Subgroups — C₁₃×#36720 #15723059

Order 3328.

2450 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2687	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2680	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2627	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2561	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2502	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2483	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2405	C₂	1	2	yes	maximal
11	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#543	—	2	8	no	—
15	C₂×C₁₃×#123	—	2	8	no	—
16	C₂×C₁₃×#123	C₂²	1	8	yes	—
17	C₂×C₁₃×#123	C₂²	1	4	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#400	C₂²	1	4	yes	complemented
30	C₁₃×#398	C₂²	1	8	yes	complemented
31	C₁₃×#398	C₂²	1	8	yes	complemented
32	C₁₃×#397	C₂²	1	4	yes	complemented
33	C₁₃×#397	C₂²	1	8	yes	complemented
34	C₁₃×#395	C₂²	1	4	yes	complemented
35	C₁₃×#394	C₂²	1	8	yes	—
36	C₁₃×#393	C₂²	1	4	yes	complemented
37	C₁₃×#391	C₂²	1	4	yes	complemented
38	C₁₃×#388	C₂²	1	8	yes	complemented
39	C₁₃×#388	C₂²	1	8	yes	complemented
40	C₁₃×#386	C₂²	1	4	yes	—
41	C₁₃×#385	C₂²	1	4	yes	—
42	C₁₃×#385	C₂²	1	4	yes	—
43	C₁₃×#385	C₂²	1	8	yes	complemented
44	C₁₃×#385	C₂²	1	4	yes	complemented
45	C₁₃×#384	C₂²	1	4	yes	complemented
46	C₁₃×#381	C₂²	1	4	yes	—
47	C₁₃×#381	C₂²	1	4	yes	complemented
48	C₁₃×#380	C₂²	1	2	yes	—
49	C₁₃×#380	C₂²	1	4	yes	complemented
50	C₁₃×#379	C₂²	1	4	yes	—
51	C₁₃×#379	C₂²	1	2	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	4	4	no	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₃	—	4	4	no	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#123	—	2	32	no	—
71	C₁₃×#123	—	4	8	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	8	no	—
74	C₁₃×C₂²⋊Q₈	—	2	16	no	—
75	C₁₃×C₂²⋊Q₈	—	2	16	no	—
76	C₁₃×C₂²⋊Q₈	—	4	8	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	8	yes	—
108	C₁₃×#95	C₂³	1	8	yes	—
109	#36720	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	4	2	no	—
115	C₂⁴×C₁₃	—	4	2	no	—
116	C₂⁴×C₁₃	—	4	2	no	—
117	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	4	4	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	16	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	4	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	—	4	16	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	4	8	no	—
163	C₁₃×C₄⋊C₄	—	4	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	16	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	4	8	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
174	C₄²×C₁₃	—	4	4	no	—
175	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic
177	#2848	C₂×C₁₃	1	2	yes	complemented
178	#2687	C₂×C₁₃	1	8	yes	complemented
179	#2680	C₂×C₁₃	1	8	yes	complemented
180	#2627	C₂×C₁₃	1	2	yes	complemented
181	#2561	C₂×C₁₃	1	2	yes	complemented
182	#2502	C₂×C₁₃	1	2	yes	complemented
183	#2483	C₂×C₁₃	1	2	yes	complemented
184	#2405	C₂×C₁₃	1	2	yes	—
185	#2312	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	8	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	2	8	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	16	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	—	8	8	no	—
203	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
204	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
206	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
207	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
208	Q₈×C₁₃	—	8	4	no	—
209	Q₈×C₁₃	—	8	4	no	—
210	D₄×C₁₃	—	4	16	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	8	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	4	4	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	16	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	8	4	no	—
233	C₂×C₄×C₁₃	—	8	4	no	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
238	#543	—	2	8	no	—
239	C₂×#123	—	2	8	no	—
240	C₂×#123	C₂²×C₁₃	1	8	yes	—
241	C₂×#123	C₂²×C₁₃	1	4	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
244	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
245	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
246	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	#400	C₂²×C₁₃	1	4	yes	complemented
254	#398	C₂²×C₁₃	1	8	yes	complemented
255	#398	C₂²×C₁₃	1	8	yes	complemented
256	#397	C₂²×C₁₃	1	4	yes	complemented
257	#397	C₂²×C₁₃	1	8	yes	complemented
258	#395	C₂²×C₁₃	1	4	yes	complemented
259	#394	C₂²×C₁₃	1	8	yes	—
260	#393	C₂²×C₁₃	1	4	yes	complemented
261	#391	C₂²×C₁₃	1	4	yes	complemented
262	#388	C₂²×C₁₃	1	8	yes	complemented
263	#388	C₂²×C₁₃	1	8	yes	complemented
264	#386	C₂²×C₁₃	1	4	yes	—
265	#385	C₂²×C₁₃	1	4	yes	—
266	#385	C₂²×C₁₃	1	4	yes	—
267	#385	C₂²×C₁₃	1	8	yes	complemented
268	#385	C₂²×C₁₃	1	4	yes	complemented
269	#384	C₂²×C₁₃	1	4	yes	complemented
270	#381	C₂²×C₁₃	1	4	yes	—
271	#381	C₂²×C₁₃	1	4	yes	complemented
272	#380	C₂²×C₁₃	1	2	yes	—
273	#380	C₂²×C₁₃	1	4	yes	complemented
274	#379	C₂²×C₁₃	1	4	yes	—
275	#379	C₂²×C₁₃	1	2	yes	—
276	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	4	no	—
284	C₂²×C₁₃	—	2	8	no	—
285	C₂²×C₁₃	—	4	16	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	8	no	—
290	C₂²×C₁₃	—	8	8	no	—
291	C₂²×C₁₃	#536	1	4	yes	—
292	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
295	C₂²×C₁₃	#585	1	2	yes	—
296	C₄×C₁₃	—	2	4	no	—
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₄×C₁₃	—	4	8	no	—
304	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
305	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
307	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	4	4	no	—
310	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
311	C₂³×C₄	—	2	4	no	—
312	C₂³×C₄	—	4	4	no	—
313	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
321	#123	—	2	32	no	—
322	#123	—	4	8	no	—
323	C₂²⋊Q₈	—	2	8	no	—
324	C₂²⋊Q₈	—	2	8	no	—
325	C₂²⋊Q₈	—	2	16	no	—
326	C₂²⋊Q₈	—	2	16	no	—
327	C₂²⋊Q₈	—	4	8	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
339	C₂×C₂²⋊C₄	—	2	4	no	—
340	C₂×C₂²⋊C₄	—	2	8	no	—
341	C₂×C₂²⋊C₄	—	2	4	no	—
342	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
354	#95	C₂³×C₁₃	1	4	yes	—
355	#95	C₂³×C₁₃	1	4	yes	—
356	#95	C₂³×C₁₃	1	8	yes	—
357	#95	C₂³×C₁₃	1	8	yes	—
358	#95	C₂³×C₁₃	1	8	yes	—
359	#95	C₂³×C₁₃	1	8	yes	—
360	C₂×C₁₃	—	2	4	no	—
361	C₂×C₁₃	—	4	4	no	—
362	C₂×C₁₃	—	4	4	no	—
363	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
364	C₂×C₁₃	#3484	1	1	yes	characteristic
365	C₂×C₁₃	#3485	1	1	yes	characteristic
366	C₂×C₁₃	#3535	1	4	yes	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
375	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
376	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
377	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	16	no	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄⋊C₄	—	4	8	no	—
420	C₄⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₂²⋊C₄	—	4	8	no	—
430	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
431	C₄²	—	4	4	no	—
432	C₁₃	#36720	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	16	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	8	8	no	—
450	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
451	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
453	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
454	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
455	Q₈	—	8	4	no	—
456	Q₈	—	8	4	no	—
457	D₄	—	4	16	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	16	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
483	C₂²	—	2	8	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	16	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	8	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	8	8	no	—
497	C₂²	C₁₃×#536	1	4	yes	—
498	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
499	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
500	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
501	C₂²	C₁₃×#585	1	2	yes	—
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	4	8	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₂	—	2	4	no	—
511	C₂	—	4	4	no	—
512	C₂	—	4	4	no	—
513	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
514	C₂	C₁₃×#3484	1	1	yes	characteristic
515	C₂	C₁₃×#3485	1	1	yes	characteristic
516	C₂	C₁₃×#3535	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#543	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2687	C₂	semidirect
5. C₁₃×#2680	C₂	semidirect
6. C₁₃×#2627	C₂	semidirect
7. C₁₃×#2561	C₂	semidirect
8. C₁₃×#2502	C₂	semidirect
9. C₁₃×#2483	C₂	semidirect
11. C₁₃×#2312	C₂	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₁₃×#400	C₂²	semidirect
30. C₁₃×#398	C₂²	semidirect
31. C₁₃×#398	C₂²	semidirect
32. C₁₃×#397	C₂²	semidirect
33. C₁₃×#397	C₂²	semidirect
34. C₁₃×#395	C₂²	semidirect
36. C₁₃×#393	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#388	C₂²	semidirect
39. C₁₃×#388	C₂²	semidirect
43. C₁₃×#385	C₂²	semidirect
44. C₁₃×#385	C₂²	semidirect
45. C₁₃×#384	C₂²	semidirect
47. C₁₃×#381	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
109. #36720	C₁₃	direct (N × H)
175. C₂×#543	C₂×C₁₃	semidirect
177. #2848	C₂×C₁₃	semidirect
178. #2687	C₂×C₁₃	semidirect
179. #2680	C₂×C₁₃	semidirect
180. #2627	C₂×C₁₃	semidirect
181. #2561	C₂×C₁₃	semidirect
182. #2502	C₂×C₁₃	semidirect
183. #2483	C₂×C₁₃	semidirect
185. #2312	C₂×C₁₃	semidirect
244. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
245. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
246. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
253. #400	C₂²×C₁₃	semidirect
254. #398	C₂²×C₁₃	semidirect
255. #398	C₂²×C₁₃	semidirect
256. #397	C₂²×C₁₃	semidirect
257. #397	C₂²×C₁₃	semidirect
258. #395	C₂²×C₁₃	semidirect
260. #393	C₂²×C₁₃	semidirect
261. #391	C₂²×C₁₃	semidirect
262. #388	C₂²×C₁₃	semidirect
263. #388	C₂²×C₁₃	semidirect
267. #385	C₂²×C₁₃	semidirect
268. #385	C₂²×C₁₃	semidirect
269. #384	C₂²×C₁₃	semidirect
271. #381	C₂²×C₁₃	semidirect
273. #380	C₂²×C₁₃	semidirect
432. C₁₃	#36720	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×#543	2
C₂²×C₁₃×#123	2
C₁₃×#2848	2
C₁₃×#2687	2
C₁₃×#2680	2
C₁₃×#2627	2
C₁₃×#2561	2
C₁₃×#2502	2
C₁₃×#2483	2
C₁₃×#2405	2
C₁₃×#2312	2
#36720	13

Subgroups — C13×#36720 #15723059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36720 #15723059