Subgroups — C₁₃×#36714 #15723053

Order 3328.

4170 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2697	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2679	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2678	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2622	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2411	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2405	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2403	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#534	—	2	8	no	—
17	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
18	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#120	—	2	8	no	—
22	C₂×C₁₃×#120	C₂²	1	2	yes	—
23	C₂×C₁₃×#120	C₂²	1	4	yes	—
24	C₂×C₁₃×#120	C₂²	1	4	yes	—
25	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#397	C₂²	1	8	yes	complemented
34	C₁₃×#396	C₂²	1	8	yes	complemented
35	C₁₃×#394	C₂²	1	8	yes	complemented
36	C₁₃×#394	C₂²	1	8	yes	complemented
37	C₁₃×#394	C₂²	1	8	yes	complemented
38	C₁₃×#392	C₂²	1	8	yes	complemented
39	C₁₃×#390	C₂²	1	4	yes	complemented
40	C₁₃×#390	C₂²	1	4	yes	complemented
41	C₁₃×#390	C₂²	1	8	yes	complemented
42	C₁₃×#388	C₂²	1	8	yes	complemented
43	C₁₃×#386	C₂²	1	4	yes	complemented
44	C₁₃×#386	C₂²	1	4	yes	complemented
45	C₁₃×#386	C₂²	1	4	yes	complemented
46	C₁₃×#385	C₂²	1	4	yes	complemented
47	C₁₃×#379	C₂²	1	2	yes	complemented
48	C₁₃×#379	C₂²	1	4	yes	complemented
49	C₁₃×#379	C₂²	1	8	yes	complemented
50	C₁₃×#379	C₂²	1	2	yes	complemented
51	C₂⁵×C₁₃	—	2	4	no	—
52	C₂⁵×C₁₃	—	4	8	no	—
53	C₂⁵×C₁₃	—	4	4	no	—
54	C₂⁵×C₁₃	C₂³	1	2	yes	—
55	C₂⁵×C₁₃	C₂³	1	4	yes	—
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
58	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	—	4	8	no	—
63	C₂²×D₄×C₁₃	—	4	4	no	—
64	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
77	C₁₃×#123	—	2	8	no	—
78	C₁₃×#123	—	2	8	no	—
79	C₁₃×#123	—	4	8	no	—
80	C₁₃×#121	—	2	16	no	—
81	C₁₃×#120	—	2	8	no	—
82	C₁₃×#120	—	2	16	no	—
83	C₁₃×#120	—	2	16	no	—
84	C₁₃×#120	—	2	8	no	—
85	C₁₃×#120	—	4	8	no	—
86	C₁₃×#120	—	4	16	no	—
87	C₁₃×#120	—	4	8	no	—
88	C₁₃×#117	—	4	4	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
92	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
109	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
110	C₁₃×#95	C₂³	1	8	yes	complemented
111	C₁₃×#95	C₂³	1	8	yes	complemented
112	#36714	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	8	no	—
118	C₂⁴×C₁₃	—	2	16	no	—
119	C₂⁴×C₁₃	—	2	8	no	—
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	—	4	4	no	—
122	C₂⁴×C₁₃	—	4	4	no	—
123	C₂⁴×C₁₃	—	4	8	no	—
124	C₂⁴×C₁₃	—	4	4	no	—
125	C₂⁴×C₁₃	—	4	4	no	—
126	C₂⁴×C₁₃	—	4	4	no	—
127	C₂⁴×C₁₃	—	4	2	no	—
128	C₂⁴×C₁₃	—	4	4	no	—
129	C₂⁴×C₁₃	—	4	32	no	—
130	C₂⁴×C₁₃	—	4	16	no	—
131	C₂⁴×C₁₃	—	4	64	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
133	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
135	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	4	16	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	2	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	4	2	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂×D₄×C₁₃	—	4	4	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	32	no	—
161	C₂×D₄×C₁₃	—	4	16	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
163	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	4	4	no	—
179	C₁₃×C₄⋊C₄	—	4	8	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	16	no	—
186	C₁₃×C₂²⋊C₄	—	2	16	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	4	8	no	—
189	C₁₃×C₂²⋊C₄	—	4	8	no	—
190	C₁₃×C₂²⋊C₄	—	4	8	no	—
191	C₁₃×C₂²⋊C₄	—	4	4	no	—
192	C₁₃×C₂²⋊C₄	—	4	8	no	—
193	C₁₃×C₂²⋊C₄	—	4	4	no	—
194	C₄²×C₁₃	—	4	4	no	—
195	C₂×#534	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2846	C₂×C₁₃	1	2	yes	complemented
198	#2697	C₂×C₁₃	1	4	yes	complemented
199	#2679	C₂×C₁₃	1	4	yes	complemented
200	#2678	C₂×C₁₃	1	8	yes	complemented
201	#2622	C₂×C₁₃	1	2	yes	complemented
202	#2411	C₂×C₁₃	1	4	yes	complemented
203	#2405	C₂×C₁₃	1	2	yes	complemented
204	#2403	C₂×C₁₃	1	2	yes	complemented
205	#2309	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	16	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	8	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	2	8	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	8	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	8	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	4	8	no	—
225	C₂³×C₁₃	—	4	8	no	—
226	C₂³×C₁₃	—	4	32	no	—
227	C₂³×C₁₃	—	4	32	no	—
228	C₂³×C₁₃	—	4	16	no	—
229	C₂³×C₁₃	—	4	8	no	—
230	C₂³×C₁₃	—	4	16	no	—
231	C₂³×C₁₃	—	4	16	no	—
232	C₂³×C₁₃	—	4	32	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	128	no	—
235	C₂³×C₁₃	—	4	16	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	8	8	no	—
238	C₂³×C₁₃	—	8	4	no	—
239	C₂³×C₁₃	—	8	8	no	—
240	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
245	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
246	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
247	D₄×C₁₃	—	4	8	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	16	no	—
250	D₄×C₁₃	—	4	16	no	—
251	D₄×C₁₃	—	4	8	no	—
252	D₄×C₁₃	—	4	8	no	—
253	D₄×C₁₃	—	8	8	no	—
254	D₄×C₁₃	—	8	16	no	—
255	C₂×C₄×C₁₃	—	2	8	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	8	no	—
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	8	no	—
264	C₂×C₄×C₁₃	—	2	8	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	8	4	no	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
272	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic, complemented
273	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
274	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	#534	—	2	8	no	—
277	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
278	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
279	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
280	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
281	C₂×#120	—	2	8	no	—
282	C₂×#120	C₂²×C₁₃	1	2	yes	—
283	C₂×#120	C₂²×C₁₃	1	4	yes	—
284	C₂×#120	C₂²×C₁₃	1	4	yes	—
285	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
286	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
287	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
288	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
289	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
290	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
292	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#397	C₂²×C₁₃	1	8	yes	complemented
294	#396	C₂²×C₁₃	1	8	yes	complemented
295	#394	C₂²×C₁₃	1	8	yes	complemented
296	#394	C₂²×C₁₃	1	8	yes	complemented
297	#394	C₂²×C₁₃	1	8	yes	complemented
298	#392	C₂²×C₁₃	1	8	yes	complemented
299	#390	C₂²×C₁₃	1	4	yes	complemented
300	#390	C₂²×C₁₃	1	4	yes	complemented
301	#390	C₂²×C₁₃	1	8	yes	complemented
302	#388	C₂²×C₁₃	1	8	yes	complemented
303	#386	C₂²×C₁₃	1	4	yes	complemented
304	#386	C₂²×C₁₃	1	4	yes	complemented
305	#386	C₂²×C₁₃	1	4	yes	complemented
306	#385	C₂²×C₁₃	1	4	yes	complemented
307	#379	C₂²×C₁₃	1	2	yes	complemented
308	#379	C₂²×C₁₃	1	4	yes	complemented
309	#379	C₂²×C₁₃	1	8	yes	complemented
310	#379	C₂²×C₁₃	1	2	yes	complemented
311	C₂²×C₁₃	—	2	4	no	—
312	C₂²×C₁₃	—	2	8	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	4	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	2	8	no	—
318	C₂²×C₁₃	—	2	4	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	2	16	no	—
321	C₂²×C₁₃	—	4	32	no	—
322	C₂²×C₁₃	—	4	16	no	—
323	C₂²×C₁₃	—	4	64	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	8	no	—
328	C₂²×C₁₃	—	4	4	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	8	no	—
334	C₂²×C₁₃	—	8	8	no	—
335	C₂²×C₁₃	—	8	8	no	—
336	C₂²×C₁₃	#534	1	4	yes	—
337	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
338	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
339	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
340	C₄×C₁₃	—	2	4	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	8	no	—
345	C₂⁵	—	2	4	no	—
346	C₂⁵	—	4	8	no	—
347	C₂⁵	—	4	4	no	—
348	C₂⁵	C₂³×C₁₃	1	2	yes	—
349	C₂⁵	C₂³×C₁₃	1	4	yes	—
350	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
351	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
352	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic, complemented
353	C₂²×D₄	—	2	8	no	—
354	C₂²×D₄	—	2	4	no	—
355	C₂²×D₄	—	4	4	no	—
356	C₂²×D₄	—	4	8	no	—
357	C₂²×D₄	—	4	4	no	—
358	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
359	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
360	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
361	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
362	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
363	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
367	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
371	#123	—	2	8	no	—
372	#123	—	2	8	no	—
373	#123	—	4	8	no	—
374	#121	—	2	16	no	—
375	#120	—	2	8	no	—
376	#120	—	2	16	no	—
377	#120	—	2	16	no	—
378	#120	—	2	8	no	—
379	#120	—	4	8	no	—
380	#120	—	4	16	no	—
381	#120	—	4	8	no	—
382	#117	—	4	4	no	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	8	no	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
399	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
403	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
404	#95	C₂³×C₁₃	1	8	yes	complemented
405	#95	C₂³×C₁₃	1	8	yes	complemented
406	C₂×C₁₃	—	2	4	no	—
407	C₂×C₁₃	—	4	4	no	—
408	C₂×C₁₃	—	4	8	no	—
409	C₂×C₁₃	—	4	2	no	—
410	C₂×C₁₃	—	4	2	no	—
411	C₂×C₁₃	—	8	2	no	—
412	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
413	C₂×C₁₃	#3484	1	2	yes	—
414	C₂×C₁₃	#3532	1	4	yes	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	2	8	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	2	8	no	—
420	C₂⁴	—	2	16	no	—
421	C₂⁴	—	2	8	no	—
422	C₂⁴	—	2	2	no	—
423	C₂⁴	—	4	4	no	—
424	C₂⁴	—	4	4	no	—
425	C₂⁴	—	4	4	no	—
426	C₂⁴	—	4	8	no	—
427	C₂⁴	—	4	4	no	—
428	C₂⁴	—	4	4	no	—
429	C₂⁴	—	4	2	no	—
430	C₂⁴	—	4	4	no	—
431	C₂⁴	—	4	32	no	—
432	C₂⁴	—	4	16	no	—
433	C₂⁴	—	4	64	no	—
434	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
435	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
436	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
437	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
438	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
439	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
441	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	16	no	—
451	C₂×D₄	—	4	16	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	2	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	8	no	—
460	C₂×D₄	—	4	8	no	—
461	C₂×D₄	—	4	8	no	—
462	C₂×D₄	—	4	32	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
465	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	4	4	no	—
481	C₄⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	16	no	—
488	C₂²⋊C₄	—	2	16	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	4	8	no	—
491	C₂²⋊C₄	—	4	8	no	—
492	C₂²⋊C₄	—	4	8	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₂²⋊C₄	—	4	8	no	—
495	C₂²⋊C₄	—	4	4	no	—
496	C₄²	—	4	4	no	—
497	C₁₃	#36714	1	1	yes	characteristic, direct product factor, Sylow
498	C₂³	—	2	4	no	—
499	C₂³	—	2	16	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	8	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	8	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	8	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	4	8	no	—
517	C₂³	—	4	8	no	—
518	C₂³	—	4	32	no	—
519	C₂³	—	4	16	no	—
520	C₂³	—	4	32	no	—
521	C₂³	—	4	16	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	32	no	—
524	C₂³	—	4	16	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	128	no	—
527	C₂³	—	4	16	no	—
528	C₂³	—	4	8	no	—
529	C₂³	—	8	8	no	—
530	C₂³	—	8	4	no	—
531	C₂³	—	8	8	no	—
532	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
533	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
534	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
535	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
536	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
537	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
538	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
539	D₄	—	4	8	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	16	no	—
542	D₄	—	4	16	no	—
543	D₄	—	4	8	no	—
544	D₄	—	4	8	no	—
545	D₄	—	8	16	no	—
546	D₄	—	8	8	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
564	C₂²	—	2	8	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	2	16	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	4	32	no	—
575	C₂²	—	4	16	no	—
576	C₂²	—	4	64	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	8	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	8	8	no	—
588	C₂²	—	8	8	no	—
589	C₂²	C₁₃×#534	1	4	yes	—
590	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
591	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
592	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
593	C₄	—	2	4	no	—
594	C₄	—	4	8	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	4	no	—
597	C₄	—	4	4	no	—
598	C₂	—	2	4	no	—
599	C₂	—	4	8	no	—
600	C₂	—	4	4	no	—
601	C₂	—	4	2	no	—
602	C₂	—	4	2	no	—
603	C₂	—	8	2	no	—
604	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
605	C₂	C₁₃×#3484	1	2	yes	—
606	C₂	C₁₃×#3532	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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×#534	C₂	semidirect
2. C₂²×C₁₃×#120	C₂	semidirect
3. C₁₃×#2846	C₂	semidirect
4. C₁₃×#2697	C₂	semidirect
5. C₁₃×#2679	C₂	semidirect
6. C₁₃×#2678	C₂	semidirect
7. C₁₃×#2622	C₂	semidirect
8. C₁₃×#2411	C₂	semidirect
9. C₁₃×#2405	C₂	semidirect
10. C₁₃×#2403	C₂	semidirect
11. C₁₃×#2309	C₂	semidirect
12. C₂⁶×C₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂×C₁₃×#123	C₂²	semidirect
18. C₂×C₁₃×#123	C₂²	semidirect
19. C₂×C₁₃×#123	C₂²	semidirect
20. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#120	C₂²	semidirect
26. C₂×C₁₃×#120	C₂²	semidirect
27. C₂×C₁₃×#120	C₂²	semidirect
28. C₂×C₁₃×#120	C₂²	semidirect
29. C₂×C₁₃×#117	C₂²	semidirect
30. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
31. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
32. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
33. C₁₃×#397	C₂²	semidirect
34. C₁₃×#396	C₂²	semidirect
35. C₁₃×#394	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#394	C₂²	semidirect
38. C₁₃×#392	C₂²	semidirect
39. C₁₃×#390	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#390	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#386	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
47. C₁₃×#379	C₂²	semidirect
48. C₁₃×#379	C₂²	semidirect
49. C₁₃×#379	C₂²	semidirect
50. C₁₃×#379	C₂²	semidirect
58. C₂⁵×C₁₃	C₂³	semidirect
64. C₂²×D₄×C₁₃	D₄	semidirect
72. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂³×C₄×C₁₃	C₂³	semidirect
76. C₂³×C₄×C₁₃	C₂³	semidirect
89. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
90. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
91. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
104. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
105. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
106. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
107. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
108. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
109. C₂×C₄²×C₁₃	C₂³	semidirect
110. C₁₃×#95	C₂³	semidirect
111. C₁₃×#95	C₂³	semidirect
112. #36714	C₁₃	direct (N × H)
195. C₂×#534	C₂×C₁₃	semidirect
196. C₂²×#120	C₂×C₁₃	semidirect
197. #2846	C₂×C₁₃	semidirect
198. #2697	C₂×C₁₃	semidirect
199. #2679	C₂×C₁₃	semidirect
200. #2678	C₂×C₁₃	semidirect
201. #2622	C₂×C₁₃	semidirect
202. #2411	C₂×C₁₃	semidirect
203. #2405	C₂×C₁₃	semidirect
204. #2403	C₂×C₁₃	semidirect
205. #2309	C₂×C₁₃	semidirect
272. C₂⁶	C₂²×C₁₃	semidirect
275. C₂³×D₄	C₂²×C₁₃	semidirect
277. C₂×#123	C₂²×C₁₃	semidirect
278. C₂×#123	C₂²×C₁₃	semidirect
279. C₂×#123	C₂²×C₁₃	semidirect
280. C₂×#121	C₂²×C₁₃	semidirect
285. C₂×#120	C₂²×C₁₃	semidirect
286. C₂×#120	C₂²×C₁₃	semidirect
287. C₂×#120	C₂²×C₁₃	semidirect
288. C₂×#120	C₂²×C₁₃	semidirect
289. C₂×#117	C₂²×C₁₃	semidirect
290. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
291. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
292. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
293. #397	C₂²×C₁₃	semidirect
294. #396	C₂²×C₁₃	semidirect
295. #394	C₂²×C₁₃	semidirect
296. #394	C₂²×C₁₃	semidirect
297. #394	C₂²×C₁₃	semidirect
298. #392	C₂²×C₁₃	semidirect
299. #390	C₂²×C₁₃	semidirect
300. #390	C₂²×C₁₃	semidirect
301. #390	C₂²×C₁₃	semidirect
302. #388	C₂²×C₁₃	semidirect
303. #386	C₂²×C₁₃	semidirect
304. #386	C₂²×C₁₃	semidirect
305. #386	C₂²×C₁₃	semidirect
306. #385	C₂²×C₁₃	semidirect
307. #379	C₂²×C₁₃	semidirect
308. #379	C₂²×C₁₃	semidirect
309. #379	C₂²×C₁₃	semidirect
310. #379	C₂²×C₁₃	semidirect
352. C₂⁵	C₂³×C₁₃	semidirect
358. C₂²×D₄	D₄×C₁₃	semidirect
366. C₂²×D₄	C₂³×C₁₃	semidirect
369. C₂³×C₄	C₂³×C₁₃	semidirect
370. C₂³×C₄	C₂³×C₁₃	semidirect
383. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
384. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
385. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
398. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
399. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
400. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
401. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
402. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
403. C₂×C₄²	C₂³×C₁₃	semidirect
404. #95	C₂³×C₁₃	semidirect
405. #95	C₂³×C₁₃	semidirect
497. C₁₃	#36714	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×#534	2
C₂²×C₁₃×#120	2
C₁₃×#2846	2
C₁₃×#2697	2
C₁₃×#2679	2
C₁₃×#2678	2
C₁₃×#2622	2
C₁₃×#2411	2
C₁₃×#2405	2
C₁₃×#2403	2
C₁₃×#2309	2
#36714	13

Subgroups — C13×#36714 #15723053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36714 #15723053