Subgroups — C₁₃×#24624 #15710963

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3095	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1822	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₁₃×#485	—	2	1	no	—
21	C₁₃×#485	—	2	1	no	—
22	C₁₃×#485	—	2	1	no	—
23	C₁₃×#485	—	2	1	no	—
24	C₁₃×#485	—	2	1	no	—
25	C₁₃×#485	—	2	1	no	—
26	C₁₃×#484	—	2	1	no	—
27	C₁₃×#483	—	2	1	no	—
28	C₁₃×#433	—	2	1	no	—
29	C₁₃×#433	—	2	1	no	—
30	C₁₃×#432	—	2	1	no	—
31	C₁₃×#431	—	2	1	no	—
32	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
34	C₁₃×#428	—	2	1	no	—
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	—	2	1	no	—
43	C₁₃×#427	—	2	1	no	—
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#419	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
54	C₁₃×#407	C₂²	1	1	yes	characteristic
55	C₁₃×#407	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#343	C₂²	1	1	yes	characteristic
65	C₁₃×#341	C₂²	1	1	yes	characteristic
66	C₁₃×#341	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	—	2	1	no	—
70	C₂×C₁₃×M₁₆	—	2	2	no	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×#117	—	2	1	no	—
86	C₁₃×#117	—	2	1	no	—
87	C₁₃×#117	—	2	1	no	—
88	C₁₃×#117	—	2	1	no	—
89	C₁₃×#117	—	2	1	no	—
90	C₁₃×#117	—	2	1	no	—
91	C₁₃×#117	D₄	1	1	yes	characteristic
92	C₁₃×#117	D₄	1	1	yes	characteristic
93	C₁₃×#117	C₂³	1	1	yes	characteristic
94	C₁₃×#117	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₁₃×#108	—	2	2	no	—
107	C₁₃×#108	—	2	2	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	—	2	1	no	—
119	C₁₃×#106	—	2	1	no	—
120	C₁₃×#106	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#101	—	2	2	no	—
137	C₁₃×#101	—	2	2	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₁₃×C₂²⋊C₈	—	2	1	no	—
142	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
144	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
145	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
146	C₁₃×#97	—	2	1	no	—
147	C₁₃×#97	—	2	1	no	—
148	C₄×C₈×C₁₃	—	2	1	no	—
149	C₄×C₈×C₁₃	—	2	1	no	—
150	#24624	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	#41	1	1	yes	characteristic
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×M₁₆	—	2	4	no	—
175	C₁₃×M₁₆	—	2	1	no	—
176	C₁₃×M₁₆	—	2	1	no	—
177	C₁₃×M₁₆	—	2	1	no	—
178	C₁₃×M₁₆	—	2	1	no	—
179	C₁₃×M₁₆	—	2	1	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	#41	1	2	yes	—
186	C₁₃×M₁₆	#41	1	2	yes	—
187	C₂×C₈×C₁₃	—	2	4	no	—
188	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	—	2	1	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	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₁₃×C₂²⋊C₄	—	2	1	no	—
217	C₁₃×C₂²⋊C₄	—	2	1	no	—
218	C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	4	1	no	—
221	C₁₃×C₂²⋊C₄	—	4	1	no	—
222	C₁₃×C₂²⋊C₄	—	4	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	4	1	no	—
229	C₄²×C₁₃	—	4	1	no	—
230	#3095	C₂×C₁₃	1	1	yes	characteristic
231	C₂×#485	C₂×C₁₃	1	1	yes	characteristic
232	#2924	C₂×C₁₃	1	1	yes	characteristic
233	#2911	C₂×C₁₃	1	1	yes	characteristic
234	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1901	C₂×C₁₃	1	1	yes	characteristic
243	#1855	C₂×C₁₃	1	1	yes	characteristic
244	#1822	C₂×C₁₃	1	1	yes	characteristic
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	#121	1	1	yes	characteristic
250	C₂³×C₁₃	#121	1	1	yes	characteristic
251	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
252	Q₈×C₁₃	—	4	1	no	—
253	Q₈×C₁₃	—	4	1	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	8	1	no	—
278	C₂×C₄×C₁₃	—	8	1	no	—
279	C₂×C₄×C₁₃	—	8	1	no	—
280	C₂×C₄×C₁₃	—	8	1	no	—
281	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
282	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
288	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
289	C₈×C₁₃	—	2	2	no	—
290	C₈×C₁₃	—	2	2	no	—
291	C₈×C₁₃	—	2	1	no	—
292	C₈×C₁₃	—	2	1	no	—
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₈×C₁₃	—	4	1	no	—
299	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
303	#485	—	2	1	no	—
304	#485	—	2	1	no	—
305	#485	—	2	1	no	—
306	#485	—	2	1	no	—
307	#485	—	2	1	no	—
308	#485	—	2	1	no	—
309	#484	—	2	1	no	—
310	#483	—	2	1	no	—
311	#433	—	2	1	no	—
312	#433	—	2	1	no	—
313	#432	—	2	1	no	—
314	#431	—	2	1	no	—
315	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
317	#428	—	2	1	no	—
318	#428	—	2	1	no	—
319	#428	C₂²×C₁₃	1	1	yes	characteristic
320	#428	C₂²×C₁₃	1	1	yes	characteristic
321	#428	C₂²×C₁₃	1	1	yes	characteristic
322	#428	C₂²×C₁₃	1	1	yes	characteristic
323	#428	C₂²×C₁₃	1	1	yes	characteristic
324	#428	C₂²×C₁₃	1	1	yes	characteristic
325	#427	—	2	1	no	—
326	#427	—	2	1	no	—
327	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
329	#424	C₂²×C₁₃	1	1	yes	characteristic
330	#424	C₂²×C₁₃	1	1	yes	characteristic
331	#419	C₂²×C₁₃	1	1	yes	characteristic
332	#419	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
337	#407	C₂²×C₁₃	1	1	yes	characteristic
338	#407	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	#405	C₂²×C₁₃	1	1	yes	characteristic
341	#405	C₂²×C₁₃	1	1	yes	characteristic
342	#343	C₂²×C₁₃	1	1	yes	characteristic
343	#343	C₂²×C₁₃	1	1	yes	characteristic
344	#343	C₂²×C₁₃	1	1	yes	characteristic
345	#343	C₂²×C₁₃	1	1	yes	characteristic
346	#343	C₂²×C₁₃	1	1	yes	characteristic
347	#343	C₂²×C₁₃	1	1	yes	characteristic
348	#341	C₂²×C₁₃	1	1	yes	characteristic
349	#341	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	1	no	—
352	C₂²×C₁₃	—	2	1	no	—
353	C₂²×C₁₃	—	2	1	no	—
354	C₂²×C₁₃	—	2	1	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	1	no	—
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	8	1	no	—
359	C₂²×C₁₃	—	8	1	no	—
360	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
361	C₂²×C₁₃	#552	1	1	yes	characteristic
362	C₂²×C₁₃	#552	1	1	yes	characteristic
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	#525	1	1	yes	characteristic
374	C₄×C₁₃	#536	1	1	yes	characteristic
375	C₄×C₁₃	#547	1	1	yes	characteristic
376	C₄×C₁₃	#547	1	1	yes	characteristic
377	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	D₄×C₁₃	1	1	yes	characteristic
402	#117	D₄×C₁₃	1	1	yes	characteristic
403	#117	C₂³×C₁₃	1	1	yes	characteristic
404	#117	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	#108	—	2	2	no	—
417	#108	—	2	2	no	—
418	#107	—	2	1	no	—
419	#107	—	2	1	no	—
420	#107	—	2	1	no	—
421	#107	—	2	1	no	—
422	#107	—	2	1	no	—
423	#107	—	2	1	no	—
424	#107	—	2	1	no	—
425	#107	—	2	1	no	—
426	#106	—	2	1	no	—
427	#106	—	2	1	no	—
428	#106	—	2	1	no	—
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	—	2	1	no	—
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	#103	—	2	1	no	—
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#101	—	2	2	no	—
447	#101	—	2	2	no	—
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
453	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
454	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
455	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
456	#97	—	2	1	no	—
457	#97	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	2	1	no	—
460	C₂×C₁₃	—	2	1	no	—
461	C₂×C₁₃	—	2	1	no	—
462	C₂×C₁₃	—	4	1	no	—
463	C₂×C₁₃	—	4	1	no	—
464	C₂×C₁₃	#2413	1	1	yes	characteristic
465	C₂×C₁₃	#3067	1	1	yes	characteristic
466	C₂×C₁₃	#3069	1	1	yes	characteristic
467	C₂⁴	C₁₃×#41	1	1	yes	characteristic
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	1	no	—
494	M₁₆	—	2	1	no	—
495	M₁₆	—	2	1	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	1	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	C₁₃×#41	1	2	yes	—
502	M₁₆	C₁₃×#41	1	2	yes	—
503	C₂×C₈	—	2	4	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	4	1	no	—
545	C₄²	—	4	1	no	—
546	C₁₃	#24624	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	C₁₃×#121	1	1	yes	characteristic
552	C₂³	C₁₃×#121	1	1	yes	characteristic
553	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	8	1	no	—
580	C₂×C₄	—	8	1	no	—
581	C₂×C₄	—	8	1	no	—
582	C₂×C₄	—	8	1	no	—
583	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
584	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
588	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
589	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
590	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
591	C₈	—	2	2	no	—
592	C₈	—	2	2	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
612	C₂²	C₁₃×#552	1	1	yes	characteristic
613	C₂²	C₁₃×#552	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	C₁₃×#525	1	1	yes	characteristic
625	C₄	C₁₃×#536	1	1	yes	characteristic
626	C₄	C₁₃×#547	1	1	yes	characteristic
627	C₄	C₁₃×#547	1	1	yes	characteristic
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	4	1	no	—
631	C₂	—	4	1	no	—
632	C₂	C₁₃×#2413	1	1	yes	characteristic
633	C₂	C₁₃×#3067	1	1	yes	characteristic
634	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2064	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1951	C₂	semidirect
11. C₁₃×#1930	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
150. #24624	C₁₃	direct (N × H)
234. #2090	C₂×C₁₃	semidirect
235. #2089	C₂×C₁₃	semidirect
236. #2064	C₂×C₁₃	semidirect
237. #2064	C₂×C₁₃	semidirect
238. #1952	C₂×C₁₃	semidirect
239. #1951	C₂×C₁₃	semidirect
240. #1930	C₂×C₁₃	semidirect
241. #1930	C₂×C₁₃	semidirect
546. C₁₃	#24624	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3095	2
C₂×C₁₃×#485	2
C₁₃×#2924	2
C₁₃×#2911	2
C₁₃×#2090	2
C₁₃×#2089	2
C₁₃×#2064	2
C₁₃×#1952	2
C₁₃×#1951	2
C₁₃×#1930	2
C₁₃×#1901	2
C₁₃×#1855	2
C₁₃×#1822	2
#24624	13

Subgroups — C13×#24624 #15710963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24624 #15710963