Subgroups — C₁₃×#2678 #13111736

Order 1664.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁵×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#123	—	2	4	no	—
26	C₁₃×#121	—	2	4	no	—
27	C₁₃×#120	—	2	4	no	—
28	C₁₃×#120	—	2	4	no	—
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#95	C₂²	1	1	yes	characteristic, complemented
55	C₂⁴×C₁₃	—	2	2	no	—
56	C₂⁴×C₁₃	—	2	2	no	—
57	C₂⁴×C₁₃	—	2	2	no	—
58	C₂⁴×C₁₃	—	4	1	no	—
59	C₂⁴×C₁₃	—	4	1	no	—
60	C₂⁴×C₁₃	—	4	1	no	—
61	C₂⁴×C₁₃	—	4	1	no	—
62	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
63	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
64	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
65	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
66	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₃	—	2	2	no	—
68	C₂×D₄×C₁₃	—	2	2	no	—
69	C₂×D₄×C₁₃	—	2	2	no	—
70	C₂×D₄×C₁₃	—	2	2	no	—
71	C₂×D₄×C₁₃	—	2	2	no	—
72	C₂×D₄×C₁₃	—	2	2	no	—
73	C₂×D₄×C₁₃	—	2	2	no	—
74	C₂×D₄×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	4	1	no	—
78	C₂×D₄×C₁₃	—	4	1	no	—
79	C₂×D₄×C₁₃	—	4	1	no	—
80	C₂×D₄×C₁₃	—	4	1	no	—
81	C₂×D₄×C₁₃	—	4	1	no	—
82	C₂×D₄×C₁₃	—	4	1	no	—
83	C₂×D₄×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	—	4	1	no	—
85	C₂×D₄×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	4	1	no	—
87	C₂×D₄×C₁₃	D₄	1	4	yes	complemented
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	4	1	no	—
105	C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₁₃×C₂²⋊C₄	—	2	2	no	—
109	C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₁₃×C₂²⋊C₄	—	4	1	no	—
115	C₁₃×C₂²⋊C₄	—	4	1	no	—
116	C₁₃×C₂²⋊C₄	—	4	1	no	—
117	C₁₃×C₂²⋊C₄	—	4	1	no	—
118	C₁₃×C₂²⋊C₄	—	4	1	no	—
119	C₁₃×C₂²⋊C₄	—	4	1	no	—
120	C₁₃×C₂²⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	D₄	1	4	yes	complemented
122	C₄²×C₁₃	—	4	1	no	—
123	#2678	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	1	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	—	2	1	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	—	2	1	no	—
138	C₂³×C₁₃	—	2	1	no	—
139	C₂³×C₁₃	—	2	1	no	—
140	C₂³×C₁₃	—	2	1	no	—
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	1	no	—
145	C₂³×C₁₃	—	2	1	no	—
146	C₂³×C₁₃	—	2	1	no	—
147	C₂³×C₁₃	—	2	1	no	—
148	C₂³×C₁₃	—	2	1	no	—
149	C₂³×C₁₃	—	2	1	no	—
150	C₂³×C₁₃	—	2	1	no	—
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	2	1	no	—
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	—	4	4	no	—
158	C₂³×C₁₃	—	4	4	no	—
159	C₂³×C₁₃	—	4	4	no	—
160	C₂³×C₁₃	—	4	4	no	—
161	C₂³×C₁₃	—	4	4	no	—
162	C₂³×C₁₃	C₂×D₄	1	2	yes	—
163	C₂³×C₁₃	C₂×D₄	1	2	yes	—
164	C₂³×C₁₃	C₂×D₄	1	2	yes	—
165	C₂³×C₁₃	#41	1	2	yes	—
166	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
167	D₄×C₁₃	—	4	4	no	—
168	D₄×C₁₃	—	4	4	no	—
169	D₄×C₁₃	—	4	4	no	—
170	D₄×C₁₃	—	4	4	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	4	4	no	—
173	D₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#397	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#396	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#394	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#392	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#392	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#388	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#386	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#379	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	4	16	no	—
233	C₂²×C₁₃	—	4	1	no	—
234	C₂²×C₁₃	—	4	1	no	—
235	C₂²×C₁₃	—	4	1	no	—
236	C₂²×C₁₃	—	4	1	no	—
237	C₂²×C₁₃	—	4	1	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	—	4	1	no	—
251	C₂²×C₁₃	—	4	1	no	—
252	C₂²×C₁₃	—	4	1	no	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	1	no	—
256	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	4	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	—	4	1	no	—
270	C₄×C₁₃	—	4	1	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₂⁵	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
278	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	#123	—	2	4	no	—
283	#121	—	2	4	no	—
284	#120	—	2	4	no	—
285	#120	—	2	4	no	—
286	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
289	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
290	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	#95	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₂×C₁₃	—	4	2	no	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	—	4	2	no	—
315	C₂×C₁₃	—	4	2	no	—
316	C₂×C₁₃	—	8	1	no	—
317	C₂×C₁₃	#534	1	1	yes	characteristic
318	C₂×C₁₃	#535	1	1	yes	characteristic
319	C₂×C₁₃	#538	1	1	yes	characteristic
320	C₂×C₁₃	D₄²	1	1	yes	characteristic
321	C₂×C₁₃	#546	1	1	yes	characteristic
322	C₂×C₁₃	#546	1	1	yes	characteristic
323	C₂×C₁₃	#560	1	1	yes	characteristic
324	C₂⁴	—	2	2	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	2	2	no	—
327	C₂⁴	—	4	1	no	—
328	C₂⁴	—	4	1	no	—
329	C₂⁴	—	4	1	no	—
330	C₂⁴	—	4	1	no	—
331	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
332	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
333	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
334	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
335	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	D₄×C₁₃	1	4	yes	complemented
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₂²⋊C₄	D₄×C₁₃	1	4	yes	complemented
391	C₄²	—	4	1	no	—
392	C₁₃	#2678	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	4	no	—
431	C₂³	C₂×D₄×C₁₃	1	2	yes	—
432	C₂³	C₂×D₄×C₁₃	1	2	yes	—
433	C₂³	C₂×D₄×C₁₃	1	2	yes	—
434	C₂³	C₁₃×#41	1	2	yes	—
435	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	4	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	4	no	—
442	D₄	—	4	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
472	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
513	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₂	—	4	2	no	—
528	C₂	—	4	2	no	—
529	C₂	—	4	2	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	1	no	—
532	C₂	C₁₃×#534	1	1	yes	characteristic
533	C₂	C₁₃×#535	1	1	yes	characteristic
534	C₂	C₁₃×#538	1	1	yes	characteristic
535	C₂	D₄²×C₁₃	1	1	yes	characteristic
536	C₂	C₁₃×#546	1	1	yes	characteristic
537	C₂	C₁₃×#546	1	1	yes	characteristic
538	C₂	C₁₃×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×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×#123	C₂	semidirect
2. C₂×C₁₃×#121	C₂	semidirect
3. C₂×C₁₃×#120	C₂	semidirect
4. C₂×C₁₃×#120	C₂	semidirect
5. C₁₃×#397	C₂	semidirect
6. C₁₃×#396	C₂	semidirect
7. C₁₃×#394	C₂	semidirect
8. C₁₃×#394	C₂	semidirect
9. C₁₃×#392	C₂	semidirect
10. C₁₃×#392	C₂	semidirect
11. C₁₃×#390	C₂	semidirect
12. C₁₃×#390	C₂	semidirect
13. C₁₃×#388	C₂	semidirect
14. C₁₃×#386	C₂	semidirect
15. C₁₃×#379	C₂	semidirect
23. C₂²×D₄×C₁₃	C₂²	semidirect
24. C₂³×C₄×C₁₃	C₂²	semidirect
29. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
32. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
46. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
48. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₄²×C₁₃	C₂²	semidirect
51. C₁₃×#95	C₂²	semidirect
52. C₁₃×#95	C₂²	semidirect
53. C₁₃×#95	C₂²	semidirect
54. C₁₃×#95	C₂²	semidirect
87. C₂×D₄×C₁₃	D₄	semidirect
121. C₁₃×C₂²⋊C₄	D₄	semidirect
123. #2678	C₁₃	direct (N × H)
205. C₂×#123	C₂×C₁₃	semidirect
206. C₂×#121	C₂×C₁₃	semidirect
207. C₂×#120	C₂×C₁₃	semidirect
208. C₂×#120	C₂×C₁₃	semidirect
209. #397	C₂×C₁₃	semidirect
210. #396	C₂×C₁₃	semidirect
211. #394	C₂×C₁₃	semidirect
212. #394	C₂×C₁₃	semidirect
213. #392	C₂×C₁₃	semidirect
214. #392	C₂×C₁₃	semidirect
215. #390	C₂×C₁₃	semidirect
216. #390	C₂×C₁₃	semidirect
217. #388	C₂×C₁₃	semidirect
218. #386	C₂×C₁₃	semidirect
219. #379	C₂×C₁₃	semidirect
280. C₂²×D₄	C₂²×C₁₃	semidirect
281. C₂³×C₄	C₂²×C₁₃	semidirect
286. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
287. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
288. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
289. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
302. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
303. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
304. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
305. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
306. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
307. C₂×C₄²	C₂²×C₁₃	semidirect
308. #95	C₂²×C₁₃	semidirect
309. #95	C₂²×C₁₃	semidirect
310. #95	C₂²×C₁₃	semidirect
311. #95	C₂²×C₁₃	semidirect
356. C₂×D₄	D₄×C₁₃	semidirect
390. C₂²⋊C₄	D₄×C₁₃	semidirect
392. C₁₃	#2678	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×#123	2
C₂×C₁₃×#121	2
C₂×C₁₃×#120	2
C₁₃×#397	2
C₁₃×#396	2
C₁₃×#394	2
C₁₃×#392	2
C₁₃×#390	2
C₁₃×#388	2
C₁₃×#386	2
C₁₃×#379	2
#2678	13

Subgroups — C13×#2678 #13111736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2678 #13111736