂×C₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	—	8	4	no	—
312	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
313	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
314	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
315	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
316	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
318	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
319	C₂×#120	C₄×C₁₃	1	16	yes	complemented
320	C₂×#120	C₂²×C₁₃	1	2	yes	—
321	C₂×#120	C₂²×C₁₃	1	4	yes	—
322	C₂×#120	C₂²×C₁₃	1	2	yes	—
323	#518	—	2	8	no	—
324	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
325	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
326	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
327	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
328	C₂²×C₂²⋊C₄	—	2	8	no	—
329	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
333	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
335	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
337	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
338	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
339	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
340	#390	C₂²×C₁₃	1	8	yes	complemented
341	#388	C₂²×C₁₃	1	8	yes	complemented
342	#388	C₂²×C₁₃	1	8	yes	complemented
343	#386	C₂²×C₁₃	1	8	yes	complemented
344	#386	C₂²×C₁₃	1	4	yes	complemented
345	#386	C₂²×C₁₃	1	4	yes	complemented
346	#386	C₂²×C₁₃	1	8	yes	complemented
347	#385	C₂²×C₁₃	1	4	yes	complemented
348	#385	C₂²×C₁₃	1	4	yes	complemented
349	#385	C₂²×C₁₃	1	8	yes	complemented
350	#381	C₂²×C₁₃	1	2	yes	complemented
351	#380	C₂²×C₁₃	1	4	yes	complemented
352	#379	C₂²×C₁₃	1	4	yes	—
353	#379	C₂²×C₁₃	1	2	yes	complemented
354	#379	C₂²×C₁₃	1	2	yes	complemented
355	#379	C₂²×C₁₃	1	2	yes	complemented
356	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
357	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
358	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
359	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
360	C₂²×C₁₃	—	2	32	no	—
361	C₂²×C₁₃	—	2	4	no	—
362	C₂²×C₁₃	—	2	4	no	—
363	C₂²×C₁₃	—	2	4	no	—
364	C₂²×C₁₃	—	2	4	no	—
365	C₂²×C₁₃	—	2	4	no	—
366	C₂²×C₁₃	—	2	4	no	—
367	C₂²×C₁₃	—	2	8	no	—
368	C₂²×C₁₃	—	2	4	no	—
369	C₂²×C₁₃	—	2	4	no	—
370	C₂²×C₁₃	—	2	4	no	—
371	C₂²×C₁₃	—	2	4	no	—
372	C₂²×C₁₃	—	2	8	no	—
373	C₂²×C₁₃	—	2	4	no	—
374	C₂²×C₁₃	—	2	4	no	—
375	C₂²×C₁₃	—	2	4	no	—
376	C₂²×C₁₃	—	2	8	no	—
377	C₂²×C₁₃	—	2	4	no	—
378	C₂²×C₁₃	—	2	4	no	—
379	C₂²×C₁₃	—	4	16	no	—
380	C₂²×C₁₃	—	4	32	no	—
381	C₂²×C₁₃	—	4	32	no	—
382	C₂²×C₁₃	—	4	16	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	—	4	4	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	—	8	8	no	—
388	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
389	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
390	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
391	C₂²×C₁₃	#518	1	8	yes	complemented
392	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
393	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
394	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
396	C₄×C₁₃	—	2	4	no	—
397	C₄×C₁₃	—	2	8	no	—
398	C₄×C₁₃	—	2	8	no	—
399	C₄×C₁₃	—	4	4	no	—
400	C₄×C₁₃	—	4	4	no	—
401	C₄×C₁₃	—	4	4	no	—
402	C₂⁵	—	2	4	no	—
403	C₂⁵	—	2	4	no	—
404	C₂⁵	—	4	8	no	—
405	C₂⁵	C₂×C₄×C₁₃	1	8	yes	complemented
406	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
407	C₂⁵	C₂³×C₁₃	1	2	yes	—
408	C₂⁵	C₂³×C₁₃	1	2	yes	—
409	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
410	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
411	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	—	2	4	no	—
413	C₂²×D₄	—	2	4	no	—
414	C₂²×D₄	—	4	8	no	—
415	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
416	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
417	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
418	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
419	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
420	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
421	C₂³×C₄	—	2	8	no	—
422	C₂³×C₄	—	4	8	no	—
423	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
424	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
426	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
427	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
428	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
430	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
431	#120	C₂×C₄×C₁₃	1	16	yes	complemented
432	#120	C₂×C₄×C₁₃	1	32	yes	complemented
433	#120	C₂×C₄×C₁₃	1	16	yes	complemented
434	C₄×D₄	—	2	16	no	—
435	C₄×D₄	—	2	16	no	—
436	C₄×D₄	—	4	16	no	—
437	#117	—	2	8	no	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
440	C₂×C₂²⋊C₄	—	2	4	no	—
441	C₂×C₂²⋊C₄	—	2	4	no	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₂²⋊C₄	—	2	8	no	—
444	C₂×C₂²⋊C₄	—	2	16	no	—
445	C₂×C₂²⋊C₄	—	2	8	no	—
446	C₂×C₂²⋊C₄	—	2	16	no	—
447	C₂×C₂²⋊C₄	—	4	8	no	—
448	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
449	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
450	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
451	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
467	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
468	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
469	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
470	#95	C₂³×C₁₃	1	8	yes	complemented
471	#95	C₂³×C₁₃	1	8	yes	complemented
472	#95	C₂³×C₁₃	1	8	yes	complemented
473	C₂×C₁₃	—	2	4	no	—
474	C₂×C₁₃	—	2	8	no	—
475	C₂×C₁₃	—	2	4	no	—
476	C₂×C₁₃	—	2	4	no	—
477	C₂×C₁₃	—	4	4	no	—
478	C₂×C₁₃	—	4	4	no	—
479	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
480	C₂×C₁₃	C₂×#518	1	2	yes	—
481	C₂×C₁₃	#3484	1	2	yes	—
482	C₂×C₁₃	#3490	1	2	yes	—
483	C₂⁴	—	2	2	no	—
484	C₂⁴	—	2	2	no	—
485	C₂⁴	—	2	8	no	—
486	C₂⁴	—	2	32	no	—
487	C₂⁴	—	2	4	no	—
488	C₂⁴	—	2	4	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	2	4	no	—
491	C₂⁴	—	2	4	no	—
492	C₂⁴	—	2	2	no	—
493	C₂⁴	—	2	8	no	—
494	C₂⁴	—	2	8	no	—
495	C₂⁴	—	2	2	no	—
496	C₂⁴	—	2	2	no	—
497	C₂⁴	—	4	32	no	—
498	C₂⁴	—	4	4	no	—
499	C₂⁴	—	4	4	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	—	4	4	no	—
502	C₂⁴	—	4	4	no	—
503	C₂⁴	—	4	32	no	—
504	C₂⁴	—	4	32	no	—
505	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
506	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
507	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
508	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
509	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
510	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	complemented
511	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
512	C₂⁴	C₁₃×#41	1	4	yes	—
513	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
514	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
515	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
519	C₂×D₄	—	2	32	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	16	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	—	4	32	no	—
527	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
528	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
529	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	complemented
530	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	complemented
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	16	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	16	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	8	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	8	no	—
546	C₂²×C₄	—	4	32	no	—
547	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	complemented
548	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
549	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	complemented
550	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	4	8	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	16	no	—
565	C₂²⋊C₄	—	2	16	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	4	8	no	—
568	C₂²⋊C₄	—	4	8	no	—
569	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
572	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
573	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
574	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	complemented
575	C₄²	—	2	8	no	—
576	C₄²	—	4	8	no	—
577	C₁₃	#34198	1	1	yes	characteristic, direct product factor, Sylow
578	C₂³	—	2	16	no	—
579	C₂³	—	2	16	no	—
580	C₂³	—	2	8	no	—
581	C₂³	—	2	16	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	16	no	—
589	C₂³	—	2	16	no	—
590	C₂³	—	2	8	no	—
591	C₂³	—	2	16	no	—
592	C₂³	—	2	16	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	8	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	8	no	—
605	C₂³	—	4	8	no	—
606	C₂³	—	4	8	no	—
607	C₂³	—	4	8	no	—
608	C₂³	—	4	16	no	—
609	C₂³	—	4	16	no	—
610	C₂³	—	4	16	no	—
611	C₂³	—	4	16	no	—
612	C₂³	—	4	128	no	—
613	C₂³	—	4	8	no	—
614	C₂³	—	4	8	no	—
615	C₂³	—	8	4	no	—
616	C₂³	—	8	4	no	—
617	C₂³	C₄×D₄×C₁₃	1	16	yes	complemented
618	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
619	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
620	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
621	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
622	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
623	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
624	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
625	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
627	C₂³	C₂×C₁₃×#41	1	2	yes	—
628	C₂³	C₂×C₁₃×#41	1	2	yes	—
629	C₂³	C₂×C₁₃×#41	1	2	yes	—
630	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
631	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
632	D₄	—	2	16	no	—
633	D₄	—	2	16	no	—
634	D₄	—	2	32	no	—
635	D₄	—	4	16	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	8	no	—
640	C₂×C₄	—	2	8	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	8	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	32	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
657	C₂²	—	2	32	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	8	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	8	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	8	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	4	16	no	—
677	C₂²	—	4	32	no	—
678	C₂²	—	4	32	no	—
679	C₂²	—	4	16	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	8	8	no	—
685	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
686	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
687	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
688	C₂²	C₁₃×#518	1	8	yes	complemented
689	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
690	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
691	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
692	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
693	C₄	—	2	4	no	—
694	C₄	—	2	8	no	—
695	C₄	—	2	8	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	4	no	—
698	C₄	—	4	4	no	—
699	C₂	—	2	4	no	—
700	C₂	—	2	8	no	—
701	C₂	—	2	4	no	—
702	C₂	—	2	4	no	—
703	C₂	—	4	4	no	—
704	C₂	—	4	4	no	—
705	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
706	C₂	C₂×C₁₃×#518	1	2	yes	—
707	C₂	C₁₃×#3484	1	2	yes	—
708	C₂	C₁₃×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#518	C₂	semidirect
3. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#2358	C₂	semidirect
5. C₁₃×#2342	C₂	semidirect
6. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#2321	C₂	semidirect
8. C₁₃×#2315	C₂	semidirect
9. C₁₃×#2308	C₂	semidirect
10. C₄×C₁₃×#120	C₂	semidirect
11. C₂×C₁₃×#379	C₂	semidirect
12. C₁₃×#2273	C₂	semidirect
16. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₂×C₁₃×#120	C₄	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₂×C₁₃×#117	C₂²	semidirect
34. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
35. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
36. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
37. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
38. C₁₃×#390	C₂²	semidirect
39. C₁₃×#388	C₂²	semidirect
40. C₁₃×#388	C₂²	semidirect
41. C₁₃×#386	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#385	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
47. C₁₃×#385	C₂²	semidirect
48. C₁₃×#381	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
51. C₁₃×#379	C₂²	semidirect
52. C₁₃×#379	C₂²	semidirect
53. C₁₃×#379	C₂²	semidirect
54. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
55. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
56. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
57. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
61. C₂⁵×C₁₃	C₂×C₄	semidirect
71. C₂²×D₄×C₁₃	C₂×C₄	semidirect
72. C₂²×D₄×C₁₃	C₂×C₄	semidirect
86. C₂³×C₄×C₁₃	C₂³	semidirect
87. C₁₃×#120	C₂×C₄	semidirect
88. C₁₃×#120	C₂×C₄	semidirect
89. C₁₃×#120	C₂×C₄	semidirect
94. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
95. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
104. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
105. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
106. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
122. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
123. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
124. C₂×C₄²×C₁₃	C₂³	semidirect
125. C₂×C₄²×C₁₃	C₂³	semidirect
126. C₁₃×#95	C₂³	semidirect
127. C₁₃×#95	C₂³	semidirect
128. C₁₃×#95	C₂³	semidirect
129. #34198	C₁₃	direct (N × H)
157. C₂⁴×C₁₃	C₂²×C₄	semidirect
176. C₂×D₄×C₁₃	C₂²×C₄	semidirect
177. C₂×D₄×C₁₃	C₂²×C₄	semidirect
194. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
195. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
196. C₂²×C₄×C₁₃	C₂×D₄	semidirect
218. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
219. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
221. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
225. C₂×#518	C₂×C₁₃	semidirect
226. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
227. #2358	C₂×C₁₃	semidirect
228. #2342	C₂×C₁₃	semidirect
229. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
230. #2321	C₂×C₁₃	semidirect
231. #2315	C₂×C₁₃	semidirect
232. #2308	C₂×C₁₃	semidirect
233. C₄×#120	C₂×C₁₃	semidirect
234. C₂×#379	C₂×C₁₃	semidirect
235. #2273	C₂×C₁₃	semidirect
275. C₂³×C₁₃	C₄×D₄	semidirect
318. C₂⁴×C₄	C₂²×C₁₃	semidirect
319. C₂×#120	C₄×C₁₃	semidirect
324. C₂×C₄×D₄	C₂²×C₁₃	semidirect
325. C₂×C₄×D₄	C₂²×C₁₃	semidirect
326. C₂×C₄×D₄	C₂²×C₁₃	semidirect
327. C₂×#117	C₂²×C₁₃	semidirect
336. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
337. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
338. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
339. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
340. #390	C₂²×C₁₃	semidirect
341. #388	C₂²×C₁₃	semidirect
342. #388	C₂²×C₁₃	semidirect
343. #386	C₂²×C₁₃	semidirect
344. #386	C₂²×C₁₃	semidirect
345. #386	C₂²×C₁₃	semidirect
346. #386	C₂²×C₁₃	semidirect
347. #385	C₂²×C₁₃	semidirect
348. #385	C₂²×C₁₃	semidirect
349. #385	C₂²×C₁₃	semidirect
350. #381	C₂²×C₁₃	semidirect
351. #380	C₂²×C₁₃	semidirect
353. #379	C₂²×C₁₃	semidirect
354. #379	C₂²×C₁₃	semidirect
355. #379	C₂²×C₁₃	semidirect
356. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
357. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
358. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
359. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
391. C₂²×C₁₃	#518	semidirect
405. C₂⁵	C₂×C₄×C₁₃	semidirect
415. C₂²×D₄	C₂×C₄×C₁₃	semidirect
416. C₂²×D₄	C₂×C₄×C₁₃	semidirect
430. C₂³×C₄	C₂³×C₁₃	semidirect
431. #120	C₂×C₄×C₁₃	semidirect
432. #120	C₂×C₄×C₁₃	semidirect
433. #120	C₂×C₄×C₁₃	semidirect
438. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
439. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
448. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
449. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
450. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
466. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
467. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
468. C₂×C₄²	C₂³×C₁₃	semidirect
469. C₂×C₄²	C₂³×C₁₃	semidirect
470. #95	C₂³×C₁₃	semidirect
471. #95	C₂³×C₁₃	semidirect
472. #95	C₂³×C₁₃	semidirect
510. C₂⁴	C₂²×C₄×C₁₃	semidirect
529. C₂×D₄	C₂²×C₄×C₁₃	semidirect
530. C₂×D₄	C₂²×C₄×C₁₃	semidirect
547. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
548. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
549. C₂²×C₄	C₂×D₄×C₁₃	semidirect
571. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
572. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
574. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
577. C₁₃	#34198	direct (N × H)
617. C₂³	C₄×D₄×C₁₃	semidirect
688. C₂²	C₁₃×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#120	2
C₂×C₁₃×#518	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2358	2
C₁₃×#2342	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2321	2
C₁₃×#2315	2
C₁₃×#2308	2
C₄×C₁₃×#120	2
C₂×C₁₃×#379	2
C₁₃×#2273	2
#34198	13

Subgroups — C13×#34198 #15720537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34198 #15720537