Subgroups — C₁₃×#22629 #15708968

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1939	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1917	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1797	C₂	1	2	yes	maximal
5	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1770	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1749	C₂	1	2	yes	maximal
8	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#97	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
20	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
22	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#95	C₄	1	2	yes	—
27	C₁₃×#336	C₂²	1	2	yes	—
28	C₁₃×#336	C₂²	1	4	yes	—
29	C₁₃×#336	C₂²	1	4	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	—	2	4	no	—
48	C₂×C₄²×C₁₃	—	4	4	no	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	—	2	4	no	—
58	C₁₃×C₄⋊C₈	—	4	4	no	—
59	C₁₃×C₂²⋊C₈	—	2	2	no	—
60	C₁₃×C₂²⋊C₈	—	2	4	no	—
61	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
62	C₁₃×#97	—	4	4	no	—
63	C₄×C₈×C₁₃	—	2	4	no	—
64	C₁₃×#95	C₂×C₄	1	2	yes	—
65	C₁₃×#95	C₂×C₄	1	2	yes	—
66	C₁₃×#95	C₂×C₄	1	2	yes	—
67	C₁₃×#95	C₂×C₄	1	2	yes	—
68	#22629	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	4	2	no	—
80	C₂²×C₄×C₁₃	—	4	2	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	—	4	2	no	—
83	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₁₃	#41	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	—	2	4	no	—
102	C₂×C₈×C₁₃	—	2	4	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
105	C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	4	no	—
115	C₄²×C₁₃	—	2	4	no	—
116	C₄²×C₁₃	—	4	2	no	—
117	C₄²×C₁₃	—	4	2	no	—
118	C₄²×C₁₃	#41	1	4	yes	—
119	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
120	#1939	C₂×C₁₃	1	2	yes	complemented
121	#1917	C₂×C₁₃	1	4	yes	complemented
122	#1797	C₂×C₁₃	1	1	yes	characteristic
123	#1797	C₂×C₁₃	1	2	yes	—
124	#1770	C₂×C₁₃	1	2	yes	complemented
125	#1749	C₂×C₁₃	1	2	yes	—
126	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	1	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
132	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
133	C₂³×C₁₃	#131	1	2	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	8	no	—
160	C₂×C₄×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	#117	1	2	yes	—
162	C₂×C₄×C₁₃	#117	1	2	yes	—
163	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
166	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₁₃	—	2	4	no	—
173	C₈×C₁₃	—	4	2	no	—
174	C₈×C₁₃	—	4	4	no	—
175	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
176	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
181	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#97	C₂²×C₁₃	1	4	yes	—
185	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
186	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
187	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
188	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
189	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#95	C₄×C₁₃	1	2	yes	—
193	#336	C₂²×C₁₃	1	2	yes	—
194	#336	C₂²×C₁₃	1	4	yes	—
195	#336	C₂²×C₁₃	1	2	yes	—
196	#336	C₂²×C₁₃	1	4	yes	—
197	C₂²×C₁₃	—	2	2	no	—
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	#446	1	4	yes	—
204	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
205	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
206	C₂²×C₁₃	#518	1	1	yes	characteristic
207	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
208	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
209	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
210	C₂²×C₁₃	#568	1	1	yes	characteristic
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	4	1	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	2	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	#432	1	4	yes	—
220	C₄×C₁₃	#553	1	2	yes	—
221	C₄×C₁₃	#554	1	2	yes	—
222	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
223	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
226	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
229	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	4	4	no	—
240	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
244	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	4	4	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
253	#97	—	4	4	no	—
254	C₄×C₈	—	2	4	no	—
255	#95	C₂×C₄×C₁₃	1	2	yes	—
256	#95	C₂×C₄×C₁₃	1	2	yes	—
257	#95	C₂×C₄×C₁₃	1	2	yes	—
258	#95	C₂×C₄×C₁₃	1	2	yes	—
259	C₂×C₁₃	—	2	4	no	—
260	C₂×C₁₃	#2345	1	1	yes	characteristic
261	C₂×C₁₃	C₂×#432	1	1	yes	characteristic
262	C₂×C₁₃	#2924	1	1	yes	characteristic
263	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
264	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
265	C₂×C₁₃	#2974	1	1	yes	characteristic
266	C₂×C₁₃	#2975	1	1	yes	characteristic
267	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
282	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
292	C₂²×C₄	C₁₃×#41	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₁₃×M₁₆	1	4	yes	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	C₁₃×#41	1	4	yes	—
317	C₁₃	#22629	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
323	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
324	C₂³	C₁₃×#131	1	2	yes	—
325	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	C₁₃×#117	1	2	yes	—
353	C₂×C₄	C₁₃×#117	1	2	yes	—
354	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
355	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
356	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
357	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
358	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
359	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
362	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
363	C₈	—	2	4	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	4	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	C₁₃×#446	1	4	yes	—
373	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
374	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
375	C₂²	C₁₃×#518	1	1	yes	characteristic
376	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
377	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
378	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
379	C₂²	C₁₃×#568	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	C₁₃×#432	1	4	yes	—
389	C₄	C₁₃×#553	1	2	yes	—
390	C₄	C₁₃×#554	1	2	yes	—
391	C₂	—	2	4	no	—
392	C₂	C₁₃×#2345	1	1	yes	characteristic
393	C₂	C₂×C₁₃×#432	1	1	yes	characteristic
394	C₂	C₁₃×#2924	1	1	yes	characteristic
395	C₂	C₂×C₁₃×#446	1	1	yes	characteristic
396	C₂	Q₈×C₁₃×M₁₆	1	1	yes	characteristic
397	C₂	C₁₃×#2974	1	1	yes	characteristic
398	C₂	C₁₃×#2975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
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. C₁₃×#1939	C₂	semidirect
3. C₁₃×#1917	C₂	semidirect
6. C₁₃×#1770	C₂	semidirect
68. #22629	C₁₃	direct (N × H)
120. #1939	C₂×C₁₃	semidirect
121. #1917	C₂×C₁₃	semidirect
124. #1770	C₂×C₁₃	semidirect
317. C₁₃	#22629	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×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1939	2
C₁₃×#1917	2
C₁₃×#1797	2
C₁₃×#1770	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
#22629	13

Subgroups — C13×#22629 #15708968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22629 #15708968