Subgroups — C₁₃×#32941 #15719280

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#471	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1908	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1907	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1815	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×#131	—	2	8	no	—
17	C₂×C₁₃×#131	—	2	1	no	—
18	C₂×C₁₃×#131	—	2	1	no	—
19	C₂×C₁₃×#131	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₂²×C₁₃×M₁₆	—	2	1	no	—
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₃	—	2	1	no	—
24	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₁₃×#471	—	2	8	no	—
28	C₁₃×#465	—	2	1	no	—
29	C₁₃×#465	—	2	1	no	—
30	C₁₃×#465	—	2	1	no	—
31	C₁₃×#465	—	2	1	no	—
32	C₁₃×#452	—	2	2	no	—
33	C₁₃×#451	—	2	1	no	—
34	C₁₃×#450	—	2	1	no	—
35	C₁₃×#449	—	2	2	no	—
36	C₁₃×#448	—	2	1	no	—
37	C₁₃×#447	—	2	1	no	—
38	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₁₃×#417	C₂²	1	2	yes	—
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
46	C₁₃×#407	C₂²	1	1	yes	characteristic
47	C₁₃×#407	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	complemented
49	C₁₃×#343	C₂²	1	2	yes	complemented
50	C₁₃×#341	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#41	—	2	4	no	—
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	D₄	1	2	yes	—
56	C₂×C₁₃×#41	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#137	—	2	4	no	—
66	C₁₃×#137	—	2	4	no	—
67	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
68	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	4	no	—
75	C₂×C₁₃×D₈	—	2	2	no	—
76	C₁₃×#131	—	2	8	no	—
77	C₁₃×#131	—	2	8	no	—
78	C₁₃×#131	—	2	4	no	—
79	C₁₃×#131	—	2	4	no	—
80	C₁₃×#131	—	2	4	no	—
81	C₁₃×#131	D₄	1	8	yes	complemented
82	C₂×C₁₃×M₁₆	—	2	8	no	—
83	C₂×C₁₃×M₁₆	—	2	1	no	—
84	C₂×C₁₃×M₁₆	—	2	4	no	—
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
88	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
89	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₃	—	2	8	no	—
91	C₂²×C₈×C₁₃	—	2	1	no	—
92	C₂²×C₈×C₁₃	—	2	2	no	—
93	C₂²×C₈×C₁₃	—	2	2	no	—
94	C₂²×C₈×C₁₃	—	2	4	no	—
95	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×C₂²⋊Q₈	—	2	1	no	—
102	C₁₃×C₂²⋊Q₈	—	2	1	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×C₂²⋊Q₈	—	2	1	no	—
105	C₁₃×#121	—	2	1	no	—
106	C₁₃×#121	—	2	1	no	—
107	C₁₃×#121	—	2	1	no	—
108	C₁₃×#121	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₁₃×#108	—	2	4	no	—
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#101	—	2	4	no	—
126	C₁₃×#100	—	2	4	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×C₂²⋊C₈	—	2	1	no	—
131	#32941	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂⁴×C₁₃	#41	1	1	yes	characteristic
135	C₁₃×#41	—	2	4	no	—
136	C₁₃×#41	—	2	8	no	—
137	C₁₃×#41	—	2	4	no	—
138	C₁₃×#41	—	2	4	no	—
139	C₁₃×#41	—	2	4	no	—
140	C₁₃×#41	—	2	2	no	—
141	C₁₃×#41	—	2	2	no	—
142	C₁₃×#41	C₂×D₄	1	4	yes	—
143	C₁₃×#41	#41	1	4	yes	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₁₃	—	2	8	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	—	8	2	no	—
163	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×Q₁₆	—	4	4	no	—
181	C₁₃×SD₁₆	—	4	4	no	—
182	C₁₃×SD₁₆	—	4	4	no	—
183	C₁₃×SD₁₆	—	4	2	no	—
184	C₁₃×SD₁₆	—	4	2	no	—
185	C₁₃×D₈	—	4	4	no	—
186	C₁₃×M₁₆	—	2	4	no	—
187	C₁₃×M₁₆	—	2	8	no	—
188	C₁₃×M₁₆	—	2	2	no	—
189	C₁₃×M₁₆	—	2	8	no	—
190	C₁₃×M₁₆	—	2	2	no	—
191	C₁₃×M₁₆	—	2	2	no	—
192	C₁₃×M₁₆	—	2	2	no	—
193	C₁₃×M₁₆	—	2	2	no	—
194	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
195	C₂×C₈×C₁₃	—	2	4	no	—
196	C₂×C₈×C₁₃	—	2	8	no	—
197	C₂×C₈×C₁₃	—	2	2	no	—
198	C₂×C₈×C₁₃	—	2	2	no	—
199	C₂×C₈×C₁₃	—	2	2	no	—
200	C₂×C₈×C₁₃	—	2	8	no	—
201	C₂×C₈×C₁₃	—	2	2	no	—
202	C₂×C₈×C₁₃	—	2	2	no	—
203	C₂×C₈×C₁₃	—	2	2	no	—
204	C₂×C₈×C₁₃	—	2	2	no	—
205	C₂×C₈×C₁₃	—	2	2	no	—
206	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	4	1	no	—
216	C₁₃×C₄⋊C₄	—	4	1	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₁₃×C₂²⋊C₄	—	4	1	no	—
219	C₁₃×C₂²⋊C₄	—	4	1	no	—
220	C₁₃×C₂²⋊C₄	—	4	1	no	—
221	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×#471	C₂×C₁₃	1	2	yes	complemented
223	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3006	C₂×C₁₃	1	1	yes	characteristic
226	#1908	C₂×C₁₃	1	2	yes	complemented
227	#1907	C₂×C₁₃	1	2	yes	complemented
228	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1815	C₂×C₁₃	1	2	yes	complemented
231	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	2	no	—
238	C₂³×C₁₃	—	4	2	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	2	no	—
241	C₂³×C₁₃	—	8	1	no	—
242	C₂³×C₁₃	—	8	1	no	—
243	C₂³×C₁₃	#121	1	1	yes	characteristic
244	C₂³×C₁₃	#121	1	1	yes	characteristic
245	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
246	Q₈×C₁₃	—	2	4	no	—
247	Q₈×C₁₃	—	2	2	no	—
248	Q₈×C₁₃	—	4	1	no	—
249	Q₈×C₁₃	—	4	2	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	#121	1	4	yes	—
252	D₄×C₁₃	—	2	8	no	—
253	D₄×C₁₃	—	2	4	no	—
254	D₄×C₁₃	—	2	4	no	—
255	D₄×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	4	1	no	—
258	D₄×C₁₃	—	4	2	no	—
259	D₄×C₁₃	—	4	1	no	—
260	D₄×C₁₃	—	8	2	no	—
261	D₄×C₁₃	—	8	2	no	—
262	D₄×C₁₃	#121	1	4	yes	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	8	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	2	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	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
287	C₈×C₁₃	—	2	1	no	—
288	C₈×C₁₃	—	2	4	no	—
289	C₈×C₁₃	—	2	1	no	—
290	C₈×C₁₃	—	4	2	no	—
291	C₈×C₁₃	—	4	2	no	—
292	C₈×C₁₃	#120	1	2	yes	—
293	C₈×C₁₃	#120	1	2	yes	—
294	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#137	C₂²×C₁₃	1	2	yes	—
296	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
297	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#131	—	2	8	no	—
299	C₂×#131	—	2	1	no	—
300	C₂×#131	—	2	1	no	—
301	C₂×#131	C₂²×C₁₃	1	2	yes	—
302	C₂×#131	C₂²×C₁₃	1	2	yes	—
303	C₂²×M₁₆	—	2	1	no	—
304	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₂³×C₈	—	2	1	no	—
306	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
309	#471	—	2	8	no	—
310	#465	—	2	1	no	—
311	#465	—	2	1	no	—
312	#465	—	2	1	no	—
313	#465	—	2	1	no	—
314	#452	—	2	2	no	—
315	#451	—	2	1	no	—
316	#450	—	2	1	no	—
317	#449	—	2	2	no	—
318	#448	—	2	1	no	—
319	#447	—	2	1	no	—
320	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
321	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#417	C₂²×C₁₃	1	2	yes	—
323	#417	C₂²×C₁₃	1	2	yes	—
324	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
327	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
328	#407	C₂²×C₁₃	1	1	yes	characteristic
329	#407	C₂²×C₁₃	1	1	yes	characteristic
330	#343	C₂²×C₁₃	1	2	yes	complemented
331	#343	C₂²×C₁₃	1	2	yes	complemented
332	#341	C₂²×C₁₃	1	2	yes	complemented
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	4	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	2	1	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	8	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	16	2	no	—
349	C₂²×C₁₃	#471	1	2	yes	complemented
350	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
351	C₂²×C₁₃	#525	1	2	yes	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	4	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
359	C₄×C₁₃	C₂×#121	1	2	yes	—
360	C₄×C₁₃	#525	1	1	yes	characteristic
361	C₂×#41	—	2	4	no	—
362	C₂×#41	—	2	4	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	D₄×C₁₃	1	2	yes	—
366	C₂×#41	C₂³×C₁₃	1	2	yes	—
367	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	#137	—	2	4	no	—
376	#137	—	2	4	no	—
377	AGL(1,ℤ/8)	—	2	4	no	—
378	AGL(1,ℤ/8)	—	2	4	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×SD₁₆	—	2	1	no	—
383	C₂×SD₁₆	—	2	1	no	—
384	C₂×SD₁₆	—	2	4	no	—
385	C₂×D₈	—	2	2	no	—
386	#131	—	2	8	no	—
387	#131	—	2	8	no	—
388	#131	—	2	4	no	—
389	#131	—	2	4	no	—
390	#131	—	2	4	no	—
391	#131	D₄×C₁₃	1	8	yes	complemented
392	C₂×M₁₆	—	2	8	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	4	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	2	no	—
397	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
398	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
399	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
400	C₂²×C₈	—	2	8	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	2	no	—
403	C₂²×C₈	—	2	2	no	—
404	C₂²×C₈	—	2	4	no	—
405	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
407	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	2	1	no	—
414	C₂²⋊Q₈	—	2	1	no	—
415	#121	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	#108	—	2	4	no	—
425	#106	—	2	1	no	—
426	#106	—	2	1	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#101	—	2	4	no	—
436	#100	—	2	4	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₂×C₁₃	—	2	2	no	—
442	C₂×C₁₃	—	2	2	no	—
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	—	4	4	no	—
445	C₂×C₁₃	—	16	1	no	—
446	C₂×C₁₃	#2847	1	1	yes	characteristic
447	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
448	C₂×C₁₃	#3067	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	C₁₃×#41	1	1	yes	characteristic
452	#41	—	2	4	no	—
453	#41	—	2	8	no	—
454	#41	—	2	4	no	—
455	#41	—	2	4	no	—
456	#41	—	2	4	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	C₂×D₄×C₁₃	1	4	yes	—
460	#41	C₁₃×#41	1	4	yes	—
461	C₂×Q₈	—	2	4	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
468	C₂×D₄	—	2	8	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	8	2	no	—
480	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	Q₁₆	—	4	4	no	—
498	SD₁₆	—	4	4	no	—
499	SD₁₆	—	4	4	no	—
500	SD₁₆	—	4	2	no	—
501	SD₁₆	—	4	2	no	—
502	D₈	—	4	4	no	—
503	M₁₆	—	2	4	no	—
504	M₁₆	—	2	8	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	8	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	2	2	no	—
511	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
512	C₂×C₈	—	2	4	no	—
513	C₂×C₈	—	2	8	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	8	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₁₃	#32941	1	1	yes	characteristic, direct product factor, Sylow
539	C₂³	—	2	4	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	8	1	no	—
549	C₂³	—	8	1	no	—
550	C₂³	C₁₃×#121	1	1	yes	characteristic
551	C₂³	C₁₃×#121	1	1	yes	characteristic
552	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
553	Q₈	—	2	4	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	1	no	—
558	Q₈	C₁₃×#121	1	4	yes	—
559	D₄	—	2	8	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	8	2	no	—
568	D₄	—	8	2	no	—
569	D₄	C₁₃×#121	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	8	1	no	—
587	C₂×C₄	—	8	1	no	—
588	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
589	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
594	C₈	—	2	1	no	—
595	C₈	—	2	4	no	—
596	C₈	—	2	1	no	—
597	C₈	—	4	2	no	—
598	C₈	—	4	2	no	—
599	C₈	C₁₃×#120	1	2	yes	—
600	C₈	C₁₃×#120	1	2	yes	—
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	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	8	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	16	2	no	—
617	C₂²	C₁₃×#471	1	2	yes	complemented
618	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
619	C₂²	C₁₃×#525	1	2	yes	—
620	C₄	—	2	1	no	—
621	C₄	—	2	4	no	—
622	C₄	—	2	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
627	C₄	C₂×C₁₃×#121	1	2	yes	—
628	C₄	C₁₃×#525	1	1	yes	characteristic
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	4	no	—
633	C₂	—	16	1	no	—
634	C₂	C₁₃×#2847	1	1	yes	characteristic
635	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
636	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3006	C₂
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
1. C₂²×C₁₃×#131	C₂	semidirect
2. C₂×C₁₃×#471	C₂	semidirect
3. C₂×C₁₃×#465	C₂	semidirect
4. C₁₃×#3007	C₂	semidirect
6. C₁₃×#1908	C₂	semidirect
7. C₁₃×#1907	C₂	semidirect
8. C₁₃×#1901	C₂	semidirect
9. C₁₃×#1900	C₂	semidirect
10. C₁₃×#1815	C₂	semidirect
11. C₁₃×#1810	C₂	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
38. C₂×C₁₃×#108	C₂²	semidirect
39. C₂×C₁₃×#106	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#101	C₂²	semidirect
45. C₂×C₁₃×#100	C₂²	semidirect
48. C₁₃×#343	C₂²	semidirect
49. C₁₃×#343	C₂²	semidirect
50. C₁₃×#341	C₂²	semidirect
81. C₁₃×#131	D₄	semidirect
131. #32941	C₁₃	direct (N × H)
221. C₂²×#131	C₂×C₁₃	semidirect
222. C₂×#471	C₂×C₁₃	semidirect
223. C₂×#465	C₂×C₁₃	semidirect
224. #3007	C₂×C₁₃	semidirect
226. #1908	C₂×C₁₃	semidirect
227. #1907	C₂×C₁₃	semidirect
228. #1901	C₂×C₁₃	semidirect
229. #1900	C₂×C₁₃	semidirect
230. #1815	C₂×C₁₃	semidirect
231. #1810	C₂×C₁₃	semidirect
297. C₂²×SD₁₆	C₂²×C₁₃	semidirect
320. C₂×#108	C₂²×C₁₃	semidirect
321. C₂×#106	C₂²×C₁₃	semidirect
324. C₂×#103	C₂²×C₁₃	semidirect
325. C₂×#102	C₂²×C₁₃	semidirect
326. C₂×#101	C₂²×C₁₃	semidirect
327. C₂×#100	C₂²×C₁₃	semidirect
330. #343	C₂²×C₁₃	semidirect
331. #343	C₂²×C₁₃	semidirect
332. #341	C₂²×C₁₃	semidirect
349. C₂²×C₁₃	#471	semidirect
391. #131	D₄×C₁₃	semidirect
538. C₁₃	#32941	direct (N × H)
617. C₂²	C₁₃×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#131	2
C₂×C₁₃×#471	2
C₂×C₁₃×#465	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1901	2
C₁₃×#1900	2
C₁₃×#1815	2
C₁₃×#1810	2
#32941	13

Subgroups — C13×#32941 #15719280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32941 #15719280