Subgroups — C₁₃×#34981 #15721320

Order 3328.

5126 conjugacy classes of subgroups.

The subgroup lattice has 544 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	2	yes	maximal, complemented
3	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2847	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2617	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2412	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2410	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2308	C₂	1	2	yes	maximal, complemented
10	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
14	C₁₃×#534	—	2	8	no	—
15	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
18	C₂×C₁₃×#120	—	2	16	no	—
19	C₂×C₁₃×#120	C₂²	1	8	yes	—
20	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
30	C₁₃×#397	C₂²	1	8	yes	complemented
31	C₁₃×#394	C₂²	1	16	yes	complemented
32	C₁₃×#392	C₂²	1	8	yes	complemented
33	C₁₃×#386	C₂²	1	8	yes	complemented
34	C₁₃×#386	C₂²	1	8	yes	complemented
35	C₁₃×#386	C₂²	1	16	yes	complemented
36	C₁₃×#385	C₂²	1	8	yes	complemented
37	C₁₃×#381	C₂²	1	4	yes	complemented
38	C₁₃×#380	C₂²	1	4	yes	complemented
39	C₁₃×#380	C₂²	1	8	yes	complemented
40	C₁₃×#379	C₂²	1	4	yes	complemented
41	C₂⁵×C₁₃	—	2	4	no	—
42	C₂⁵×C₁₃	—	2	4	no	—
43	C₂⁵×C₁₃	—	4	8	no	—
44	C₂⁵×C₁₃	D₄	1	8	yes	complemented
45	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
46	C₂⁵×C₁₃	C₂³	1	4	yes	—
47	C₂⁵×C₁₃	C₂³	1	2	yes	—
48	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
49	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	—	2	8	no	—
51	C₂²×D₄×C₁₃	—	2	16	no	—
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	4	16	no	—
55	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	—	4	8	no	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₁₃×#123	—	2	16	no	—
68	C₁₃×#121	—	2	16	no	—
69	C₁₃×#121	—	4	16	no	—
70	C₁₃×#120	—	2	32	no	—
71	C₁₃×#120	—	2	16	no	—
72	C₁₃×#120	—	2	16	no	—
73	C₁₃×#120	—	2	16	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
76	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
81	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
91	C₁₃×#95	C₂³	1	16	yes	complemented
92	C₁₃×#95	C₂³	1	8	yes	complemented
93	#34981	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	—	2	8	no	—
97	C₂⁴×C₁₃	—	2	32	no	—
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	2	no	—
100	C₂⁴×C₁₃	—	2	8	no	—
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂⁴×C₁₃	—	2	16	no	—
103	C₂⁴×C₁₃	—	2	4	no	—
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	4	no	—
106	C₂⁴×C₁₃	—	4	32	no	—
107	C₂⁴×C₁₃	—	4	4	no	—
108	C₂⁴×C₁₃	—	4	8	no	—
109	C₂⁴×C₁₃	—	4	4	no	—
110	C₂⁴×C₁₃	—	4	8	no	—
111	C₂⁴×C₁₃	—	4	32	no	—
112	C₂⁴×C₁₃	—	4	32	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
114	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
115	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
116	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
117	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
118	C₂⁴×C₁₃	#41	1	4	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
121	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
122	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
124	C₂×D₄×C₁₃	—	2	16	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	16	no	—
128	C₂×D₄×C₁₃	—	2	8	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	8	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	32	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	4	16	no	—
135	C₂×D₄×C₁₃	—	4	8	no	—
136	C₂×D₄×C₁₃	—	4	64	no	—
137	C₂×D₄×C₁₃	—	4	32	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	16	no	—
144	C₂²×C₄×C₁₃	—	2	16	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	4	no	—
148	C₂²×C₄×C₁₃	—	4	8	no	—
149	C₂²×C₄×C₁₃	—	4	32	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	4	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	16	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	16	no	—
162	C₁₃×C₂²⋊C₄	—	2	16	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	4	16	no	—
165	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
166	C₂×#534	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂²×#120	C₂×C₁₃	1	2	yes	complemented
168	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2847	C₂×C₁₃	1	4	yes	complemented
170	#2617	C₂×C₁₃	1	4	yes	complemented
171	#2412	C₂×C₁₃	1	8	yes	complemented
172	#2410	C₂×C₁₃	1	8	yes	complemented
173	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2308	C₂×C₁₃	1	2	yes	complemented
175	C₂³×C₁₃	—	2	16	no	—
176	C₂³×C₁₃	—	2	16	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	16	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	2	8	no	—
184	C₂³×C₁₃	—	2	32	no	—
185	C₂³×C₁₃	—	2	8	no	—
186	C₂³×C₁₃	—	2	32	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	16	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	4	16	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	32	no	—
200	C₂³×C₁₃	—	4	32	no	—
201	C₂³×C₁₃	—	4	128	no	—
202	C₂³×C₁₃	—	4	8	no	—
203	C₂³×C₁₃	—	4	8	no	—
204	C₂³×C₁₃	—	4	16	no	—
205	C₂³×C₁₃	—	4	8	no	—
206	C₂³×C₁₃	—	8	8	no	—
207	C₂³×C₁₃	—	8	8	no	—
208	C₂³×C₁₃	#121	1	16	yes	complemented
209	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
215	C₂³×C₁₃	C₂×#41	1	4	yes	—
216	C₂³×C₁₃	C₂×#41	1	2	yes	—
217	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
218	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
219	D₄×C₁₃	—	4	32	no	—
220	D₄×C₁₃	—	4	16	no	—
221	D₄×C₁₃	—	4	16	no	—
222	D₄×C₁₃	—	4	32	no	—
223	D₄×C₁₃	—	8	8	no	—
224	C₂×C₄×C₁₃	—	2	8	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	16	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	32	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	—	4	16	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
238	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
239	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
240	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
241	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
242	#534	—	2	8	no	—
243	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
244	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
245	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
246	C₂×#120	—	2	16	no	—
247	C₂×#120	C₂²×C₁₃	1	8	yes	—
248	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
249	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
250	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
251	C₂²×C₂²⋊C₄	—	2	8	no	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
254	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
256	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
257	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
258	#397	C₂²×C₁₃	1	8	yes	complemented
259	#394	C₂²×C₁₃	1	16	yes	complemented
260	#392	C₂²×C₁₃	1	8	yes	complemented
261	#386	C₂²×C₁₃	1	8	yes	complemented
262	#386	C₂²×C₁₃	1	8	yes	complemented
263	#386	C₂²×C₁₃	1	16	yes	complemented
264	#385	C₂²×C₁₃	1	8	yes	complemented
265	#381	C₂²×C₁₃	1	4	yes	complemented
266	#380	C₂²×C₁₃	1	4	yes	complemented
267	#380	C₂²×C₁₃	1	8	yes	complemented
268	#379	C₂²×C₁₃	1	4	yes	complemented
269	C₂²×C₁₃	—	2	32	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	2	8	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	—	2	8	no	—
277	C₂²×C₁₃	—	2	4	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	8	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	8	no	—
282	C₂²×C₁₃	—	4	16	no	—
283	C₂²×C₁₃	—	4	64	no	—
284	C₂²×C₁₃	—	4	16	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	4	4	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	4	8	no	—
289	C₂²×C₁₃	—	4	8	no	—
290	C₂²×C₁₃	—	4	8	no	—
291	C₂²×C₁₃	—	8	16	no	—
292	C₂²×C₁₃	C₂×#121	1	8	yes	—
293	C₂²×C₁₃	C₂×#121	1	4	yes	—
294	C₂²×C₁₃	#534	1	8	yes	complemented
295	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
296	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
297	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
299	C₄×C₁₃	—	2	8	no	—
300	C₄×C₁₃	—	4	4	no	—
301	C₄×C₁₃	—	4	8	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₂⁵	—	2	4	no	—
304	C₂⁵	—	2	4	no	—
305	C₂⁵	—	4	8	no	—
306	C₂⁵	D₄×C₁₃	1	8	yes	complemented
307	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
308	C₂⁵	C₂³×C₁₃	1	4	yes	—
309	C₂⁵	C₂³×C₁₃	1	2	yes	—
310	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
311	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	—	2	8	no	—
313	C₂²×D₄	—	2	16	no	—
314	C₂²×D₄	—	2	8	no	—
315	C₂²×D₄	—	2	8	no	—
316	C₂²×D₄	—	4	16	no	—
317	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
319	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
322	C₂³×C₄	—	2	8	no	—
323	C₂³×C₄	—	4	8	no	—
324	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
328	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
329	#123	—	2	16	no	—
330	#121	—	2	16	no	—
331	#121	—	4	16	no	—
332	#120	—	2	32	no	—
333	#120	—	2	16	no	—
334	#120	—	2	16	no	—
335	#120	—	2	16	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	—	2	16	no	—
341	C₂×C₂²⋊C₄	—	2	8	no	—
342	C₂×C₂²⋊C₄	—	2	32	no	—
343	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
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	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
353	#95	C₂³×C₁₃	1	16	yes	complemented
354	#95	C₂³×C₁₃	1	8	yes	complemented
355	C₂×C₁₃	—	2	4	no	—
356	C₂×C₁₃	—	2	8	no	—
357	C₂×C₁₃	—	2	8	no	—
358	C₂×C₁₃	—	4	4	no	—
359	C₂×C₁₃	—	8	4	no	—
360	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
361	C₂×C₁₃	C₂×#534	1	2	yes	—
362	C₂×C₁₃	#3484	1	2	yes	—
363	C₂×C₁₃	#3490	1	2	yes	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	8	no	—
367	C₂⁴	—	2	32	no	—
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	2	8	no	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	16	no	—
373	C₂⁴	—	2	4	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	4	32	no	—
377	C₂⁴	—	4	4	no	—
378	C₂⁴	—	4	8	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	—	4	8	no	—
381	C₂⁴	—	4	32	no	—
382	C₂⁴	—	4	32	no	—
383	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
384	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
385	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
386	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
387	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
388	C₂⁴	C₁₃×#41	1	4	yes	—
389	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
390	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
391	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
392	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
394	C₂×D₄	—	2	16	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	32	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	4	16	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	—	4	64	no	—
407	C₂×D₄	—	4	32	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	16	no	—
414	C₂²×C₄	—	2	16	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	8	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	8	no	—
419	C₂²×C₄	—	4	32	no	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	complemented
421	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	4	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	16	no	—
432	C₂²⋊C₄	—	2	16	no	—
433	C₂²⋊C₄	—	2	16	no	—
434	C₂²⋊C₄	—	4	16	no	—
435	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
436	C₁₃	#34981	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	16	no	—
438	C₂³	—	2	16	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	32	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	32	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	16	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	16	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	32	no	—
462	C₂³	—	4	32	no	—
463	C₂³	—	4	128	no	—
464	C₂³	—	4	8	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	16	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	8	8	no	—
469	C₂³	—	8	8	no	—
470	C₂³	C₁₃×#121	1	16	yes	complemented
471	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
472	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
474	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
476	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
477	C₂³	C₂×C₁₃×#41	1	4	yes	—
478	C₂³	C₂×C₁₃×#41	1	2	yes	—
479	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
480	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
481	D₄	—	4	32	no	—
482	D₄	—	4	16	no	—
483	D₄	—	4	16	no	—
484	D₄	—	4	32	no	—
485	D₄	—	8	8	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	16	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	32	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	16	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
500	C₂²	—	2	32	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	8	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	2	8	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	4	64	no	—
515	C₂²	—	4	16	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	8	no	—
520	C₂²	—	4	8	no	—
521	C₂²	—	4	8	no	—
522	C₂²	—	8	16	no	—
523	C₂²	C₂×C₁₃×#121	1	8	yes	—
524	C₂²	C₂×C₁₃×#121	1	4	yes	—
525	C₂²	C₁₃×#534	1	8	yes	complemented
526	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
527	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
528	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
529	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
530	C₄	—	2	8	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	8	no	—
533	C₄	—	4	4	no	—
534	C₂	—	2	4	no	—
535	C₂	—	2	8	no	—
536	C₂	—	2	8	no	—
537	C₂	—	4	4	no	—
538	C₂	—	8	4	no	—
539	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
540	C₂	C₂×C₁₃×#534	1	2	yes	—
541	C₂	C₁₃×#3484	1	2	yes	—
542	C₂	C₁₃×#3490	1	2	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. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2617	C₂	semidirect
6. C₁₃×#2412	C₂	semidirect
7. C₁₃×#2410	C₂	semidirect
8. C₁₃×#2315	C₂	semidirect
9. C₁₃×#2308	C₂	semidirect
12. C₂³×D₄×C₁₃	C₂²	semidirect
13. C₂⁴×C₄×C₁₃	C₂²	semidirect
15. C₂×C₁₃×#123	C₂²	semidirect
16. C₂×C₁₃×#121	C₂²	semidirect
17. C₂×C₁₃×#121	C₂²	semidirect
20. C₂×C₁₃×#120	C₂²	semidirect
21. C₂×C₁₃×#120	C₂²	semidirect
22. C₂×C₁₃×#120	C₂²	semidirect
27. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
29. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
30. C₁₃×#397	C₂²	semidirect
31. C₁₃×#394	C₂²	semidirect
32. C₁₃×#392	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#386	C₂²	semidirect
35. C₁₃×#386	C₂²	semidirect
36. C₁₃×#385	C₂²	semidirect
37. C₁₃×#381	C₂²	semidirect
38. C₁₃×#380	C₂²	semidirect
39. C₁₃×#380	C₂²	semidirect
40. C₁₃×#379	C₂²	semidirect
44. C₂⁵×C₁₃	D₄	semidirect
59. C₂²×D₄×C₁₃	C₂³	semidirect
74. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
75. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
81. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
89. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
90. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
91. C₁₃×#95	C₂³	semidirect
92. C₁₃×#95	C₂³	semidirect
93. #34981	C₁₃	direct (N × H)
150. C₂²×C₄×C₁₃	C₂×D₄	semidirect
165. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
166. C₂×#534	C₂×C₁₃	semidirect
167. C₂²×#120	C₂×C₁₃	semidirect
168. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
169. #2847	C₂×C₁₃	semidirect
170. #2617	C₂×C₁₃	semidirect
171. #2412	C₂×C₁₃	semidirect
172. #2410	C₂×C₁₃	semidirect
173. #2315	C₂×C₁₃	semidirect
174. #2308	C₂×C₁₃	semidirect
208. C₂³×C₁₃	#121	semidirect
240. C₂³×D₄	C₂²×C₁₃	semidirect
241. C₂⁴×C₄	C₂²×C₁₃	semidirect
243. C₂×#123	C₂²×C₁₃	semidirect
244. C₂×#121	C₂²×C₁₃	semidirect
245. C₂×#121	C₂²×C₁₃	semidirect
248. C₂×#120	C₂²×C₁₃	semidirect
249. C₂×#120	C₂²×C₁₃	semidirect
250. C₂×#120	C₂²×C₁₃	semidirect
255. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
256. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
257. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
258. #397	C₂²×C₁₃	semidirect
259. #394	C₂²×C₁₃	semidirect
260. #392	C₂²×C₁₃	semidirect
261. #386	C₂²×C₁₃	semidirect
262. #386	C₂²×C₁₃	semidirect
263. #386	C₂²×C₁₃	semidirect
264. #385	C₂²×C₁₃	semidirect
265. #381	C₂²×C₁₃	semidirect
266. #380	C₂²×C₁₃	semidirect
267. #380	C₂²×C₁₃	semidirect
268. #379	C₂²×C₁₃	semidirect
294. C₂²×C₁₃	#534	semidirect
306. C₂⁵	D₄×C₁₃	semidirect
321. C₂²×D₄	C₂³×C₁₃	semidirect
336. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
337. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
343. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
351. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
352. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
353. #95	C₂³×C₁₃	semidirect
354. #95	C₂³×C₁₃	semidirect
420. C₂²×C₄	C₂×D₄×C₁₃	semidirect
435. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
436. C₁₃	#34981	direct (N × H)
470. C₂³	C₁₃×#121	semidirect
525. C₂²	C₁₃×#534	semidirect

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
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2847	2
C₁₃×#2617	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2315	2
C₁₃×#2308	2
#34981	13

Subgroups — C13×#34981 #15721320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34981 #15721320