Subgroups — C₁₃×#24663 #15711002

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1802	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	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₁₃×#463	—	2	4	no	—
25	C₁₃×#433	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#396	—	2	1	no	—
43	C₁₃×#396	—	2	1	no	—
44	C₁₃×#394	—	2	1	no	—
45	C₁₃×#394	—	2	1	no	—
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#390	—	2	1	no	—
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#388	—	2	1	no	—
52	C₁₃×#386	—	2	1	no	—
53	C₁₃×#385	—	2	1	no	—
54	C₁₃×#384	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	4	1	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂×C₁₃×D₈	—	2	2	no	—
73	C₂×C₁₃×D₈	—	4	1	no	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	4	1	no	—
81	C₁₃×C₂²⋊Q₈	—	4	1	no	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	4	1	no	—
85	C₁₃×#121	—	4	1	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₁₃×#117	—	2	2	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#107	—	4	1	no	—
118	C₁₃×#107	—	4	1	no	—
119	C₁₃×C₄⋊C₈	—	2	2	no	—
120	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	2	2	no	—
123	C₁₃×#103	—	4	1	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	4	1	no	—
127	C₁₃×#102	—	4	1	no	—
128	C₁₃×#102	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	—	2	2	no	—
131	C₁₃×#97	—	2	2	no	—
132	C₄×C₈×C₁₃	—	2	2	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	#24663	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	—	2	1	no	—
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	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	—	4	2	no	—
161	C₂×D₄×C₁₃	—	8	1	no	—
162	C₂×D₄×C₁₃	—	8	1	no	—
163	C₂×D₄×C₁₃	—	8	1	no	—
164	C₂×D₄×C₁₃	—	8	1	no	—
165	C₂×D₄×C₁₃	#41	1	2	yes	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	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	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	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	—	8	1	no	—
180	C₂²×C₄×C₁₃	—	8	1	no	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×SD₁₆	—	4	4	no	—
188	C₁₃×D₈	—	4	4	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
200	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	4	2	no	—
213	C₁₃×C₄⋊C₄	—	8	1	no	—
214	C₁₃×C₄⋊C₄	—	8	1	no	—
215	C₁₃×C₄⋊C₄	—	8	1	no	—
216	C₁₃×C₄⋊C₄	#41	1	2	yes	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₁₃×C₂²⋊C₄	—	2	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₁₃×C₂²⋊C₄	—	4	2	no	—
224	C₁₃×C₂²⋊C₄	—	4	2	no	—
225	C₁₃×C₂²⋊C₄	—	8	1	no	—
226	C₁₃×C₂²⋊C₄	—	8	1	no	—
227	C₁₃×C₂²⋊C₄	—	8	1	no	—
228	C₁₃×C₂²⋊C₄	—	8	1	no	—
229	C₁₃×C₂²⋊C₄	—	8	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	8	1	no	—
233	C₄²×C₁₃	C₂×D₄	1	2	yes	—
234	C₄²×C₁₃	#41	1	2	yes	—
235	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2620	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2324	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1999	C₂×C₁₃	1	1	yes	characteristic
243	#1983	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	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	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₁₃	—	4	1	no	—
273	Q₈×C₁₃	—	4	1	no	—
274	Q₈×C₁₃	—	4	1	no	—
275	Q₈×C₁₃	—	4	1	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	—	4	1	no	—
283	D₄×C₁₃	—	4	1	no	—
284	D₄×C₁₃	—	8	4	no	—
285	D₄×C₁₃	—	8	4	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	1	no	—
293	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	8	4	no	—
322	C₂×C₄×C₁₃	#121	1	2	yes	—
323	C₂×C₄×C₁₃	#121	1	2	yes	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₈×C₁₃	—	2	2	no	—
331	C₈×C₁₃	—	2	2	no	—
332	C₈×C₁₃	—	4	1	no	—
333	C₈×C₁₃	—	4	1	no	—
334	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
342	#463	—	2	4	no	—
343	#433	—	2	4	no	—
344	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#102	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×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
360	#396	—	2	1	no	—
361	#396	—	2	1	no	—
362	#394	—	2	1	no	—
363	#394	—	2	1	no	—
364	#391	C₂²×C₁₃	1	1	yes	characteristic
365	#390	—	2	1	no	—
366	#390	C₂²×C₁₃	1	1	yes	characteristic
367	#390	C₂²×C₁₃	1	1	yes	characteristic
368	#389	C₂²×C₁₃	1	1	yes	characteristic
369	#388	—	2	1	no	—
370	#386	—	2	1	no	—
371	#385	—	2	1	no	—
372	#384	C₂²×C₁₃	1	1	yes	characteristic
373	#380	C₂²×C₁₃	1	1	yes	characteristic
374	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	#340	C₂²×C₁₃	1	1	yes	characteristic
376	#340	C₂²×C₁₃	1	1	yes	characteristic
377	#340	C₂²×C₁₃	1	1	yes	characteristic
378	#340	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	1	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	1	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	1	no	—
386	C₂²×C₁₃	—	4	1	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	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	—	8	1	no	—
394	C₂²×C₁₃	—	8	1	no	—
395	C₂²×C₁₃	—	8	1	no	—
396	C₂²×C₁₃	—	8	1	no	—
397	C₂²×C₁₃	—	8	1	no	—
398	C₂²×C₁₃	—	8	1	no	—
399	C₂²×C₁₃	—	8	1	no	—
400	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
401	C₂²×C₁₃	#525	1	1	yes	characteristic
402	C₂²×C₁₃	#535	1	1	yes	characteristic
403	C₂²×C₁₃	#576	1	1	yes	characteristic
404	C₂²×C₁₃	#576	1	1	yes	characteristic
405	C₂²×C₁₃	#577	1	1	yes	characteristic
406	C₂²×C₁₃	#578	1	1	yes	characteristic
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	1	no	—
411	C₄×C₁₃	—	4	1	no	—
412	C₄×C₁₃	—	4	1	no	—
413	C₄×C₁₃	—	8	1	no	—
414	C₄×C₁₃	—	8	1	no	—
415	C₄×C₁₃	—	8	1	no	—
416	C₄×C₁₃	—	8	1	no	—
417	C₄×C₁₃	—	8	1	no	—
418	C₄×C₁₃	#546	1	1	yes	characteristic
419	C₄×C₁₃	#550	1	1	yes	characteristic
420	C₄×C₁₃	#553	1	1	yes	characteristic
421	C₄×C₁₃	#555	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×SD₁₆	—	2	2	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	4	1	no	—
432	C₂×D₈	—	2	2	no	—
433	C₂×D₈	—	2	2	no	—
434	C₂×D₈	—	4	1	no	—
435	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	#124	—	2	2	no	—
440	#124	—	2	2	no	—
441	C₂²⋊Q₈	—	4	1	no	—
442	C₂²⋊Q₈	—	4	1	no	—
443	#121	—	2	2	no	—
444	#121	—	2	2	no	—
445	#121	—	4	1	no	—
446	#121	—	4	1	no	—
447	C₄×D₄	—	2	2	no	—
448	C₄×D₄	—	2	2	no	—
449	#117	—	2	2	no	—
450	#117	—	2	2	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄²	—	2	1	no	—
476	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	#107	—	4	1	no	—
479	#107	—	4	1	no	—
480	C₄⋊C₈	—	2	2	no	—
481	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
482	#103	—	2	2	no	—
483	#103	—	2	2	no	—
484	#103	—	4	1	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	4	1	no	—
488	#102	—	4	1	no	—
489	#102	—	4	1	no	—
490	C₂²⋊C₈	—	2	2	no	—
491	C₂²⋊C₈	—	2	2	no	—
492	#97	—	2	2	no	—
493	C₄×C₈	—	2	2	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	C₂×C₁₃	—	8	1	no	—
500	C₂×C₁₃	—	8	2	no	—
501	C₂×C₁₃	—	16	1	no	—
502	C₂×C₁₃	#2414	1	1	yes	characteristic
503	C₂×C₁₃	#3061	1	1	yes	characteristic
504	C₂×C₁₃	#3062	1	1	yes	characteristic
505	C₂×C₁₃	#3118	1	1	yes	characteristic
506	C₂×C₁₃	#3124	1	1	yes	characteristic
507	C₂×C₁₃	#3220	1	1	yes	characteristic
508	C₂×C₁₃	#3225	1	1	yes	characteristic
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×D₄	—	2	4	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	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	8	1	no	—
532	C₂×D₄	—	8	1	no	—
533	C₂×D₄	—	8	1	no	—
534	C₂×D₄	—	8	1	no	—
535	C₂×D₄	C₁₃×#41	1	2	yes	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	8	1	no	—
550	C₂²×C₄	—	8	1	no	—
551	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
557	SD₁₆	—	4	4	no	—
558	D₈	—	4	4	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	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
570	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	1	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	—	2	1	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	8	1	no	—
584	C₄⋊C₄	—	8	1	no	—
585	C₄⋊C₄	—	8	1	no	—
586	C₄⋊C₄	C₁₃×#41	1	2	yes	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	8	1	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₂²⋊C₄	—	8	1	no	—
598	C₂²⋊C₄	—	8	1	no	—
599	C₂²⋊C₄	—	8	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	8	1	no	—
603	C₄²	C₂×D₄×C₁₃	1	2	yes	—
604	C₄²	C₁₃×#41	1	2	yes	—
605	C₁₃	#24663	1	1	yes	characteristic, direct product factor, Sylow
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	4	1	no	—
640	D₄	—	8	4	no	—
641	D₄	—	8	4	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	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	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	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	C₁₃×#121	1	2	yes	—
679	C₂×C₄	C₁₃×#121	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
682	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
683	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
684	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
712	C₂²	C₁₃×#525	1	1	yes	characteristic
713	C₂²	C₁₃×#535	1	1	yes	characteristic
714	C₂²	C₁₃×#576	1	1	yes	characteristic
715	C₂²	C₁₃×#576	1	1	yes	characteristic
716	C₂²	C₁₃×#577	1	1	yes	characteristic
717	C₂²	C₁₃×#578	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	—	8	1	no	—
728	C₄	—	8	1	no	—
729	C₄	C₁₃×#546	1	1	yes	characteristic
730	C₄	C₁₃×#550	1	1	yes	characteristic
731	C₄	C₁₃×#553	1	1	yes	characteristic
732	C₄	C₁₃×#555	1	1	yes	characteristic
733	C₂	—	8	1	no	—
734	C₂	—	8	2	no	—
735	C₂	—	16	1	no	—
736	C₂	C₁₃×#2414	1	1	yes	characteristic
737	C₂	C₁₃×#3061	1	1	yes	characteristic
738	C₂	C₁₃×#3062	1	1	yes	characteristic
739	C₂	C₁₃×#3118	1	1	yes	characteristic
740	C₂	C₁₃×#3124	1	1	yes	characteristic
741	C₂	C₁₃×#3220	1	1	yes	characteristic
742	C₂	C₁₃×#3225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#463	C₂	semidirect
2. C₂×C₁₃×#433	C₂	semidirect
3. C₁₃×#2620	C₂	semidirect
4. C₁₃×#2324	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#2033	C₂	semidirect
7. C₁₃×#2000	C₂	semidirect
9. C₁₃×#1983	C₂	semidirect
10. C₁₃×#1973	C₂	semidirect
11. C₁₃×#1970	C₂	semidirect
12. C₁₃×#1947	C₂	semidirect
13. C₁₃×#1936	C₂	semidirect
14. C₁₃×#1933	C₂	semidirect
15. C₁₃×#1802	C₂	semidirect
120. C₁₃×C₄⋊C₈	D₄	semidirect
138. #24663	C₁₃	direct (N × H)
235. C₂×#463	C₂×C₁₃	semidirect
236. C₂×#433	C₂×C₁₃	semidirect
237. #2620	C₂×C₁₃	semidirect
238. #2324	C₂×C₁₃	semidirect
239. #2036	C₂×C₁₃	semidirect
240. #2033	C₂×C₁₃	semidirect
241. #2000	C₂×C₁₃	semidirect
243. #1983	C₂×C₁₃	semidirect
244. #1973	C₂×C₁₃	semidirect
245. #1970	C₂×C₁₃	semidirect
246. #1947	C₂×C₁₃	semidirect
247. #1936	C₂×C₁₃	semidirect
248. #1933	C₂×C₁₃	semidirect
249. #1802	C₂×C₁₃	semidirect
481. C₄⋊C₈	D₄×C₁₃	semidirect
605. C₁₃	#24663	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×#463	2
C₂×C₁₃×#433	2
C₁₃×#2620	2
C₁₃×#2324	2
C₁₃×#2036	2
C₁₃×#2033	2
C₁₃×#2000	2
C₁₃×#1999	2
C₁₃×#1983	2
C₁₃×#1973	2
C₁₃×#1970	2
C₁₃×#1947	2
C₁₃×#1936	2
C₁₃×#1933	2
C₁₃×#1802	2
#24663	13

Subgroups — C13×#24663 #15711002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24663 #15711002