Subgroups — C₁₃×#34273 #15720612

Order 3328.

3578 conjugacy classes of subgroups.

The subgroup lattice has 504 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
2	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2359	C₂	1	8	yes	maximal, complemented
4	C₁₃×#2358	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₃×#121	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#534	C₄	1	16	yes	complemented
13	C₂×C₁₃×#123	C₂²	1	4	yes	—
14	C₂×C₁₃×#121	C₂²	1	4	yes	—
15	C₂×C₁₃×#120	C₂²	1	4	yes	—
16	C₁₃×#518	—	2	16	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#390	C₂²	1	4	yes	complemented
28	C₁₃×#389	C₂²	1	4	yes	complemented
29	C₁₃×#388	C₂²	1	8	yes	complemented
30	C₁₃×#388	C₂²	1	8	yes	complemented
31	C₁₃×#387	C₂²	1	8	yes	complemented
32	C₁₃×#386	C₂²	1	8	yes	—
33	C₁₃×#386	C₂²	1	4	yes	complemented
34	C₁₃×#386	C₂²	1	4	yes	complemented
35	C₁₃×#386	C₂²	1	8	yes	complemented
36	C₁₃×#385	C₂²	1	8	yes	complemented
37	C₁₃×#385	C₂²	1	8	yes	complemented
38	C₁₃×#380	C₂²	1	4	yes	complemented
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
42	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
44	C₂⁵×C₁₃	C₂³	1	2	yes	—
45	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	8	no	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
49	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	—	2	4	no	—
53	C₂³×C₄×C₁₃	—	4	4	no	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₁₃×#123	C₂×C₄	1	32	yes	complemented
63	C₁₃×#121	C₂×C₄	1	32	yes	complemented
64	C₁₃×#120	C₂×C₄	1	32	yes	complemented
65	C₄×D₄×C₁₃	—	2	32	no	—
66	C₄×D₄×C₁₃	—	2	32	no	—
67	C₄×D₄×C₁₃	—	4	8	no	—
68	C₁₃×#117	—	2	16	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
77	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₃	—	4	4	no	—
87	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₁₃×#95	C₂³	1	8	yes	—
92	C₁₃×#95	C₂³	1	8	yes	—
93	C₁₃×#95	C₂³	1	8	yes	—
94	#34273	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	4	2	no	—
98	C₂⁴×C₁₃	—	4	2	no	—
99	C₂⁴×C₁₃	—	4	4	no	—
100	C₂⁴×C₁₃	—	4	4	no	—
101	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
102	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
104	C₂⁴×C₁₃	#41	1	4	yes	—
105	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×D₄×C₁₃	—	2	64	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
116	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
117	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	complemented
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	16	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	4	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	—	4	8	no	—
135	C₂²×C₄×C₁₃	—	4	8	no	—
136	C₂²×C₄×C₁₃	—	4	4	no	—
137	C₂²×C₄×C₁₃	—	4	16	no	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₁₃×C₄⋊C₄	—	2	16	no	—
148	C₁₃×C₄⋊C₄	—	4	4	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	16	no	—
154	C₁₃×C₂²⋊C₄	—	2	16	no	—
155	C₁₃×C₂²⋊C₄	—	4	8	no	—
156	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
157	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
158	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
159	C₄²×C₁₃	—	2	16	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₄²×C₁₃	—	4	4	no	—
162	C₂×#534	C₂×C₁₃	1	1	yes	characteristic
163	C₂×#518	C₂×C₁₃	1	2	yes	complemented
164	#2359	C₂×C₁₃	1	8	yes	complemented
165	#2358	C₂×C₁₃	1	8	yes	complemented
166	#2325	C₂×C₁₃	1	4	yes	complemented
167	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₄×#121	C₂×C₁₃	1	4	yes	complemented
169	C₂×#386	C₂×C₁₃	1	2	yes	complemented
170	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	8	no	—
179	C₂³×C₁₃	—	2	16	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	—	4	8	no	—
182	C₂³×C₁₃	—	4	8	no	—
183	C₂³×C₁₃	—	4	4	no	—
184	C₂³×C₁₃	—	4	16	no	—
185	C₂³×C₁₃	—	8	4	no	—
186	C₂³×C₁₃	—	8	4	no	—
187	C₂³×C₁₃	—	8	8	no	—
188	C₂³×C₁₃	C₄×D₄	1	16	yes	complemented
189	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
190	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
191	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
192	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
194	C₂³×C₁₃	C₂×#41	1	4	yes	—
195	C₂³×C₁₃	C₂×#41	1	2	yes	—
196	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
197	D₄×C₁₃	—	2	32	no	—
198	D₄×C₁₃	—	2	32	no	—
199	D₄×C₁₃	—	4	16	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	2	16	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	4	8	no	—
216	C₂×C₄×C₁₃	—	4	8	no	—
217	C₂×C₄×C₁₃	—	4	16	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	8	16	no	—
220	C₂×C₄×C₁₃	—	8	8	no	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
222	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
224	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
225	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
226	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#534	C₄×C₁₃	1	16	yes	complemented
228	C₂×#123	C₂²×C₁₃	1	4	yes	—
229	C₂×#121	C₂²×C₁₃	1	4	yes	—
230	C₂×#120	C₂²×C₁₃	1	4	yes	—
231	#518	—	2	16	no	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
233	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
234	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
235	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
236	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
240	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
241	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
242	#390	C₂²×C₁₃	1	4	yes	complemented
243	#389	C₂²×C₁₃	1	4	yes	complemented
244	#388	C₂²×C₁₃	1	8	yes	complemented
245	#388	C₂²×C₁₃	1	8	yes	complemented
246	#387	C₂²×C₁₃	1	8	yes	complemented
247	#386	C₂²×C₁₃	1	8	yes	—
248	#386	C₂²×C₁₃	1	4	yes	complemented
249	#386	C₂²×C₁₃	1	8	yes	complemented
250	#386	C₂²×C₁₃	1	4	yes	complemented
251	#385	C₂²×C₁₃	1	8	yes	complemented
252	#385	C₂²×C₁₃	1	8	yes	complemented
253	#380	C₂²×C₁₃	1	4	yes	complemented
254	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
255	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
256	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
257	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
258	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	2	8	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	4	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	2	4	no	—
266	C₂²×C₁₃	—	2	8	no	—
267	C₂²×C₁₃	—	2	8	no	—
268	C₂²×C₁₃	—	2	16	no	—
269	C₂²×C₁₃	—	4	16	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	8	no	—
273	C₂²×C₁₃	—	8	16	no	—
274	C₂²×C₁₃	C₂×C₄×D₄	1	8	yes	—
275	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
276	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
277	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
280	C₂²×C₁₃	#585	1	2	yes	—
281	C₄×C₁₃	—	2	8	no	—
282	C₄×C₁₃	—	2	8	no	—
283	C₄×C₁₃	—	2	4	no	—
284	C₄×C₁₃	—	2	8	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	8	no	—
287	C₂⁵	C₂³×C₁₃	1	2	yes	—
288	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	—	2	8	no	—
291	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
292	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
293	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
294	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
295	C₂³×C₄	—	2	4	no	—
296	C₂³×C₄	—	4	4	no	—
297	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
302	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
304	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
305	#123	C₂×C₄×C₁₃	1	32	yes	complemented
306	#121	C₂×C₄×C₁₃	1	32	yes	complemented
307	#120	C₂×C₄×C₁₃	1	32	yes	complemented
308	C₄×D₄	—	2	32	no	—
309	C₄×D₄	—	2	32	no	—
310	C₄×D₄	—	4	8	no	—
311	#117	—	2	16	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
316	C₂×C₂²⋊C₄	—	2	8	no	—
317	C₂×C₂²⋊C₄	—	2	16	no	—
318	C₂×C₂²⋊C₄	—	4	8	no	—
319	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
320	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
321	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₄²	—	4	4	no	—
330	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
331	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
333	#95	C₂³×C₁₃	1	8	yes	—
334	#95	C₂³×C₁₃	1	8	yes	—
335	#95	C₂³×C₁₃	1	8	yes	—
336	#95	C₂³×C₁₃	1	8	yes	—
337	C₂×C₁₃	—	2	8	no	—
338	C₂×C₁₃	—	2	4	no	—
339	C₂×C₁₃	—	4	8	no	—
340	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
341	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
342	C₂×C₁₃	#3490	1	1	yes	characteristic
343	C₂×C₁₃	#3491	1	1	yes	characteristic
344	C₂×C₁₃	#3496	1	2	yes	—
345	C₂⁴	—	2	4	no	—
346	C₂⁴	—	2	4	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	—	4	4	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
352	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
353	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
354	C₂⁴	C₁₃×#41	1	4	yes	—
355	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
356	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
357	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₂×D₄	—	2	64	no	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
366	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
367	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	complemented
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	16	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	16	no	—
388	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
393	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
397	C₄⋊C₄	—	2	16	no	—
398	C₄⋊C₄	—	4	4	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	16	no	—
404	C₂²⋊C₄	—	2	16	no	—
405	C₂²⋊C₄	—	4	8	no	—
406	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
407	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
408	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
409	C₄²	—	2	16	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	4	4	no	—
412	C₁₃	#34273	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	16	no	—
422	C₂³	—	4	4	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	16	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	8	no	—
430	C₂³	C₄×D₄×C₁₃	1	16	yes	complemented
431	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
432	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
433	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
434	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
436	C₂³	C₂×C₁₃×#41	1	4	yes	—
437	C₂³	C₂×C₁₃×#41	1	2	yes	—
438	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
439	D₄	—	2	32	no	—
440	D₄	—	2	32	no	—
441	D₄	—	4	16	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	16	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	16	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	8	16	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
464	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
466	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	8	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	16	no	—
477	C₂²	—	4	16	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	8	16	no	—
482	C₂²	C₂×C₄×D₄×C₁₃	1	8	yes	—
483	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
484	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
485	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
486	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
487	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
488	C₂²	C₁₃×#585	1	2	yes	—
489	C₄	—	2	8	no	—
490	C₄	—	2	8	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	8	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	8	no	—
495	C₂	—	2	8	no	—
496	C₂	—	2	4	no	—
497	C₂	—	4	8	no	—
498	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
499	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
500	C₂	C₁₃×#3490	1	1	yes	characteristic
501	C₂	C₁₃×#3491	1	1	yes	characteristic
502	C₂	C₁₃×#3496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#518	C₂	semidirect
3. C₁₃×#2359	C₂	semidirect
4. C₁₃×#2358	C₂	semidirect
5. C₁₃×#2325	C₂	semidirect
6. C₁₃×#2315	C₂	semidirect
7. C₄×C₁₃×#121	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₁₃×#534	C₄	semidirect
18. C₂×C₄×D₄×C₁₃	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₂×C₁₃×#117	C₂²	semidirect
24. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₁₃	C₂²	semidirect
27. C₁₃×#390	C₂²	semidirect
28. C₁₃×#389	C₂²	semidirect
29. C₁₃×#388	C₂²	semidirect
30. C₁₃×#388	C₂²	semidirect
31. C₁₃×#387	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#386	C₂²	semidirect
35. C₁₃×#386	C₂²	semidirect
36. C₁₃×#385	C₂²	semidirect
37. C₁₃×#385	C₂²	semidirect
38. C₁₃×#380	C₂²	semidirect
39. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
40. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
41. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂×C₁₃×#95	C₂²	semidirect
43. C₂×C₁₃×#95	C₂²	semidirect
48. C₂²×D₄×C₁₃	C₂×C₄	semidirect
62. C₁₃×#123	C₂×C₄	semidirect
63. C₁₃×#121	C₂×C₄	semidirect
64. C₁₃×#120	C₂×C₄	semidirect
76. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
77. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
94. #34273	C₁₃	direct (N × H)
117. C₂×D₄×C₁₃	C₂²×C₄	semidirect
150. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
157. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
163. C₂×#518	C₂×C₁₃	semidirect
164. #2359	C₂×C₁₃	semidirect
165. #2358	C₂×C₁₃	semidirect
166. #2325	C₂×C₁₃	semidirect
167. #2315	C₂×C₁₃	semidirect
168. C₄×#121	C₂×C₁₃	semidirect
169. C₂×#386	C₂×C₁₃	semidirect
170. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
188. C₂³×C₁₃	C₄×D₄	semidirect
227. #534	C₄×C₁₃	semidirect
233. C₂×C₄×D₄	C₂²×C₁₃	semidirect
234. C₂×C₄×D₄	C₂²×C₁₃	semidirect
235. C₂×#117	C₂²×C₁₃	semidirect
239. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
240. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
241. C₂²×C₄²	C₂²×C₁₃	semidirect
242. #390	C₂²×C₁₃	semidirect
243. #389	C₂²×C₁₃	semidirect
244. #388	C₂²×C₁₃	semidirect
245. #388	C₂²×C₁₃	semidirect
246. #387	C₂²×C₁₃	semidirect
248. #386	C₂²×C₁₃	semidirect
249. #386	C₂²×C₁₃	semidirect
250. #386	C₂²×C₁₃	semidirect
251. #385	C₂²×C₁₃	semidirect
252. #385	C₂²×C₁₃	semidirect
253. #380	C₂²×C₁₃	semidirect
254. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
255. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
256. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
257. C₂×#95	C₂²×C₁₃	semidirect
258. C₂×#95	C₂²×C₁₃	semidirect
291. C₂²×D₄	C₂×C₄×C₁₃	semidirect
305. #123	C₂×C₄×C₁₃	semidirect
306. #121	C₂×C₄×C₁₃	semidirect
307. #120	C₂×C₄×C₁₃	semidirect
319. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
320. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
367. C₂×D₄	C₂²×C₄×C₁₃	semidirect
400. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
407. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
412. C₁₃	#34273	direct (N × H)
430. C₂³	C₄×D₄×C₁₃	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
C₂×C₁₃×#518	2
C₁₃×#2359	2
C₁₃×#2358	2
C₁₃×#2325	2
C₁₃×#2315	2
C₄×C₁₃×#121	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34273	13

Subgroups — C13×#34273 #15720612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34273 #15720612