Subgroups — C₁₃×#21147 #15707486

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1940	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1939	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#424	—	2	4	no	—
18	C₁₃×#424	—	2	4	no	—
19	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₃×#405	—	2	4	no	—
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#389	C₄	1	2	yes	—
29	C₁₃×#389	C₄	1	2	yes	—
30	C₁₃×#385	C₄	1	2	yes	—
31	C₁₃×#385	C₄	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
33	C₁₃×#336	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	4	yes	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₁₃×M₁₆	—	2	2	no	—
39	C₂×C₁₃×M₁₆	—	2	2	no	—
40	C₂×C₁₃×M₁₆	—	2	2	no	—
41	C₂×C₁₃×M₁₆	—	2	2	no	—
42	C₂×C₁₃×M₁₆	—	2	2	no	—
43	C₂×C₁₃×M₁₆	Q₈	1	4	yes	—
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	D₄	1	4	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	D₄	1	4	yes	—
58	C₁₃×#117	Q₈	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	2	4	no	—
74	C₁₃×C₄⋊C₈	—	2	4	no	—
75	C₁₃×C₄⋊C₈	—	2	4	no	—
76	C₁₃×C₄⋊C₈	—	2	8	no	—
77	C₁₃×#97	—	2	4	no	—
78	C₄×C₈×C₁₃	—	2	4	no	—
79	C₁₃×#95	C₂×C₄	1	4	yes	—
80	C₁₃×#95	C₂×C₄	1	4	yes	—
81	#21147	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₁₃	#41	1	2	yes	—
98	C₂²×C₄×C₁₃	#41	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
100	C₁₃×M₁₆	—	2	8	no	—
101	C₁₃×M₁₆	—	4	4	no	—
102	C₂×C₈×C₁₃	—	2	8	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	1	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	4	4	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	8	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
124	C₁₃×C₂²⋊C₄	—	2	4	no	—
125	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₄²×C₁₃	—	2	4	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	C₂×D₄	1	4	yes	—
132	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
133	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
134	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
135	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
136	C₂×#405	C₂×C₁₃	1	1	yes	characteristic
137	#2296	C₂×C₁₃	1	1	yes	characteristic
138	#1940	C₂×C₁₃	1	4	yes	complemented
139	#1939	C₂×C₁₃	1	4	yes	complemented
140	#1729	C₂×C₁₃	1	1	yes	characteristic
141	#1728	C₂×C₁₃	1	1	yes	characteristic
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₁₃	C₄×D₄	1	2	yes	—
146	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
147	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	—	2	8	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	4	no	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₁₃	#121	1	4	yes	—
166	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
167	C₂×C₄×C₁₃	#125	1	4	yes	—
168	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₃	#131	1	4	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₈×C₁₃	—	2	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	2	4	no	—
179	C₈×C₁₃	—	4	2	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
182	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
183	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
188	#424	—	2	4	no	—
189	#424	—	2	4	no	—
190	C₂×C₄⋊C₈	—	2	4	no	—
191	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
196	#405	—	2	4	no	—
197	C₂×#97	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
199	#389	C₄×C₁₃	1	2	yes	—
200	#389	C₄×C₁₃	1	2	yes	—
201	#385	C₄×C₁₃	1	2	yes	—
202	#385	C₄×C₁₃	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
204	#336	C₂²×C₁₃	1	4	yes	—
205	#336	C₂²×C₁₃	1	4	yes	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	2	4	no	—
210	C₂²×C₁₃	#389	1	4	yes	—
211	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#131	1	2	yes	—
215	C₂²×C₁₃	#568	1	2	yes	—
216	C₄×C₁₃	—	2	8	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	#389	1	4	yes	—
222	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
223	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
225	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
226	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	Q₈×C₁₃	1	4	yes	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	D₄×C₁₃	1	4	yes	—
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	D₄×C₁₃	1	4	yes	—
249	#117	Q₈×C₁₃	1	4	yes	—
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
263	C₄⋊C₈	—	2	4	no	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	4	no	—
266	C₄⋊C₈	—	2	4	no	—
267	C₄⋊C₈	—	2	8	no	—
268	#97	—	2	4	no	—
269	C₄×C₈	—	2	4	no	—
270	#95	C₂×C₄×C₁₃	1	4	yes	—
271	#95	C₂×C₄×C₁₃	1	4	yes	—
272	C₂×C₁₃	—	2	4	no	—
273	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
274	C₂×C₁₃	#2906	1	2	yes	—
275	C₂×C₁₃	#2929	1	1	yes	characteristic
276	C₂×C₁₃	#2930	1	1	yes	characteristic
277	C₂×C₁₃	#2962	1	2	yes	—
278	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
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	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
292	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
293	C₂²×C₄	C₁₃×#41	1	2	yes	—
294	C₂²×C₄	C₁₃×#41	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
296	M₁₆	—	2	8	no	—
297	M₁₆	—	4	4	no	—
298	C₂×C₈	—	2	8	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	C₂×D₄×C₁₃	1	4	yes	—
328	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
329	C₁₃	#21147	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
333	C₂³	C₄×D₄×C₁₃	1	2	yes	—
334	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
335	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
350	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
352	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
353	C₂×C₄	C₁₃×#121	1	4	yes	—
354	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
355	C₂×C₄	C₁₃×#125	1	4	yes	—
356	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
357	C₂×C₄	C₁₃×#131	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
363	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	4	no	—
367	C₈	—	4	2	no	—
368	C₈	—	4	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	4	no	—
373	C₂²	C₁₃×#389	1	4	yes	—
374	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
375	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
376	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
377	C₂²	C₂×C₁₃×#131	1	2	yes	—
378	C₂²	C₁₃×#568	1	2	yes	—
379	C₄	—	2	8	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₁₃×#389	1	4	yes	—
385	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
386	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
387	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
388	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	C₂×C₁₃×#389	1	1	yes	characteristic
391	C₂	C₁₃×#2906	1	2	yes	—
392	C₂	C₁₃×#2929	1	1	yes	characteristic
393	C₂	C₁₃×#2930	1	1	yes	characteristic
394	C₂	C₁₃×#2962	1	2	yes	—

	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
6. C₁₃×#1940	C₂	semidirect
7. C₁₃×#1939	C₂	semidirect
81. #21147	C₁₃	direct (N × H)
138. #1940	C₂×C₁₃	semidirect
139. #1939	C₂×C₁₃	semidirect
329. C₁₃	#21147	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×#424	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×C₁₃×#405	2
C₁₃×#2296	2
C₁₃×#1940	2
C₁₃×#1939	2
C₁₃×#1729	2
C₁₃×#1728	2
#21147	13

Subgroups — C13×#21147 #15707486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21147 #15707486