Subgroups — C₁₃×#34742 #15721081

Order 3328.

2738 conjugacy classes of subgroups.

The subgroup lattice has 728 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
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2423	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2422	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2421	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2420	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2419	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2418	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#525	—	2	8	no	—
19	C₂×C₁₃×#123	C₂²	1	4	yes	—
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#120	C₂²	1	2	yes	—
24	C₄×C₁₃×#41	—	2	8	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#400	C₂²	1	4	yes	complemented
38	C₁₃×#399	C₂²	1	4	yes	—
39	C₁₃×#398	C₂²	1	4	yes	complemented
40	C₁₃×#397	C₂²	1	4	yes	—
41	C₁₃×#397	C₂²	1	4	yes	complemented
42	C₁₃×#397	C₂²	1	4	yes	complemented
43	C₁₃×#394	C₂²	1	4	yes	—
44	C₁₃×#394	C₂²	1	4	yes	—
45	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#389	C₂²	1	2	yes	complemented
50	C₁₃×#389	C₂²	1	2	yes	complemented
51	C₁₃×#388	C₂²	1	4	yes	—
52	C₁₃×#388	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	4	yes	complemented
54	C₁₃×#387	C₂²	1	4	yes	complemented
55	C₁₃×#386	C₂²	1	4	yes	—
56	C₁₃×#386	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#385	C₂²	1	4	yes	complemented
59	C₁₃×#384	C₂²	1	2	yes	complemented
60	C₁₃×#382	C₂²	1	2	yes	complemented
61	C₁₃×#381	C₂²	1	2	yes	—
62	C₁₃×#381	C₂²	1	4	yes	complemented
63	C₁₃×#380	C₂²	1	2	yes	—
64	C₁₃×#380	C₂²	1	2	yes	—
65	C₁₃×#380	C₂²	1	4	yes	—
66	C₁₃×#379	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
76	C₂×C₁₃×#95	C₂²	1	2	yes	—
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×#41	—	2	4	no	—
79	C₂×C₁₃×#41	—	2	4	no	—
80	C₂×C₁₃×#41	D₄	1	8	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#123	—	2	8	no	—
97	C₁₃×#123	—	2	16	no	—
98	C₁₃×C₂²⋊Q₈	—	2	8	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#120	—	2	8	no	—
101	C₄×Q₈×C₁₃	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	16	no	—
103	C₄×D₄×C₁₃	—	2	8	no	—
104	C₄×D₄×C₁₃	—	2	16	no	—
105	C₁₃×#117	—	2	4	no	—
106	C₁₃×#117	—	2	4	no	—
107	C₁₃×#117	—	2	8	no	—
108	C₁₃×#117	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
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	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	2	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	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	—	2	4	no	—
135	C₂×C₄²×C₁₃	—	2	8	no	—
136	C₂×C₄²×C₁₃	—	2	4	no	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	#34742	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂⁴×C₁₃	—	2	4	no	—
161	C₂⁴×C₁₃	—	2	2	no	—
162	C₂⁴×C₁₃	—	2	2	no	—
163	C₂⁴×C₁₃	—	2	2	no	—
164	C₂⁴×C₁₃	—	4	2	no	—
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×#41	—	2	32	no	—
169	C₂×Q₈×C₁₃	—	2	2	no	—
170	C₂×Q₈×C₁₃	—	2	2	no	—
171	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	8	no	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	2	no	—
178	C₂×D₄×C₁₃	—	4	4	no	—
179	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
180	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	8	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	8	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	4	2	no	—
199	C₂²×C₄×C₁₃	—	4	4	no	—
200	C₂²×C₄×C₁₃	—	4	2	no	—
201	C₂²×C₄×C₁₃	—	4	16	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃	#41	1	4	yes	—
205	C₂²×C₄×C₁₃	#41	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	2	4	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	8	no	—
225	C₁₃×C₄⋊C₄	—	2	8	no	—
226	C₁₃×C₄⋊C₄	—	4	4	no	—
227	C₁₃×C₄⋊C₄	—	4	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	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	—	2	8	no	—
235	C₁₃×C₂²⋊C₄	—	2	8	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	8	no	—
239	C₁₃×C₂²⋊C₄	—	4	4	no	—
240	C₁₃×C₂²⋊C₄	—	4	4	no	—
241	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	2	no	—
244	C₄²×C₁₃	—	2	4	no	—
245	C₄²×C₁₃	—	2	8	no	—
246	C₄²×C₁₃	—	2	4	no	—
247	C₄²×C₁₃	—	2	4	no	—
248	C₄²×C₁₃	—	2	2	no	—
249	C₄²×C₁₃	—	2	4	no	—
250	C₄²×C₁₃	—	2	2	no	—
251	C₄²×C₁₃	—	2	4	no	—
252	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
253	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2423	C₂×C₁₃	1	2	yes	complemented
255	#2422	C₂×C₁₃	1	2	yes	complemented
256	#2421	C₂×C₁₃	1	2	yes	complemented
257	#2420	C₂×C₁₃	1	2	yes	complemented
258	#2419	C₂×C₁₃	1	4	yes	complemented
259	#2418	C₂×C₁₃	1	4	yes	complemented
260	#2395	C₂×C₁₃	1	4	yes	complemented
261	C₄×#123	C₂×C₁₃	1	4	yes	complemented
262	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	8	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	2	4	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	2	2	no	—
277	C₂³×C₁₃	—	2	2	no	—
278	C₂³×C₁₃	—	2	4	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	4	8	no	—
281	C₂³×C₁₃	—	4	8	no	—
282	C₂³×C₁₃	—	4	4	no	—
283	C₂³×C₁₃	—	4	4	no	—
284	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
285	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₃	C₂×#41	1	4	yes	—
287	C₂³×C₁₃	C₂×#41	1	2	yes	—
288	C₂³×C₁₃	C₂×#41	1	2	yes	—
289	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
290	Q₈×C₁₃	—	2	8	no	—
291	D₄×C₁₃	—	2	16	no	—
292	D₄×C₁₃	—	2	8	no	—
293	D₄×C₁₃	—	4	16	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	16	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	4	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	2	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	4	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	4	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	4	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	4	8	no	—
321	C₂×C₄×C₁₃	—	4	16	no	—
322	C₂×C₄×C₁₃	—	4	8	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	4	8	no	—
325	C₂×C₄×C₁₃	—	4	8	no	—
326	C₂×C₄×C₁₃	#123	1	16	yes	complemented
327	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
331	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
332	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
334	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
335	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
336	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
338	#525	—	2	8	no	—
339	C₂×#123	C₂²×C₁₃	1	2	yes	—
340	C₂×#123	C₂²×C₁₃	1	4	yes	—
341	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
342	C₂×#121	C₂²×C₁₃	1	2	yes	—
343	C₂×#120	C₂²×C₁₃	1	2	yes	—
344	C₄×#41	—	2	8	no	—
345	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
346	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
347	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
348	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
349	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
353	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
354	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
355	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
357	#400	C₂²×C₁₃	1	4	yes	complemented
358	#399	C₂²×C₁₃	1	4	yes	—
359	#398	C₂²×C₁₃	1	4	yes	complemented
360	#397	C₂²×C₁₃	1	4	yes	—
361	#397	C₂²×C₁₃	1	4	yes	complemented
362	#397	C₂²×C₁₃	1	4	yes	complemented
363	#394	C₂²×C₁₃	1	4	yes	—
364	#394	C₂²×C₁₃	1	4	yes	—
365	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
366	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
368	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
369	#389	C₂²×C₁₃	1	2	yes	complemented
370	#389	C₂²×C₁₃	1	2	yes	complemented
371	#388	C₂²×C₁₃	1	4	yes	—
372	#388	C₂²×C₁₃	1	4	yes	—
373	#387	C₂²×C₁₃	1	4	yes	complemented
374	#387	C₂²×C₁₃	1	4	yes	complemented
375	#386	C₂²×C₁₃	1	4	yes	—
376	#386	C₂²×C₁₃	1	4	yes	—
377	#385	C₂²×C₁₃	1	4	yes	—
378	#385	C₂²×C₁₃	1	4	yes	complemented
379	#384	C₂²×C₁₃	1	2	yes	complemented
380	#382	C₂²×C₁₃	1	2	yes	complemented
381	#381	C₂²×C₁₃	1	2	yes	—
382	#381	C₂²×C₁₃	1	4	yes	complemented
383	#380	C₂²×C₁₃	1	4	yes	—
384	#380	C₂²×C₁₃	1	2	yes	—
385	#380	C₂²×C₁₃	1	2	yes	—
386	#379	C₂²×C₁₃	1	2	yes	—
387	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
388	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
389	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
390	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
392	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
396	C₂×#95	C₂²×C₁₃	1	2	yes	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	4	no	—
402	C₂²×C₁₃	—	2	4	no	—
403	C₂²×C₁₃	—	2	8	no	—
404	C₂²×C₁₃	—	2	4	no	—
405	C₂²×C₁₃	—	2	4	no	—
406	C₂²×C₁₃	—	4	16	no	—
407	C₂²×C₁₃	—	4	2	no	—
408	C₂²×C₁₃	—	4	2	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	4	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	C₂×#123	1	4	yes	—
415	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
416	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
418	C₂²×C₁₃	C₂²×#41	1	2	yes	—
419	C₂²×C₁₃	#585	1	2	yes	—
420	C₄×C₁₃	—	2	4	no	—
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	2	4	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	4	no	—
428	C₄×C₁₃	—	4	4	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	C₂×#123	1	4	yes	—
431	C₄×C₁₃	C₂×#123	1	4	yes	—
432	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×#41	—	2	4	no	—
434	C₂×#41	—	2	4	no	—
435	C₂×#41	D₄×C₁₃	1	8	yes	—
436	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
438	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
439	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	—	2	4	no	—
441	C₂³×C₄	—	2	4	no	—
442	C₂³×C₄	—	2	4	no	—
443	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
448	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
449	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
450	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
451	#123	—	2	8	no	—
452	#123	—	2	16	no	—
453	C₂²⋊Q₈	—	2	8	no	—
454	#121	—	2	8	no	—
455	#120	—	2	8	no	—
456	C₄×Q₈	—	2	8	no	—
457	C₄×D₄	—	2	16	no	—
458	C₄×D₄	—	2	8	no	—
459	C₄×D₄	—	2	16	no	—
460	#117	—	2	4	no	—
461	#117	—	2	4	no	—
462	#117	—	2	8	no	—
463	#117	—	2	4	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
474	C₂×C₂²⋊C₄	—	2	8	no	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄²	—	2	4	no	—
490	C₂×C₄²	—	2	8	no	—
491	C₂×C₄²	—	2	4	no	—
492	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
497	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
502	#95	C₂³×C₁₃	1	2	yes	—
503	#95	C₂³×C₁₃	1	2	yes	—
504	#95	C₂³×C₁₃	1	2	yes	—
505	#95	C₂³×C₁₃	1	2	yes	—
506	#95	C₂³×C₁₃	1	4	yes	—
507	#95	C₂³×C₁₃	1	4	yes	—
508	#95	C₂³×C₁₃	1	4	yes	—
509	#95	C₂³×C₁₃	1	4	yes	—
510	#95	C₂³×C₁₃	1	4	yes	—
511	#95	C₂³×C₁₃	1	4	yes	—
512	#95	C₂³×C₁₃	1	4	yes	—
513	#95	C₂³×C₁₃	1	4	yes	—
514	C₂×C₁₃	—	2	4	no	—
515	C₂×C₁₃	—	4	4	no	—
516	C₂×C₁₃	—	4	4	no	—
517	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
518	C₂×C₁₃	#3444	1	1	yes	characteristic
519	C₂×C₁₃	#3455	1	1	yes	characteristic
520	C₂×C₁₃	D₄×#41	1	2	yes	—
521	C₂×C₁₃	#3475	1	2	yes	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	4	2	no	—
527	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
528	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
529	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
530	#41	—	2	32	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	8	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
542	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	8	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	8	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	16	no	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
566	C₂²×C₄	C₁₃×#41	1	4	yes	—
567	C₂²×C₄	C₁₃×#41	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	8	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	8	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	4	no	—
614	C₁₃	#34742	1	1	yes	characteristic, direct product factor, Sylow
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	8	no	—
630	C₂³	—	4	4	no	—
631	C₂³	—	4	4	no	—
632	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
633	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
634	C₂³	C₂×C₁₃×#41	1	4	yes	—
635	C₂³	C₂×C₁₃×#41	1	2	yes	—
636	C₂³	C₂×C₁₃×#41	1	2	yes	—
637	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
638	Q₈	—	2	8	no	—
639	D₄	—	2	16	no	—
640	D₄	—	2	8	no	—
641	D₄	—	4	16	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	16	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	16	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	8	no	—
673	C₂×C₄	—	4	8	no	—
674	C₂×C₄	C₁₃×#123	1	16	yes	complemented
675	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
678	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
679	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
680	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
681	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
682	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
683	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	8	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	4	16	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	2	no	—
701	C₂²	C₂×C₁₃×#123	1	4	yes	—
702	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
703	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
704	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
705	C₂²	C₂²×C₁₃×#41	1	2	yes	—
706	C₂²	C₁₃×#585	1	2	yes	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	4	no	—
716	C₄	—	4	2	no	—
717	C₄	C₂×C₁₃×#123	1	4	yes	—
718	C₄	C₂×C₁₃×#123	1	4	yes	—
719	C₂	—	2	4	no	—
720	C₂	—	4	4	no	—
721	C₂	—	4	4	no	—
722	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
723	C₂	C₁₃×#3444	1	1	yes	characteristic
724	C₂	C₁₃×#3455	1	1	yes	characteristic
725	C₂	D₄×C₁₃×#41	1	2	yes	—
726	C₂	C₁₃×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2423	C₂	semidirect
4. C₁₃×#2422	C₂	semidirect
5. C₁₃×#2421	C₂	semidirect
6. C₁₃×#2420	C₂	semidirect
7. C₁₃×#2419	C₂	semidirect
8. C₁₃×#2418	C₂	semidirect
9. C₁₃×#2395	C₂	semidirect
10. C₄×C₁₃×#123	C₂	semidirect
11. C₁₃×#2297	C₂	semidirect
12. C₁₃×#2296	C₂	semidirect
13. C₁₃×#2285	C₂	semidirect
14. C₁₃×#2280	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×C₁₃×#117	C₂²	semidirect
36. C₂²×C₄²×C₁₃	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
41. C₁₃×#397	C₂²	semidirect
42. C₁₃×#397	C₂²	semidirect
45. C₁₃×#391	C₂²	semidirect
46. C₁₃×#391	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#390	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
53. C₁₃×#387	C₂²	semidirect
54. C₁₃×#387	C₂²	semidirect
58. C₁₃×#385	C₂²	semidirect
59. C₁₃×#384	C₂²	semidirect
60. C₁₃×#382	C₂²	semidirect
62. C₁₃×#381	C₂²	semidirect
67. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
68. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
69. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
75. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
159. #34742	C₁₃	direct (N × H)
241. C₁₃×C₂²⋊C₄	#41	semidirect
253. C₂×C₄×#41	C₂×C₁₃	semidirect
254. #2423	C₂×C₁₃	semidirect
255. #2422	C₂×C₁₃	semidirect
256. #2421	C₂×C₁₃	semidirect
257. #2420	C₂×C₁₃	semidirect
258. #2419	C₂×C₁₃	semidirect
259. #2418	C₂×C₁₃	semidirect
260. #2395	C₂×C₁₃	semidirect
261. C₄×#123	C₂×C₁₃	semidirect
262. #2297	C₂×C₁₃	semidirect
263. #2296	C₂×C₁₃	semidirect
264. #2285	C₂×C₁₃	semidirect
265. #2280	C₂×C₁₃	semidirect
266. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
326. C₂×C₄×C₁₃	#123	semidirect
345. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
348. C₂×C₄×D₄	C₂²×C₁₃	semidirect
352. C₂×#117	C₂²×C₁₃	semidirect
356. C₂²×C₄²	C₂²×C₁₃	semidirect
357. #400	C₂²×C₁₃	semidirect
359. #398	C₂²×C₁₃	semidirect
361. #397	C₂²×C₁₃	semidirect
362. #397	C₂²×C₁₃	semidirect
365. #391	C₂²×C₁₃	semidirect
366. #391	C₂²×C₁₃	semidirect
367. #390	C₂²×C₁₃	semidirect
368. #390	C₂²×C₁₃	semidirect
369. #389	C₂²×C₁₃	semidirect
370. #389	C₂²×C₁₃	semidirect
373. #387	C₂²×C₁₃	semidirect
374. #387	C₂²×C₁₃	semidirect
378. #385	C₂²×C₁₃	semidirect
379. #384	C₂²×C₁₃	semidirect
380. #382	C₂²×C₁₃	semidirect
382. #381	C₂²×C₁₃	semidirect
387. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
388. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
389. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
395. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
603. C₂²⋊C₄	C₁₃×#41	semidirect
614. C₁₃	#34742	direct (N × H)
674. C₂×C₄	C₁₃×#123	semidirect

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
C₂×C₄×C₁₃×#41	2
C₁₃×#2423	2
C₁₃×#2422	2
C₁₃×#2421	2
C₁₃×#2420	2
C₁₃×#2419	2
C₁₃×#2418	2
C₁₃×#2395	2
C₄×C₁₃×#123	2
C₁₃×#2297	2
C₁₃×#2296	2
C₁₃×#2285	2
C₁₃×#2280	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34742	13

Subgroups — C13×#34742 #15721081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34742 #15721081