Subgroups — C₁₃×#25938 #15712277

Order 3328.

1104 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#554	—	2	4	no	—
19	C₁₃×#554	—	2	4	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₁₃×#488	—	2	4	no	—
33	C₁₃×#463	—	2	4	no	—
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#397	—	2	1	no	—
45	C₁₃×#393	—	2	1	no	—
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#388	—	2	1	no	—
51	C₁₃×#388	—	2	1	no	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	2	no	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×D₈	—	2	2	no	—
75	C₂×C₁₃×D₈	—	2	2	no	—
76	C₂×C₁₃×D₈	—	2	2	no	—
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	—	2	2	no	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	—	2	2	no	—
85	C₁₃×#125	—	2	2	no	—
86	C₁₃×#125	D₄	1	4	yes	—
87	C₁₃×#124	—	2	2	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	8	no	—
90	C₁₃×C₂²⋊Q₈	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	D₄	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊C₈	—	2	2	no	—
128	C₁₃×#103	—	2	2	no	—
129	C₁₃×#103	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#102	—	2	2	no	—
132	C₁₃×#102	—	2	2	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₄×C₈×C₁₃	—	2	2	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	#25938	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	1	no	—
144	C₂⁴×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	4	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	4	1	no	—
155	C₂×Q₈×C₁₃	—	8	1	no	—
156	C₂×Q₈×C₁₃	—	8	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₃	#41	1	2	yes	—
168	C₂×D₄×C₁₃	#41	1	2	yes	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	8	1	no	—
181	C₂²×C₄×C₁₃	—	8	1	no	—
182	C₂²×C₄×C₁₃	—	8	1	no	—
183	C₂²×C₄×C₁₃	—	8	1	no	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×SD₁₆	—	4	4	no	—
192	C₁₃×D₈	—	4	4	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
221	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
222	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	4	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	2	no	—
229	C₁₃×C₂²⋊C₄	—	4	2	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	8	1	no	—
237	C₄²×C₁₃	C₂×D₄	1	2	yes	—
238	C₄²×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
242	#2592	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1879	C₂×C₁₃	1	1	yes	characteristic
250	#1879	C₂×C₁₃	1	1	yes	characteristic
251	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₁₃	—	4	4	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	Q₈×C₁₃	—	4	1	no	—
272	Q₈×C₁₃	—	4	1	no	—
273	Q₈×C₁₃	—	4	1	no	—
274	Q₈×C₁₃	—	8	4	no	—
275	D₄×C₁₃	—	2	2	no	—
276	D₄×C₁₃	—	2	2	no	—
277	D₄×C₁₃	—	2	2	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	4	1	no	—
280	D₄×C₁₃	—	4	1	no	—
281	D₄×C₁₃	—	4	1	no	—
282	D₄×C₁₃	#124	1	4	yes	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	4	8	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	—	8	4	no	—
319	C₂×C₄×C₁₃	#120	1	2	yes	—
320	C₂×C₄×C₁₃	#120	1	2	yes	—
321	C₂×C₄×C₁₃	#135	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
327	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
328	C₈×C₁₃	—	4	1	no	—
329	C₈×C₁₃	—	4	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₈×C₁₃	—	4	1	no	—
332	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
334	#554	—	2	4	no	—
335	#554	—	2	4	no	—
336	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₂²⋊Q₈	—	2	1	no	—
341	C₂×C₂²⋊Q₈	—	2	1	no	—
342	C₂×C₂²⋊Q₈	—	2	1	no	—
343	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	—	2	1	no	—
348	#488	—	2	4	no	—
349	#463	—	2	4	no	—
350	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
360	#397	—	2	1	no	—
361	#393	—	2	1	no	—
362	#391	C₂²×C₁₃	1	1	yes	characteristic
363	#391	C₂²×C₁₃	1	1	yes	characteristic
364	#390	C₂²×C₁₃	1	1	yes	characteristic
365	#390	C₂²×C₁₃	1	1	yes	characteristic
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#340	C₂²×C₁₃	1	1	yes	characteristic
372	#340	C₂²×C₁₃	1	1	yes	characteristic
373	#340	C₂²×C₁₃	1	1	yes	characteristic
374	#340	C₂²×C₁₃	1	1	yes	characteristic
375	#336	C₂²×C₁₃	1	1	yes	characteristic
376	#336	C₂²×C₁₃	1	1	yes	characteristic
377	#336	C₂²×C₁₃	1	1	yes	characteristic
378	#336	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₁₃	—	2	4	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	2	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	8	1	no	—
387	C₂²×C₁₃	—	8	1	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	—	8	1	no	—
390	C₂²×C₁₃	—	8	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	—	8	1	no	—
393	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
394	C₂²×C₁₃	#548	1	1	yes	characteristic
395	C₂²×C₁₃	#548	1	1	yes	characteristic
396	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
397	C₂²×C₁₃	#575	1	1	yes	characteristic
398	C₂²×C₁₃	#576	1	1	yes	characteristic
399	C₂²×C₁₃	#577	1	1	yes	characteristic
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	2	no	—
403	C₄×C₁₃	—	4	1	no	—
404	C₄×C₁₃	—	4	2	no	—
405	C₄×C₁₃	—	4	1	no	—
406	C₄×C₁₃	—	4	1	no	—
407	C₄×C₁₃	—	4	2	no	—
408	C₄×C₁₃	—	4	2	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	—	8	1	no	—
411	C₄×C₁₃	—	8	1	no	—
412	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
413	C₄×C₁₃	#536	1	1	yes	characteristic
414	C₄×C₁₃	#548	1	1	yes	characteristic
415	C₄×C₁₃	#548	1	1	yes	characteristic
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂³×C₄	—	2	1	no	—
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	—	2	1	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₂×D₈	—	2	2	no	—
428	C₂×D₈	—	2	2	no	—
429	C₂×D₈	—	2	2	no	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₄⋊Q₈	—	2	2	no	—
435	C₄⋊Q₈	—	2	2	no	—
436	#125	—	2	2	no	—
437	#125	—	2	2	no	—
438	#125	—	2	2	no	—
439	#125	D₄×C₁₃	1	4	yes	—
440	#124	—	2	2	no	—
441	#124	—	2	2	no	—
442	C₂²⋊Q₈	—	2	8	no	—
443	C₂²⋊Q₈	—	2	8	no	—
444	C₂²⋊Q₈	—	2	8	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	2	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	D₄×C₁₃	1	4	yes	—
453	C₂×C₄⋊C₄	—	2	8	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₄²	—	2	1	no	—
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊C₈	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	#103	—	2	2	no	—
484	#102	—	2	2	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	2	2	no	—
488	#102	—	2	2	no	—
489	C₄×C₈	—	2	2	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	C₂×C₁₃	—	4	4	no	—
496	C₂×C₁₃	—	16	1	no	—
497	C₂×C₁₃	#2436	1	1	yes	characteristic
498	C₂×C₁₃	#3002	1	1	yes	characteristic
499	C₂×C₁₃	#3012	1	1	yes	characteristic
500	C₂×C₁₃	#3360	1	1	yes	characteristic
501	C₂×C₁₃	#3361	1	1	yes	characteristic
502	C₂×C₁₃	#3370	1	1	yes	characteristic
503	C₂×C₁₃	#3376	1	1	yes	characteristic
504	C₂⁴	—	2	1	no	—
505	C₂⁴	—	2	1	no	—
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	4	1	no	—
516	C₂×Q₈	—	8	1	no	—
517	C₂×Q₈	—	8	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
528	C₂×D₄	C₁₃×#41	1	2	yes	—
529	C₂×D₄	C₁₃×#41	1	2	yes	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	—	8	1	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	SD₁₆	—	4	4	no	—
553	D₈	—	4	4	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	8	1	no	—
592	C₂²⋊C₄	—	8	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	8	1	no	—
598	C₄²	C₂×D₄×C₁₃	1	2	yes	—
599	C₄²	C₂×D₄×C₁₃	1	2	yes	—
600	C₁₃	#25938	1	1	yes	characteristic, direct product factor, Sylow
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
616	Q₈	—	4	4	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	8	4	no	—
622	D₄	—	2	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	2	2	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	C₁₃×#124	1	4	yes	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	8	4	no	—
665	C₂×C₄	—	8	4	no	—
666	C₂×C₄	C₁₃×#120	1	2	yes	—
667	C₂×C₄	C₁₃×#120	1	2	yes	—
668	C₂×C₄	C₁₃×#135	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
672	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
673	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
694	C₂²	C₁₃×#548	1	1	yes	characteristic
695	C₂²	C₁₃×#548	1	1	yes	characteristic
696	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
697	C₂²	C₁₃×#575	1	1	yes	characteristic
698	C₂²	C₁₃×#576	1	1	yes	characteristic
699	C₂²	C₁₃×#577	1	1	yes	characteristic
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	2	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
713	C₄	C₁₃×#536	1	1	yes	characteristic
714	C₄	C₁₃×#548	1	1	yes	characteristic
715	C₄	C₁₃×#548	1	1	yes	characteristic
716	C₂	—	4	4	no	—
717	C₂	—	16	1	no	—
718	C₂	C₁₃×#2436	1	1	yes	characteristic
719	C₂	C₁₃×#3002	1	1	yes	characteristic
720	C₂	C₁₃×#3012	1	1	yes	characteristic
721	C₂	C₁₃×#3360	1	1	yes	characteristic
722	C₂	C₁₃×#3361	1	1	yes	characteristic
723	C₂	C₁₃×#3370	1	1	yes	characteristic
724	C₂	C₁₃×#3376	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#488	C₂	semidirect
4. C₁₃×#2592	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
8. C₁₃×#2023	C₂	semidirect
9. C₁₃×#1989	C₂	semidirect
10. C₁₃×#1984	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1877	C₂	semidirect
15. C₄×C₁₃×#102	C₂	semidirect
142. #25938	C₁₃	direct (N × H)
239. C₂×#554	C₂×C₁₃	semidirect
240. C₂×#488	C₂×C₁₃	semidirect
242. #2592	C₂×C₁₃	semidirect
243. #2026	C₂×C₁₃	semidirect
244. #2025	C₂×C₁₃	semidirect
245. #2024	C₂×C₁₃	semidirect
246. #2023	C₂×C₁₃	semidirect
247. #1989	C₂×C₁₃	semidirect
248. #1984	C₂×C₁₃	semidirect
251. #1877	C₂×C₁₃	semidirect
252. #1877	C₂×C₁₃	semidirect
253. C₄×#102	C₂×C₁₃	semidirect
600. C₁₃	#25938	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×#554	2
C₂×C₁₃×#488	2
C₂×C₁₃×#463	2
C₁₃×#2592	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1989	2
C₁₃×#1984	2
C₁₃×#1879	2
C₁₃×#1877	2
C₄×C₁₃×#102	2
#25938	13

Subgroups — C13×#25938 #15712277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25938 #15712277