Subgroups — C₁₃×#34275 #15720614

Order 3328.

3410 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2361	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2358	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2326	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#127	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#535	C₄	1	16	yes	complemented
18	C₂×C₁₃×#127	C₂²	1	2	yes	—
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	4	yes	—
21	C₂×C₁₃×#120	C₂²	1	4	yes	—
22	C₁₃×#520	—	2	8	no	—
23	C₁₃×#518	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#390	C₂²	1	2	yes	—
44	C₁₃×#390	C₂²	1	2	yes	—
45	C₁₃×#390	C₂²	1	4	yes	—
46	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#390	C₂²	1	8	yes	complemented
49	C₁₃×#389	C₂²	1	4	yes	complemented
50	C₁₃×#388	C₂²	1	8	yes	complemented
51	C₁₃×#388	C₂²	1	8	yes	complemented
52	C₁₃×#386	C₂²	1	4	yes	—
53	C₁₃×#386	C₂²	1	8	yes	complemented
54	C₁₃×#386	C₂²	1	8	yes	complemented
55	C₁₃×#385	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	8	yes	complemented
57	C₁₃×#384	C₂²	1	2	yes	complemented
58	C₁₃×#382	C₂²	1	2	yes	complemented
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
64	C₁₃×#376	C₂²	1	2	yes	complemented
65	C₄³×C₁₃	C₂²	1	2	yes	complemented
66	C₂⁵×C₁₃	C₂³	1	2	yes	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	—	2	4	no	—
69	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	4	no	—
72	C₂²×D₄×C₁₃	—	2	4	no	—
73	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#127	C₂×C₄	1	16	yes	complemented
87	C₁₃×#124	C₂×C₄	1	16	yes	complemented
88	C₁₃×#121	C₂×C₄	1	32	yes	complemented
89	C₁₃×#120	C₂×C₄	1	32	yes	complemented
90	C₄×Q₈×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	8	no	—
93	C₄×D₄×C₁₃	—	2	16	no	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	8	no	—
96	C₄×D₄×C₁₃	—	2	8	no	—
97	C₄×D₄×C₁₃	—	4	16	no	—
98	C₁₃×#117	—	2	4	no	—
99	C₁₃×#117	—	2	8	no	—
100	C₁₃×#117	C₂×C₄	1	8	yes	complemented
101	C₁₃×#117	D₄	1	8	yes	complemented
102	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃	—	2	4	no	—
127	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	8	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	#34275	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	4	no	—
143	C₂⁴×C₁₃	—	2	4	no	—
144	C₂⁴×C₁₃	—	4	4	no	—
145	C₂⁴×C₁₃	—	4	4	no	—
146	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
149	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×#41	—	2	32	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	32	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	4	8	no	—
164	C₂×D₄×C₁₃	—	4	8	no	—
165	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
166	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
167	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
168	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
169	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	8	no	—
176	C₂²×C₄×C₁₃	—	2	8	no	—
177	C₂²×C₄×C₁₃	—	2	8	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	—	4	8	no	—
181	C₂²×C₄×C₁₃	—	4	8	no	—
182	C₂²×C₄×C₁₃	—	4	8	no	—
183	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₁₃	#41	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	8	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	4	8	no	—
204	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
206	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	8	no	—
209	C₁₃×C₂²⋊C₄	—	2	8	no	—
210	C₁₃×C₂²⋊C₄	—	2	8	no	—
211	C₁₃×C₂²⋊C₄	—	2	16	no	—
212	C₁₃×C₂²⋊C₄	—	2	8	no	—
213	C₁₃×C₂²⋊C₄	—	4	8	no	—
214	C₁₃×C₂²⋊C₄	—	4	4	no	—
215	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
216	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
217	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	—	2	8	no	—
220	C₄²×C₁₃	—	2	2	no	—
221	C₄²×C₁₃	—	2	4	no	—
222	C₄²×C₁₃	—	2	2	no	—
223	C₄²×C₁₃	—	2	8	no	—
224	C₄²×C₁₃	—	4	4	no	—
225	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
226	C₄²×C₁₃	C₂×D₄	1	8	yes	—
227	C₂×#535	C₂×C₁₃	1	1	yes	characteristic
228	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2363	C₂×C₁₃	1	4	yes	complemented
231	#2361	C₂×C₁₃	1	4	yes	complemented
232	#2358	C₂×C₁₃	1	8	yes	complemented
233	#2328	C₂×C₁₃	1	2	yes	complemented
234	#2326	C₂×C₁₃	1	2	yes	complemented
235	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₄×#127	C₂×C₁₃	1	2	yes	complemented
237	C₄×#124	C₂×C₁₃	1	2	yes	complemented
238	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
239	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	2	4	no	—
247	C₂³×C₁₃	—	2	8	no	—
248	C₂³×C₁₃	—	2	4	no	—
249	C₂³×C₁₃	—	2	4	no	—
250	C₂³×C₁₃	—	2	8	no	—
251	C₂³×C₁₃	—	2	16	no	—
252	C₂³×C₁₃	—	4	16	no	—
253	C₂³×C₁₃	—	8	8	no	—
254	C₂³×C₁₃	—	8	4	no	—
255	C₂³×C₁₃	—	8	4	no	—
256	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
257	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
258	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
259	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
260	C₂³×C₁₃	C₂×#41	1	2	yes	—
261	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
262	Q₈×C₁₃	—	2	8	no	—
263	D₄×C₁₃	—	2	16	no	—
264	D₄×C₁₃	—	2	16	no	—
265	D₄×C₁₃	—	2	16	no	—
266	D₄×C₁₃	—	2	8	no	—
267	D₄×C₁₃	—	4	32	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	16	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	8	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	4	8	no	—
287	C₂×C₄×C₁₃	—	8	8	no	—
288	C₂×C₄×C₁₃	—	8	8	no	—
289	C₂×C₄×C₁₃	—	8	8	no	—
290	C₂×C₄×C₁₃	—	8	4	no	—
291	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
292	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
293	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
301	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
302	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
303	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
304	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
305	#535	C₄×C₁₃	1	16	yes	complemented
306	C₂×#127	C₂²×C₁₃	1	2	yes	—
307	C₂×#124	C₂²×C₁₃	1	2	yes	—
308	C₂×#121	C₂²×C₁₃	1	4	yes	—
309	C₂×#120	C₂²×C₁₃	1	4	yes	—
310	#520	—	2	8	no	—
311	#518	—	2	8	no	—
312	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
313	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
314	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
315	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
316	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
317	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
319	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
320	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
324	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
326	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
327	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
328	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
329	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	#390	C₂²×C₁₃	1	2	yes	—
332	#390	C₂²×C₁₃	1	2	yes	—
333	#390	C₂²×C₁₃	1	4	yes	—
334	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
335	#390	C₂²×C₁₃	1	8	yes	complemented
336	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	#389	C₂²×C₁₃	1	4	yes	complemented
338	#388	C₂²×C₁₃	1	8	yes	complemented
339	#388	C₂²×C₁₃	1	8	yes	complemented
340	#386	C₂²×C₁₃	1	4	yes	—
341	#386	C₂²×C₁₃	1	8	yes	complemented
342	#386	C₂²×C₁₃	1	8	yes	complemented
343	#385	C₂²×C₁₃	1	4	yes	—
344	#385	C₂²×C₁₃	1	8	yes	complemented
345	#384	C₂²×C₁₃	1	2	yes	complemented
346	#382	C₂²×C₁₃	1	2	yes	complemented
347	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
348	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
349	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
351	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
352	#376	C₂²×C₁₃	1	2	yes	complemented
353	C₄³	C₂²×C₁₃	1	2	yes	complemented
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	2	4	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	4	no	—
359	C₂²×C₁₃	—	2	8	no	—
360	C₂²×C₁₃	—	2	8	no	—
361	C₂²×C₁₃	—	2	16	no	—
362	C₂²×C₁₃	—	4	4	no	—
363	C₂²×C₁₃	—	4	8	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	4	no	—
366	C₂²×C₁₃	—	4	4	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	8	16	no	—
369	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
370	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
371	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
372	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₂²×C₁₃	#585	1	2	yes	—
375	C₄×C₁₃	—	2	4	no	—
376	C₄×C₁₃	—	2	8	no	—
377	C₄×C₁₃	—	2	4	no	—
378	C₄×C₁₃	—	2	4	no	—
379	C₄×C₁₃	—	2	4	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	—	4	2	no	—
382	C₄×C₁₃	—	4	4	no	—
383	C₄×C₁₃	—	4	2	no	—
384	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
385	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
386	C₂⁵	C₂³×C₁₃	1	2	yes	—
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
390	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
394	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
395	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
396	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
397	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
399	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
401	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
403	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
404	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
405	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
406	#127	C₂×C₄×C₁₃	1	16	yes	complemented
407	#124	C₂×C₄×C₁₃	1	16	yes	complemented
408	#121	C₂×C₄×C₁₃	1	32	yes	complemented
409	#120	C₂×C₄×C₁₃	1	32	yes	complemented
410	C₄×Q₈	—	2	8	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	16	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	8	no	—
417	C₄×D₄	—	4	16	no	—
418	#117	—	2	4	no	—
419	#117	—	2	8	no	—
420	#117	C₂×C₄×C₁₃	1	8	yes	complemented
421	#117	D₄×C₁₃	1	8	yes	complemented
422	C₂×C₄⋊C₄	—	2	4	no	—
423	C₂×C₄⋊C₄	—	2	8	no	—
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	16	no	—
434	C₂×C₂²⋊C₄	—	4	8	no	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄²	—	2	4	no	—
447	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
449	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
453	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
454	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
455	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
456	#95	C₂³×C₁₃	1	4	yes	—
457	#95	C₂³×C₁₃	1	4	yes	—
458	#95	C₂³×C₁₃	1	4	yes	—
459	#95	C₂³×C₁₃	1	8	yes	—
460	#95	C₂³×C₁₃	1	4	yes	—
461	C₂×C₁₃	—	2	4	no	—
462	C₂×C₁₃	—	4	4	no	—
463	C₂×C₁₃	—	4	8	no	—
464	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
465	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
466	C₂×C₁₃	#3494	1	2	yes	—
467	C₂×C₁₃	#3498	1	1	yes	characteristic
468	C₂×C₁₃	#3500	1	1	yes	characteristic
469	C₂⁴	—	2	4	no	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	4	4	no	—
472	C₂⁴	—	4	4	no	—
473	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
474	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
475	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
476	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
477	#41	—	2	32	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	32	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	—	4	8	no	—
492	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
493	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
494	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
495	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
496	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	8	no	—
503	C₂²×C₄	—	2	8	no	—
504	C₂²×C₄	—	2	8	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	—	4	8	no	—
508	C₂²×C₄	—	4	8	no	—
509	C₂²×C₄	—	4	8	no	—
510	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
511	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
512	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
513	C₂²×C₄	C₁₃×#41	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	4	8	no	—
531	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
532	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	8	no	—
538	C₂²⋊C₄	—	2	16	no	—
539	C₂²⋊C₄	—	2	8	no	—
540	C₂²⋊C₄	—	4	8	no	—
541	C₂²⋊C₄	—	4	4	no	—
542	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
543	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
544	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
545	C₄²	—	2	4	no	—
546	C₄²	—	2	8	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	4	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	2	8	no	—
551	C₄²	—	4	4	no	—
552	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
553	C₄²	C₂×D₄×C₁₃	1	8	yes	—
554	C₁₃	#34275	1	1	yes	characteristic, direct product factor, Sylow
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	2	8	no	—
565	C₂³	—	2	16	no	—
566	C₂³	—	4	16	no	—
567	C₂³	—	8	8	no	—
568	C₂³	—	8	4	no	—
569	C₂³	—	8	4	no	—
570	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
571	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
572	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
573	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
574	C₂³	C₂×C₁₃×#41	1	2	yes	—
575	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
576	Q₈	—	2	8	no	—
577	D₄	—	2	16	no	—
578	D₄	—	2	16	no	—
579	D₄	—	2	16	no	—
580	D₄	—	2	8	no	—
581	D₄	—	4	32	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	16	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	8	8	no	—
602	C₂×C₄	—	8	8	no	—
603	C₂×C₄	—	8	8	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
606	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
607	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
608	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
609	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
611	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
614	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
615	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
616	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	8	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	2	16	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	8	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	16	no	—
632	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
633	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
634	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
635	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
636	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
637	C₂²	C₁₃×#585	1	2	yes	—
638	C₄	—	2	4	no	—
639	C₄	—	2	8	no	—
640	C₄	—	2	4	no	—
641	C₄	—	2	4	no	—
642	C₄	—	2	4	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	4	no	—
646	C₄	—	4	2	no	—
647	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
648	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
649	C₂	—	2	4	no	—
650	C₂	—	4	8	no	—
651	C₂	—	4	4	no	—
652	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
653	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
654	C₂	C₁₃×#3494	1	2	yes	—
655	C₂	C₁₃×#3498	1	1	yes	characteristic
656	C₂	C₁₃×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#535	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×#520	C₂	semidirect
3. C₂×C₁₃×#518	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2361	C₂	semidirect
6. C₁₃×#2358	C₂	semidirect
7. C₁₃×#2328	C₂	semidirect
8. C₁₃×#2326	C₂	semidirect
9. C₁₃×#2317	C₂	semidirect
10. C₄×C₁₃×#127	C₂	semidirect
11. C₄×C₁₃×#124	C₂	semidirect
12. C₁₃×#2297	C₂	semidirect
13. C₂×C₁₃×#390	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
17. C₁₃×#535	C₄	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₁₃×#117	C₂²	semidirect
37. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
41. C₁₃×#391	C₂²	semidirect
42. C₁₃×#391	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#390	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#388	C₂²	semidirect
51. C₁₃×#388	C₂²	semidirect
53. C₁₃×#386	C₂²	semidirect
54. C₁₃×#386	C₂²	semidirect
56. C₁₃×#385	C₂²	semidirect
57. C₁₃×#384	C₂²	semidirect
58. C₁₃×#382	C₂²	semidirect
59. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
60. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
62. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
63. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
64. C₁₃×#376	C₂²	semidirect
65. C₄³×C₁₃	C₂²	semidirect
69. C₂×C₁₃×#41	C₂×C₄	semidirect
73. C₂²×D₄×C₁₃	C₂×C₄	semidirect
86. C₁₃×#127	C₂×C₄	semidirect
87. C₁₃×#124	C₂×C₄	semidirect
88. C₁₃×#121	C₂×C₄	semidirect
89. C₁₃×#120	C₂×C₄	semidirect
100. C₁₃×#117	C₂×C₄	semidirect
101. C₁₃×#117	D₄	semidirect
141. #34275	C₁₃	direct (N × H)
228. C₂×#520	C₂×C₁₃	semidirect
229. C₂×#518	C₂×C₁₃	semidirect
230. #2363	C₂×C₁₃	semidirect
231. #2361	C₂×C₁₃	semidirect
232. #2358	C₂×C₁₃	semidirect
233. #2328	C₂×C₁₃	semidirect
234. #2326	C₂×C₁₃	semidirect
235. #2317	C₂×C₁₃	semidirect
236. C₄×#127	C₂×C₁₃	semidirect
237. C₄×#124	C₂×C₁₃	semidirect
238. #2297	C₂×C₁₃	semidirect
239. C₂×#390	C₂×C₁₃	semidirect
240. C₄×#117	C₂×C₁₃	semidirect
291. C₂×C₄×C₁₃	C₄×D₄	semidirect
305. #535	C₄×C₁₃	semidirect
312. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
318. C₂×C₄×D₄	C₂²×C₁₃	semidirect
319. C₂×C₄×D₄	C₂²×C₁₃	semidirect
323. C₂×#117	C₂²×C₁₃	semidirect
325. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
329. #391	C₂²×C₁₃	semidirect
330. #391	C₂²×C₁₃	semidirect
334. #390	C₂²×C₁₃	semidirect
335. #390	C₂²×C₁₃	semidirect
336. #390	C₂²×C₁₃	semidirect
337. #389	C₂²×C₁₃	semidirect
338. #388	C₂²×C₁₃	semidirect
339. #388	C₂²×C₁₃	semidirect
341. #386	C₂²×C₁₃	semidirect
342. #386	C₂²×C₁₃	semidirect
344. #385	C₂²×C₁₃	semidirect
345. #384	C₂²×C₁₃	semidirect
346. #382	C₂²×C₁₃	semidirect
347. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
348. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
350. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
351. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
352. #376	C₂²×C₁₃	semidirect
353. C₄³	C₂²×C₁₃	semidirect
389. C₂×#41	C₂×C₄×C₁₃	semidirect
393. C₂²×D₄	C₂×C₄×C₁₃	semidirect
406. #127	C₂×C₄×C₁₃	semidirect
407. #124	C₂×C₄×C₁₃	semidirect
408. #121	C₂×C₄×C₁₃	semidirect
409. #120	C₂×C₄×C₁₃	semidirect
420. #117	C₂×C₄×C₁₃	semidirect
421. #117	D₄×C₁₃	semidirect
554. C₁₃	#34275	direct (N × H)
605. C₂×C₄	C₄×D₄×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#535	2
C₂×C₁₃×#520	2
C₂×C₁₃×#518	2
C₁₃×#2363	2
C₁₃×#2361	2
C₁₃×#2358	2
C₁₃×#2328	2
C₁₃×#2326	2
C₁₃×#2317	2
C₄×C₁₃×#127	2
C₄×C₁₃×#124	2
C₁₃×#2297	2
C₂×C₁₃×#390	2
C₄×C₁₃×#117	2
#34275	13

Subgroups — C13×#34275 #15720614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34275 #15720614