Subgroups — C₁₃×#21068 #15707407

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1927	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1926	C₂	1	4	yes	maximal, complemented
8	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	—	2	4	no	—
18	C₂×C₁₃×#106	C₂²	1	4	yes	—
19	C₁₃×#417	—	2	4	no	—
20	C₁₃×#416	C₄	1	8	yes	complemented
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₁₃×#391	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	2	yes	—
27	C₁₃×#386	—	2	2	no	—
28	C₁₃×#380	—	2	2	no	—
29	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
31	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
32	C₁₃×#340	C₂²	1	4	yes	—
33	C₁₃×#336	C₂²	1	4	yes	—
34	C₂×C₁₃×#41	—	2	2	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
40	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#117	—	2	2	no	—
56	C₁₃×#117	—	2	2	no	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	C₂×C₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	4	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₁₃×#106	—	2	8	no	—
76	C₁₃×#103	—	2	4	no	—
77	C₁₃×#103	C₂×C₄	1	8	yes	complemented
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×#102	C₂×C₄	1	8	yes	complemented
80	C₁₃×#95	—	2	4	no	—
81	C₁₃×#95	—	2	4	no	—
82	#21068	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	1	no	—
84	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₁₃×#41	—	2	8	no	—
86	C₁₃×#41	—	2	8	no	—
87	C₁₃×#41	—	4	4	no	—
88	C₁₃×#41	—	4	4	no	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	—	8	2	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	#41	1	2	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×M₁₆	—	4	4	no	—
125	C₂×C₈×C₁₃	—	2	8	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	8	4	no	—
144	C₄²×C₁₃	—	2	4	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	8	4	no	—
148	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
150	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
151	#2311	C₂×C₁₃	1	1	yes	characteristic
152	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1927	C₂×C₁₃	1	4	yes	complemented
154	#1926	C₂×C₁₃	1	4	yes	complemented
155	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	C₄×D₄	1	2	yes	—
165	C₂³×C₁₃	#121	1	2	yes	—
166	C₂³×C₁₃	#123	1	2	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	4	1	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	—	4	8	no	—
175	D₄×C₁₃	—	4	1	no	—
176	D₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	8	4	no	—
193	C₂×C₄×C₁₃	#117	1	4	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	#121	1	2	yes	—
197	C₂×C₄×C₁₃	#123	1	2	yes	—
198	C₂×C₄×C₁₃	#124	1	4	yes	—
199	C₂×C₄×C₁₃	#126	1	4	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃	—	2	4	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#106	—	2	4	no	—
216	C₂×#106	C₂²×C₁₃	1	4	yes	—
217	#417	—	2	4	no	—
218	#416	C₄×C₁₃	1	8	yes	complemented
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×#102	C₂²×C₁₃	1	2	yes	—
223	#391	C₂²×C₁₃	1	2	yes	—
224	#390	C₂²×C₁₃	1	2	yes	—
225	#386	—	2	2	no	—
226	#380	—	2	2	no	—
227	C₄×C₄⋊C₄	—	2	2	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
229	C₄×C₂²⋊C₄	—	2	2	no	—
230	#340	C₂²×C₁₃	1	4	yes	—
231	#336	C₂²×C₁₃	1	4	yes	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	4	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	—	8	1	no	—
241	C₂²×C₁₃	#388	1	4	yes	—
242	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
245	C₂²×C₁₃	#577	1	2	yes	—
246	C₂²×C₁₃	#577	1	2	yes	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	#388	1	4	yes	—
253	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
254	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
263	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
276	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	C₂×C₄×C₁₃	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	4	no	—
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	#106	—	2	8	no	—
299	#103	—	2	4	no	—
300	#103	C₂×C₄×C₁₃	1	8	yes	complemented
301	#102	—	2	4	no	—
302	#102	C₂×C₄×C₁₃	1	8	yes	complemented
303	#95	—	2	4	no	—
304	#95	—	2	4	no	—
305	C₂×C₁₃	—	2	4	no	—
306	C₂×C₁₃	—	8	2	no	—
307	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
308	C₂×C₁₃	#2952	1	2	yes	—
309	C₂×C₁₃	#3042	1	1	yes	characteristic
310	C₂×C₁₃	#3043	1	1	yes	characteristic
311	C₂×C₁₃	#3099	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
314	#41	—	2	8	no	—
315	#41	—	2	8	no	—
316	#41	—	4	4	no	—
317	#41	—	4	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	—	8	2	no	—
344	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₁₃×#41	1	2	yes	—
349	C₂²×C₄	C₁₃×#41	1	2	yes	—
350	C₂²×C₄	C₁₃×#41	1	2	yes	—
351	C₂²×C₄	C₁₃×#41	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	M₁₆	—	4	4	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
369	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	8	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	8	4	no	—
377	C₁₃	#21068	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₄×D₄×C₁₃	1	2	yes	—
386	C₂³	C₁₃×#121	1	2	yes	—
387	C₂³	C₁₃×#123	1	2	yes	—
388	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	4	1	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	1	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	—	8	4	no	—
414	C₂×C₄	C₁₃×#117	1	4	yes	—
415	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
416	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
417	C₂×C₄	C₁₃×#121	1	2	yes	—
418	C₂×C₄	C₁₃×#123	1	2	yes	—
419	C₂×C₄	C₁₃×#124	1	4	yes	—
420	C₂×C₄	C₁₃×#126	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	C₁₃×#388	1	4	yes	—
439	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
440	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
441	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
442	C₂²	C₁₃×#577	1	2	yes	—
443	C₂²	C₁₃×#577	1	2	yes	—
444	C₄	—	4	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	—	8	2	no	—
449	C₄	C₁₃×#388	1	4	yes	—
450	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
451	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
452	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
453	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
454	C₂	—	2	4	no	—
455	C₂	—	8	2	no	—
456	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
457	C₂	C₁₃×#2952	1	2	yes	—
458	C₂	C₁₃×#3042	1	1	yes	characteristic
459	C₂	C₁₃×#3043	1	1	yes	characteristic
460	C₂	C₁₃×#3099	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	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#106	C₂	semidirect
5. C₁₃×#2274	C₂	semidirect
6. C₁₃×#1927	C₂	semidirect
7. C₁₃×#1926	C₂	semidirect
8. C₁₃×#1736	C₂	semidirect
9. C₁₃×#1729	C₂	semidirect
20. C₁₃×#416	C₄	semidirect
77. C₁₃×#103	C₂×C₄	semidirect
79. C₁₃×#102	C₂×C₄	semidirect
82. #21068	C₁₃	direct (N × H)
148. C₂²×#106	C₂×C₁₃	semidirect
152. #2274	C₂×C₁₃	semidirect
153. #1927	C₂×C₁₃	semidirect
154. #1926	C₂×C₁₃	semidirect
155. #1736	C₂×C₁₃	semidirect
156. #1729	C₂×C₁₃	semidirect
218. #416	C₄×C₁₃	semidirect
300. #103	C₂×C₄×C₁₃	semidirect
302. #102	C₂×C₄×C₁₃	semidirect
377. C₁₃	#21068	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#106	2
C₂×C₁₃×#417	2
C₂×C₁₃×#416	2
C₁₃×#2311	2
C₁₃×#2274	2
C₁₃×#1927	2
C₁₃×#1926	2
C₁₃×#1736	2
C₁₃×#1729	2
#21068	13

Subgroups — C13×#21068 #15707407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21068 #15707407