Subgroups — C₁₃×#21861 #15708200

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1991	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1958	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1874	C₂	1	2	yes	maximal
7	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1805	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1804	C₂	1	2	yes	maximal, complemented
10	C₁₃×#529	—	2	4	no	—
11	C₁₃×#529	C₄	1	8	yes	complemented
12	C₂×C₁₃×#126	—	2	1	no	—
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#123	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	—	2	1	no	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#431	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#102	C₂²	1	4	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
30	C₁₃×#382	—	2	1	no	—
31	C₁₃×#382	—	2	1	no	—
32	C₁₃×#382	C₂²	1	2	yes	—
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	—	2	1	no	—
35	C₂×C₁₃×#95	—	2	1	no	—
36	C₁₃×#340	C₂²	1	4	yes	—
37	C₁₃×#340	C₂²	1	4	yes	—
38	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
47	C₁₃×#126	—	2	8	no	—
48	C₁₃×#125	—	2	2	no	—
49	C₁₃×#125	C₂×C₄	1	4	yes	complemented
50	C₁₃×#124	—	2	2	no	—
51	C₁₃×#124	C₂×C₄	1	4	yes	complemented
52	C₁₃×#123	—	2	8	no	—
53	C₁₃×C₂²⋊Q₈	—	2	2	no	—
54	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
55	C₁₃×#121	—	2	2	no	—
56	C₁₃×#121	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
59	C₄×D₄×C₁₃	—	2	8	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	complemented
62	C₁₃×#117	—	2	8	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
79	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	D₄	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	—	2	4	no	—
85	C₁₃×#103	—	4	4	no	—
86	C₁₃×#102	—	4	4	no	—
87	C₁₃×C₂²⋊C₈	—	2	4	no	—
88	C₄×C₈×C₁₃	—	2	4	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	#21861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	4	4	no	—
105	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₁₃	—	2	4	no	—
130	C₂×C₈×C₁₃	—	2	4	no	—
131	C₂×C₈×C₁₃	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	—	4	4	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	2	4	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
151	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
152	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₃	C₂×D₄	1	2	yes	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
156	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1991	C₂×C₁₃	1	2	yes	complemented
159	#1958	C₂×C₁₃	1	2	yes	complemented
160	#1874	C₂×C₁₃	1	2	yes	—
161	#1872	C₂×C₁₃	1	2	yes	complemented
162	#1805	C₂×C₁₃	1	2	yes	complemented
163	#1804	C₂×C₁₃	1	2	yes	complemented
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂³×C₁₃	#135	1	4	yes	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	4	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	2	4	no	—
178	D₄×C₁₃	—	4	8	no	—
179	D₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	8	8	no	—
202	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
210	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
211	C₈×C₁₃	—	4	4	no	—
212	#529	—	2	4	no	—
213	#529	C₄×C₁₃	1	8	yes	complemented
214	C₂×#126	—	2	1	no	—
215	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#123	—	2	1	no	—
218	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
226	#431	—	2	4	no	—
227	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#103	C₂²×C₁₃	1	4	yes	—
229	C₂×#102	C₂²×C₁₃	1	4	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
232	#382	—	2	1	no	—
233	#382	—	2	1	no	—
234	#382	C₂²×C₁₃	1	2	yes	—
235	#382	C₂²×C₁₃	1	2	yes	—
236	C₂×#95	—	2	1	no	—
237	C₂×#95	—	2	1	no	—
238	#340	C₂²×C₁₃	1	4	yes	—
239	#340	C₂²×C₁₃	1	4	yes	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	#416	1	4	yes	—
250	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₁₃	#535	1	1	yes	characteristic
252	C₂²×C₁₃	#536	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#135	1	2	yes	—
254	C₂²×C₁₃	#575	1	2	yes	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	4	no	—
264	C₄×C₁₃	#520	1	2	yes	—
265	C₄×C₁₃	#537	1	2	yes	—
266	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
275	#126	—	2	8	no	—
276	#125	—	2	2	no	—
277	#125	C₂×C₄×C₁₃	1	4	yes	complemented
278	#124	—	2	2	no	—
279	#124	C₂×C₄×C₁₃	1	4	yes	complemented
280	#123	—	2	8	no	—
281	C₂²⋊Q₈	—	2	2	no	—
282	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
283	#121	—	2	2	no	—
284	#121	C₂×C₄×C₁₃	1	4	yes	—
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
287	C₄×D₄	—	2	8	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	complemented
290	#117	—	2	8	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	4	4	no	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
307	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	D₄×C₁₃	1	4	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₄⋊C₈	—	2	4	no	—
313	#103	—	4	4	no	—
314	#102	—	4	4	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	C₄×C₈	—	2	4	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	C₂×C₁₃	—	2	4	no	—
322	C₂×C₁₃	—	8	2	no	—
323	C₂×C₁₃	#2311	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
325	C₂×C₁₃	#2896	1	1	yes	characteristic
326	C₂×C₁₃	#3211	1	2	yes	—
327	C₂×C₁₃	#3232	1	2	yes	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
354	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
384	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
385	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
386	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
387	C₄²	C₂×D₄×C₁₃	1	2	yes	—
388	C₄²	C₂×D₄×C₁₃	1	2	yes	—
389	C₁₃	#21861	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
399	C₂³	C₁₃×#135	1	4	yes	—
400	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	Q₈	—	2	4	no	—
402	Q₈	—	4	2	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	8	8	no	—
428	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
429	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
430	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
431	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
432	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
437	C₈	—	4	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	C₁₃×#416	1	4	yes	—
448	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
449	C₂²	C₁₃×#535	1	1	yes	characteristic
450	C₂²	C₁₃×#536	1	1	yes	characteristic
451	C₂²	C₂×C₁₃×#135	1	2	yes	—
452	C₂²	C₁₃×#575	1	2	yes	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	4	no	—
462	C₄	C₁₃×#520	1	2	yes	—
463	C₄	C₁₃×#537	1	2	yes	—
464	C₂	—	2	4	no	—
465	C₂	—	8	2	no	—
466	C₂	C₁₃×#2311	1	1	yes	characteristic
467	C₂	C₂×C₁₃×#416	1	1	yes	characteristic
468	C₂	C₁₃×#2896	1	1	yes	characteristic
469	C₂	C₁₃×#3211	1	2	yes	—
470	C₂	C₁₃×#3232	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#431	C₂	semidirect
3. C₂×C₁₃×#382	C₂	semidirect
4. C₁₃×#1991	C₂	semidirect
5. C₁₃×#1958	C₂	semidirect
7. C₁₃×#1872	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
9. C₁₃×#1804	C₂	semidirect
11. C₁₃×#529	C₄	semidirect
49. C₁₃×#125	C₂×C₄	semidirect
51. C₁₃×#124	C₂×C₄	semidirect
58. C₄×Q₈×C₁₃	C₂×C₄	semidirect
61. C₄×D₄×C₁₃	C₂×C₄	semidirect
93. #21861	C₁₃	direct (N × H)
156. C₂×#431	C₂×C₁₃	semidirect
157. C₂×#382	C₂×C₁₃	semidirect
158. #1991	C₂×C₁₃	semidirect
159. #1958	C₂×C₁₃	semidirect
161. #1872	C₂×C₁₃	semidirect
162. #1805	C₂×C₁₃	semidirect
163. #1804	C₂×C₁₃	semidirect
213. #529	C₄×C₁₃	semidirect
277. #125	C₂×C₄×C₁₃	semidirect
279. #124	C₂×C₄×C₁₃	semidirect
286. C₄×Q₈	C₂×C₄×C₁₃	semidirect
289. C₄×D₄	C₂×C₄×C₁₃	semidirect
389. C₁₃	#21861	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×#529	2
C₂×C₁₃×#431	2
C₂×C₁₃×#382	2
C₁₃×#1991	2
C₁₃×#1958	2
C₁₃×#1874	2
C₁₃×#1872	2
C₁₃×#1805	2
C₁₃×#1804	2
#21861	13

Subgroups — C13×#21861 #15708200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21861 #15708200