Subgroups — C₁₃×#24675 #15711014

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#464	—	2	1	no	—
25	C₁₃×#464	—	2	1	no	—
26	C₁₃×#464	—	2	1	no	—
27	C₁₃×#464	—	2	1	no	—
28	C₁₃×#464	—	2	1	no	—
29	C₁₃×#464	—	2	1	no	—
30	C₁₃×#463	—	2	1	no	—
31	C₁₃×#463	—	2	1	no	—
32	C₁₃×#441	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×Q₁₆	—	2	1	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₁₃×#433	—	2	1	no	—
37	C₁₃×#433	—	2	1	no	—
38	C₁₃×#432	—	2	1	no	—
39	C₁₃×#431	—	2	1	no	—
40	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#423	C₂²	1	1	yes	characteristic
44	C₁₃×#423	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#419	C₂²	1	1	yes	characteristic
47	C₁₃×#419	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₁₃×#408	C₂²	1	1	yes	characteristic
59	C₁₃×#408	C₂²	1	1	yes	characteristic
60	C₁₃×#405	C₂²	1	1	yes	characteristic
61	C₁₃×#405	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×M₁₆	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	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#137	—	2	2	no	—
72	C₁₃×#137	—	2	2	no	—
73	C₁₃×#137	—	4	1	no	—
74	C₁₃×#137	—	4	1	no	—
75	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
76	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
77	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×Q₁₆	—	2	2	no	—
80	C₂×C₁₃×Q₁₆	—	2	1	no	—
81	C₂×C₁₃×Q₁₆	—	2	1	no	—
82	C₂×C₁₃×Q₁₆	—	4	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	2	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	—	2	1	no	—
88	C₂×C₁₃×SD₁₆	—	2	1	no	—
89	C₂×C₁₃×SD₁₆	—	4	1	no	—
90	C₂×C₁₃×D₈	—	2	1	no	—
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#124	—	2	1	no	—
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₄×Q₈×C₁₃	—	2	1	no	—
104	C₄×Q₈×C₁₃	—	2	1	no	—
105	C₄×Q₈×C₁₃	—	2	1	no	—
106	C₄×Q₈×C₁₃	—	2	1	no	—
107	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
109	C₄×D₄×C₁₃	—	2	1	no	—
110	C₄×D₄×C₁₃	—	2	1	no	—
111	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
112	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
113	C₁₃×#117	—	2	1	no	—
114	C₁₃×#117	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₄²×C₁₃	—	2	1	no	—
120	C₂×C₄²×C₁₃	—	2	1	no	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#108	—	4	1	no	—
123	C₁₃×#108	—	4	1	no	—
124	C₁₃×#107	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₄⋊C₈	—	2	1	no	—
129	C₁₃×C₄⋊C₈	—	2	1	no	—
130	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
133	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#102	—	2	1	no	—
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#101	—	2	2	no	—
147	C₁₃×#101	—	4	1	no	—
148	C₁₃×#101	—	4	1	no	—
149	C₁₃×#101	—	4	1	no	—
150	C₁₃×#100	—	2	2	no	—
151	C₁₃×#100	—	4	1	no	—
152	C₁₃×C₂²⋊C₈	—	2	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×C₂²⋊C₈	—	2	1	no	—
155	C₁₃×C₂²⋊C₈	—	2	1	no	—
156	C₁₃×#97	—	2	1	no	—
157	C₁₃×#97	—	2	1	no	—
158	C₁₃×#97	—	2	1	no	—
159	C₄×C₈×C₁₃	—	2	1	no	—
160	C₄×C₈×C₁₃	—	2	1	no	—
161	C₄×C₈×C₁₃	—	2	1	no	—
162	#24675	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₁₃×#41	—	2	1	no	—
165	C₁₃×#41	—	2	1	no	—
166	C₁₃×#41	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₁₃	#41	1	2	yes	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×Q₁₆	—	2	4	no	—
199	C₁₃×Q₁₆	—	4	2	no	—
200	C₁₃×Q₁₆	—	4	2	no	—
201	C₁₃×Q₁₆	—	4	2	no	—
202	C₁₃×SD₁₆	—	2	4	no	—
203	C₁₃×SD₁₆	—	4	2	no	—
204	C₁₃×SD₁₆	—	4	2	no	—
205	C₁₃×SD₁₆	—	4	2	no	—
206	C₁₃×SD₁₆	—	4	2	no	—
207	C₁₃×D₈	—	4	2	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	2	1	no	—
211	C₁₃×M₁₆	—	2	1	no	—
212	C₁₃×M₁₆	—	2	1	no	—
213	C₁₃×M₁₆	—	2	1	no	—
214	C₁₃×M₁₆	—	2	1	no	—
215	C₁₃×M₁₆	—	2	1	no	—
216	C₁₃×M₁₆	—	2	1	no	—
217	C₁₃×M₁₆	—	2	1	no	—
218	C₁₃×M₁₆	—	2	1	no	—
219	C₁₃×M₁₆	#41	1	2	yes	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	4	1	no	—
239	C₁₃×C₄⋊C₄	—	4	1	no	—
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₁₃×C₂²⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	1	no	—
246	C₁₃×C₂²⋊C₄	—	4	1	no	—
247	C₁₃×C₂²⋊C₄	—	4	1	no	—
248	C₁₃×C₂²⋊C₄	—	4	1	no	—
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	4	1	no	—
253	C₄²×C₁₃	—	4	1	no	—
254	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
258	#3040	C₂×C₁₃	1	1	yes	characteristic
259	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2051	C₂×C₁₃	1	1	yes	characteristic
264	#2020	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2019	C₂×C₁₃	1	1	yes	characteristic
266	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	8	1	no	—
278	C₂³×C₁₃	—	8	1	no	—
279	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
280	Q₈×C₁₃	—	2	2	no	—
281	Q₈×C₁₃	—	2	1	no	—
282	Q₈×C₁₃	—	2	1	no	—
283	Q₈×C₁₃	—	2	2	no	—
284	Q₈×C₁₃	—	4	1	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	Q₈×C₁₃	—	4	1	no	—
287	Q₈×C₁₃	—	4	1	no	—
288	Q₈×C₁₃	—	4	1	no	—
289	Q₈×C₁₃	—	4	1	no	—
290	D₄×C₁₃	—	2	1	no	—
291	D₄×C₁₃	—	2	1	no	—
292	D₄×C₁₃	—	4	1	no	—
293	D₄×C₁₃	—	4	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	4	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	—	2	2	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	2	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	—	8	1	no	—
314	C₂×C₄×C₁₃	—	8	1	no	—
315	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
316	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
317	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
318	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
325	C₈×C₁₃	—	2	2	no	—
326	C₈×C₁₃	—	2	1	no	—
327	C₈×C₁₃	—	2	1	no	—
328	C₈×C₁₃	—	2	1	no	—
329	C₈×C₁₃	—	2	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₈×C₁₃	—	4	1	no	—
332	C₈×C₁₃	—	4	1	no	—
333	C₈×C₁₃	—	4	1	no	—
334	C₈×C₁₃	—	4	1	no	—
335	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
338	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
341	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
343	#464	—	2	1	no	—
344	#464	—	2	1	no	—
345	#464	—	2	1	no	—
346	#464	—	2	1	no	—
347	#464	—	2	1	no	—
348	#464	—	2	1	no	—
349	#463	—	2	1	no	—
350	#463	—	2	1	no	—
351	#441	—	2	1	no	—
352	#440	—	2	1	no	—
353	C₄×Q₁₆	—	2	1	no	—
354	C₄×SD₁₆	—	2	1	no	—
355	#433	—	2	1	no	—
356	#433	—	2	1	no	—
357	#432	—	2	1	no	—
358	#431	—	2	1	no	—
359	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
361	#428	C₂²×C₁₃	1	1	yes	characteristic
362	#423	C₂²×C₁₃	1	1	yes	characteristic
363	#423	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
365	#419	C₂²×C₁₃	1	1	yes	characteristic
366	#419	C₂²×C₁₃	1	1	yes	characteristic
367	#418	C₂²×C₁₃	1	1	yes	characteristic
368	#417	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
377	#408	C₂²×C₁₃	1	1	yes	characteristic
378	#408	C₂²×C₁₃	1	1	yes	characteristic
379	#405	C₂²×C₁₃	1	1	yes	characteristic
380	#405	C₂²×C₁₃	1	1	yes	characteristic
381	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
382	#343	C₂²×C₁₃	1	1	yes	characteristic
383	#343	C₂²×C₁₃	1	1	yes	characteristic
384	#341	C₂²×C₁₃	1	1	yes	characteristic
385	#341	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₁₃	—	2	1	no	—
387	C₂²×C₁₃	—	2	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	—	4	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	—	8	1	no	—
393	C₂²×C₁₃	—	8	1	no	—
394	C₂²×C₁₃	—	16	1	no	—
395	C₂²×C₁₃	—	16	1	no	—
396	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
397	C₂²×C₁₃	#553	1	1	yes	characteristic
398	C₂²×C₁₃	#555	1	1	yes	characteristic
399	C₄×C₁₃	—	2	1	no	—
400	C₄×C₁₃	—	2	1	no	—
401	C₄×C₁₃	—	2	1	no	—
402	C₄×C₁₃	—	2	1	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	—	8	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	#525	1	1	yes	characteristic
410	C₄×C₁₃	#535	1	1	yes	characteristic
411	C₄×C₁₃	#546	1	1	yes	characteristic
412	C₄×C₁₃	#550	1	1	yes	characteristic
413	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
417	#137	—	2	2	no	—
418	#137	—	2	2	no	—
419	#137	—	4	1	no	—
420	#137	—	4	1	no	—
421	AGL(1,ℤ/8)	—	4	1	no	—
422	AGL(1,ℤ/8)	—	4	1	no	—
423	C₂×Q₁₆	—	2	1	no	—
424	C₂×Q₁₆	—	2	1	no	—
425	C₂×Q₁₆	—	2	2	no	—
426	C₂×Q₁₆	—	2	1	no	—
427	C₂×Q₁₆	—	2	1	no	—
428	C₂×Q₁₆	—	4	1	no	—
429	C₂×SD₁₆	—	2	1	no	—
430	C₂×SD₁₆	—	2	1	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×SD₁₆	—	2	1	no	—
434	C₂×SD₁₆	—	2	1	no	—
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×D₈	—	2	1	no	—
437	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	#124	—	2	1	no	—
446	#124	—	2	1	no	—
447	#124	—	2	1	no	—
448	#124	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	—	2	1	no	—
453	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
454	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
458	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
459	#117	—	2	1	no	—
460	#117	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	#108	—	4	1	no	—
469	#108	—	4	1	no	—
470	#107	—	2	1	no	—
471	#106	—	2	1	no	—
472	C₄⋊C₈	—	2	1	no	—
473	C₄⋊C₈	—	2	1	no	—
474	C₄⋊C₈	—	2	1	no	—
475	C₄⋊C₈	—	2	1	no	—
476	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
478	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
479	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
480	#103	—	2	1	no	—
481	#103	—	2	1	no	—
482	#103	—	2	1	no	—
483	#103	—	2	1	no	—
484	#103	—	2	1	no	—
485	#103	—	2	1	no	—
486	#103	—	2	1	no	—
487	#102	—	2	1	no	—
488	#102	—	2	1	no	—
489	#102	—	2	1	no	—
490	#102	—	2	1	no	—
491	#102	—	2	1	no	—
492	#101	—	2	2	no	—
493	#101	—	4	1	no	—
494	#101	—	4	1	no	—
495	#101	—	4	1	no	—
496	#100	—	2	2	no	—
497	#100	—	4	1	no	—
498	C₂²⋊C₈	—	2	1	no	—
499	C₂²⋊C₈	—	2	1	no	—
500	C₂²⋊C₈	—	2	1	no	—
501	C₂²⋊C₈	—	2	1	no	—
502	#97	—	2	1	no	—
503	#97	—	2	1	no	—
504	#97	—	2	1	no	—
505	C₄×C₈	—	2	1	no	—
506	C₄×C₈	—	2	1	no	—
507	C₄×C₈	—	2	1	no	—
508	C₂×C₁₃	—	2	1	no	—
509	C₂×C₁₃	—	2	1	no	—
510	C₂×C₁₃	—	8	1	no	—
511	C₂×C₁₃	—	16	1	no	—
512	C₂×C₁₃	#2414	1	1	yes	characteristic
513	C₂×C₁₃	#3067	1	1	yes	characteristic
514	C₂×C₁₃	#3069	1	1	yes	characteristic
515	C₂⁴	—	2	1	no	—
516	#41	—	2	1	no	—
517	#41	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂×Q₈	C₁₃×#41	1	2	yes	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₁₃×#41	1	1	yes	characteristic
548	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	Q₁₆	—	2	4	no	—
551	Q₁₆	—	4	2	no	—
552	Q₁₆	—	4	2	no	—
553	Q₁₆	—	4	2	no	—
554	SD₁₆	—	2	4	no	—
555	SD₁₆	—	4	2	no	—
556	SD₁₆	—	4	2	no	—
557	SD₁₆	—	4	2	no	—
558	SD₁₆	—	4	2	no	—
559	D₈	—	4	2	no	—
560	M₁₆	—	2	1	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	—	2	1	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	2	1	no	—
565	M₁₆	—	2	1	no	—
566	M₁₆	—	2	1	no	—
567	M₁₆	—	2	1	no	—
568	M₁₆	—	2	1	no	—
569	M₁₆	—	2	1	no	—
570	M₁₆	—	2	1	no	—
571	M₁₆	C₁₃×#41	1	2	yes	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	4	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	4	1	no	—
605	C₄²	—	4	1	no	—
606	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
610	C₁₃	#24675	1	1	yes	characteristic, direct product factor, Sylow
611	C₂³	—	2	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	8	1	no	—
616	C₂³	—	8	1	no	—
617	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
618	Q₈	—	2	2	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	2	1	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	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	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	—	8	1	no	—
653	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
654	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
655	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
656	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
660	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
661	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
663	C₈	—	2	2	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	16	1	no	—
682	C₂²	—	16	1	no	—
683	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
684	C₂²	C₁₃×#553	1	1	yes	characteristic
685	C₂²	C₁₃×#555	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₁₃×#525	1	1	yes	characteristic
697	C₄	C₁₃×#535	1	1	yes	characteristic
698	C₄	C₁₃×#546	1	1	yes	characteristic
699	C₄	C₁₃×#550	1	1	yes	characteristic
700	C₂	—	2	1	no	—
701	C₂	—	2	1	no	—
702	C₂	—	8	1	no	—
703	C₂	—	16	1	no	—
704	C₂	C₁₃×#2414	1	1	yes	characteristic
705	C₂	C₁₃×#3067	1	1	yes	characteristic
706	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	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#464	C₂	semidirect
3. C₄×C₁₃×#137	C₂	semidirect
4. C₁₃×#2925	C₂	semidirect
5. C₁₃×#2052	C₂	semidirect
7. C₁₃×#2020	C₂	semidirect
9. C₁₃×#1979	C₂	semidirect
10. C₁₃×#1977	C₂	semidirect
11. C₁₃×#1967	C₂	semidirect
12. C₁₃×#1950	C₂	semidirect
13. C₁₃×#1931	C₂	semidirect
14. C₁₃×#1930	C₂	semidirect
15. C₁₃×#1801	C₂	semidirect
162. #24675	C₁₃	direct (N × H)
259. C₂×#464	C₂×C₁₃	semidirect
260. C₄×#137	C₂×C₁₃	semidirect
261. #2925	C₂×C₁₃	semidirect
262. #2052	C₂×C₁₃	semidirect
264. #2020	C₂×C₁₃	semidirect
266. #1979	C₂×C₁₃	semidirect
267. #1977	C₂×C₁₃	semidirect
268. #1967	C₂×C₁₃	semidirect
269. #1950	C₂×C₁₃	semidirect
270. #1931	C₂×C₁₃	semidirect
271. #1930	C₂×C₁₃	semidirect
272. #1801	C₂×C₁₃	semidirect
610. C₁₃	#24675	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×#3040	2
C₂×C₁₃×#464	2
C₄×C₁₃×#137	2
C₁₃×#2925	2
C₁₃×#2052	2
C₁₃×#2051	2
C₁₃×#2020	2
C₁₃×#2019	2
C₁₃×#1979	2
C₁₃×#1977	2
C₁₃×#1967	2
C₁₃×#1950	2
C₁₃×#1931	2
C₁₃×#1930	2
C₁₃×#1801	2
#24675	13

Subgroups — C13×#24675 #15711014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24675 #15711014