Subgroups — C₁₃×#20504 #15706843

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#440	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×#103	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#102	C₂	1	2	yes	maximal
11	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#440	C₄	1	16	yes	complemented
18	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#376	—	2	1	no	—
38	C₁₃×#376	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#95	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₁₃×#107	C₂×C₄	1	8	yes	complemented
77	C₁₃×#106	C₂×C₄	1	4	yes	complemented
78	C₁₃×#103	C₂×C₄	1	4	yes	complemented
79	C₁₃×#103	C₂×C₄	1	8	yes	complemented
80	C₁₃×#102	C₂×C₄	1	4	yes	—
81	C₁₃×#102	C₂×C₄	1	8	yes	—
82	C₁₃×#97	—	2	2	no	—
83	C₁₃×#97	C₂×C₄	1	8	yes	complemented
84	C₄×C₈×C₁₃	—	2	4	no	—
85	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	D₄	1	2	yes	—
91	C₁₃×#95	D₄	1	1	yes	characteristic
92	C₁₃×#95	D₄	1	1	yes	characteristic
93	#20504	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	8	2	no	—
111	C₂²×C₄×C₁₃	—	8	2	no	—
112	C₂²×C₄×C₁₃	—	8	2	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×SD₁₆	C₄²	1	16	yes	complemented
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₄²×C₁₃	—	2	8	no	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	—	8	1	no	—
141	C₄²×C₁₃	—	8	1	no	—
142	C₄²×C₁₃	—	8	2	no	—
143	C₄²×C₁₃	—	8	2	no	—
144	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
145	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
146	C₄²×C₁₃	#41	1	4	yes	—
147	C₄²×C₁₃	#41	1	2	yes	—
148	C₂×#440	C₂×C₁₃	1	2	yes	—
149	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
150	#2276	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2275	C₂×C₁₃	1	1	yes	characteristic
152	#1776	C₂×C₁₃	1	2	yes	complemented
153	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1763	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1762	C₂×C₁₃	1	1	yes	characteristic
156	C₄×#103	C₂×C₁₃	1	2	yes	complemented
157	C₄×#102	C₂×C₁₃	1	2	yes	—
158	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	2	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	C₂×C₄²	1	4	yes	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	C₂×C₄²	1	4	yes	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	8	8	no	—
192	C₂×C₄×C₁₃	—	8	4	no	—
193	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
197	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₈×C₁₃	—	2	2	no	—
202	C₈×C₁₃	—	2	4	no	—
203	C₈×C₁₃	C₂×C₄²	1	4	yes	—
204	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
209	#440	C₄×C₁₃	1	16	yes	complemented
210	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
211	C₂×#107	C₂²×C₁₃	1	2	yes	—
212	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#103	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#97	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	2	1	no	—
222	C₄×C₄⋊C₄	—	2	2	no	—
223	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×C₂²⋊C₄	—	2	1	no	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	#376	—	2	1	no	—
230	#376	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#95	—	2	1	no	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
241	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₁₃	#576	1	1	yes	characteristic
243	C₂²×C₁₃	#577	1	2	yes	—
244	C₂²×C₁₃	#578	1	1	yes	characteristic
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	—	4	4	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
255	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
256	C₄×C₁₃	C₄×#41	1	2	yes	—
257	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
262	C₂×SD₁₆	C₂×C₄×C₁₃	1	8	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
269	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
273	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	#107	C₂×C₄×C₁₃	1	8	yes	complemented
291	#106	C₂×C₄×C₁₃	1	4	yes	complemented
292	#103	C₂×C₄×C₁₃	1	4	yes	complemented
293	#103	C₂×C₄×C₁₃	1	8	yes	complemented
294	#102	C₂×C₄×C₁₃	1	4	yes	—
295	#102	C₂×C₄×C₁₃	1	8	yes	—
296	#97	—	2	2	no	—
297	#97	C₂×C₄×C₁₃	1	8	yes	complemented
298	C₄×C₈	—	2	4	no	—
299	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	D₄×C₁₃	1	1	yes	characteristic
305	#95	D₄×C₁₃	1	1	yes	characteristic
306	#95	D₄×C₁₃	1	2	yes	—
307	C₂×C₁₃	—	4	4	no	—
308	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
309	C₂×C₁₃	#2946	1	2	yes	—
310	C₂×C₁₃	#2947	1	2	yes	—
311	C₂×C₁₃	#2949	1	1	yes	characteristic
312	C₂×C₁₃	#2951	1	1	yes	characteristic
313	C₂⁴	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
317	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	—	8	2	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
337	SD₁₆	C₄²×C₁₃	1	16	yes	complemented
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
342	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
343	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
344	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
352	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
353	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
354	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₄²	—	2	8	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	8	1	no	—
360	C₄²	—	8	1	no	—
361	C₄²	—	8	2	no	—
362	C₄²	—	8	2	no	—
363	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
364	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
365	C₄²	C₁₃×#41	1	4	yes	—
366	C₄²	C₁₃×#41	1	2	yes	—
367	C₁₃	#20504	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	4	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	4	no	—
376	Q₈	C₂×C₄²×C₁₃	1	4	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	2	4	no	—
379	D₄	C₂×C₄²×C₁₃	1	4	yes	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	8	8	no	—
401	C₂×C₄	—	8	4	no	—
402	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
403	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
404	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
405	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
406	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
409	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	2	4	no	—
412	C₈	C₂×C₄²×C₁₃	1	4	yes	—
413	C₂²	—	2	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
419	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
420	C₂²	C₁₃×#576	1	1	yes	characteristic
421	C₂²	C₁₃×#577	1	2	yes	—
422	C₂²	C₁₃×#578	1	1	yes	characteristic
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	C₂²×C₄²×C₁₃	1	1	yes	characteristic
433	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
434	C₄	C₄×C₁₃×#41	1	2	yes	—
435	C₂	—	4	4	no	—
436	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
437	C₂	C₁₃×#2946	1	2	yes	—
438	C₂	C₁₃×#2947	1	2	yes	—
439	C₂	C₁₃×#2949	1	1	yes	characteristic
440	C₂	C₁₃×#2951	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₄	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2276	C₂	semidirect
5. C₁₃×#1776	C₂	semidirect
6. C₄×C₁₃×#107	C₂	semidirect
7. C₁₃×#1763	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
11. C₁₃×#1726	C₂	semidirect
17. C₁₃×#440	C₄	semidirect
18. C₄×C₁₃×SD₁₆	C₄	semidirect
54. C₄×Q₈×C₁₃	C₂×C₄	semidirect
55. C₄×Q₈×C₁₃	C₂×C₄	semidirect
76. C₁₃×#107	C₂×C₄	semidirect
77. C₁₃×#106	C₂×C₄	semidirect
78. C₁₃×#103	C₂×C₄	semidirect
79. C₁₃×#103	C₂×C₄	semidirect
83. C₁₃×#97	C₂×C₄	semidirect
85. C₄×C₈×C₁₃	C₂×C₄	semidirect
93. #20504	C₁₃	direct (N × H)
118. C₁₃×SD₁₆	C₄²	semidirect
150. #2276	C₂×C₁₃	semidirect
152. #1776	C₂×C₁₃	semidirect
153. C₄×#107	C₂×C₁₃	semidirect
154. #1763	C₂×C₁₃	semidirect
156. C₄×#103	C₂×C₁₃	semidirect
158. #1726	C₂×C₁₃	semidirect
209. #440	C₄×C₁₃	semidirect
210. C₄×SD₁₆	C₄×C₁₃	semidirect
268. C₄×Q₈	C₂×C₄×C₁₃	semidirect
269. C₄×Q₈	C₂×C₄×C₁₃	semidirect
290. #107	C₂×C₄×C₁₃	semidirect
291. #106	C₂×C₄×C₁₃	semidirect
292. #103	C₂×C₄×C₁₃	semidirect
293. #103	C₂×C₄×C₁₃	semidirect
297. #97	C₂×C₄×C₁₃	semidirect
299. C₄×C₈	C₂×C₄×C₁₃	semidirect
337. SD₁₆	C₄²×C₁₃	semidirect
367. C₁₃	#20504	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×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2276	2
C₁₃×#2275	2
C₁₃×#1776	2
C₄×C₁₃×#107	2
C₁₃×#1763	2
C₁₃×#1762	2
C₄×C₁₃×#103	2
C₄×C₁₃×#102	2
C₁₃×#1726	2
#20504	13

Subgroups — C13×#20504 #15706843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20504 #15706843