Subgroups — C₁₃×#32944 #15719283

Order 3328.

1320 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#471	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#468	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×#1816	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1811	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	C₁₃×#568	—	2	8	no	—
17	C₂×C₁₃×#131	—	2	2	no	—
18	C₂×C₁₃×#131	C₂²	1	2	yes	—
19	C₂×C₁₃×#131	C₂²	1	2	yes	—
20	C₂²×C₁₃×M₁₆	—	2	2	no	—
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₁₃×#471	—	2	8	no	—
26	C₁₃×#468	—	2	2	no	—
27	C₁₃×#468	—	2	2	no	—
28	C₁₃×#452	—	2	2	no	—
29	C₁₃×#451	—	2	1	no	—
30	C₁₃×#450	—	2	1	no	—
31	C₁₃×#449	—	2	2	no	—
32	C₁₃×#448	—	2	1	no	—
33	C₁₃×#447	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#417	C₂²	1	2	yes	—
37	C₁₃×#417	C₂²	1	2	yes	—
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
42	C₁₃×#407	C₂²	1	1	yes	characteristic
43	C₁₃×#407	C₂²	1	1	yes	characteristic
44	C₁₃×#343	C₂²	1	2	yes	complemented
45	C₁₃×#343	C₂²	1	2	yes	complemented
46	C₁₃×#341	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	D₄	1	2	yes	—
52	C₂×C₁₃×#41	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#137	—	2	4	no	—
62	C₁₃×#137	—	2	4	no	—
63	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
65	C₂×C₁₃×Q₁₆	—	2	2	no	—
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	4	no	—
70	C₂×C₁₃×D₈	—	2	2	no	—
71	C₁₃×#131	—	2	16	no	—
72	C₁₃×#131	—	2	4	no	—
73	C₁₃×#131	—	2	4	no	—
74	C₁₃×#131	—	2	4	no	—
75	C₁₃×#131	D₄	1	8	yes	complemented
76	C₂×C₁₃×M₁₆	—	2	16	no	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	4	no	—
79	C₂×C₁₃×M₁₆	—	2	2	no	—
80	C₂×C₁₃×M₁₆	—	2	2	no	—
81	C₂×C₁₃×M₁₆	—	2	4	no	—
82	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
83	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
84	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
87	C₂²×C₈×C₁₃	—	2	1	no	—
88	C₂²×C₈×C₁₃	—	2	2	no	—
89	C₂²×C₈×C₁₃	—	2	2	no	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	2	1	no	—
98	C₁₃×#121	—	2	1	no	—
99	C₁₃×#121	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₁₃×#108	—	2	4	no	—
106	C₁₃×#107	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#103	—	2	2	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#101	—	2	4	no	—
114	C₁₃×#100	—	2	4	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₁₃×C₂²⋊C₈	—	2	1	no	—
117	C₁₃×C₂²⋊C₈	—	2	1	no	—
118	C₁₃×C₂²⋊C₈	—	2	1	no	—
119	#32944	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂⁴×C₁₃	—	2	1	no	—
122	C₂⁴×C₁₃	#41	1	1	yes	characteristic
123	C₁₃×#41	—	2	4	no	—
124	C₁₃×#41	—	2	8	no	—
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	4	no	—
127	C₁₃×#41	—	2	4	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	—	2	2	no	—
130	C₁₃×#41	C₂×D₄	1	4	yes	—
131	C₁₃×#41	#41	1	4	yes	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	4	1	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	—	8	2	no	—
151	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×Q₁₆	—	4	4	no	—
169	C₁₃×SD₁₆	—	4	4	no	—
170	C₁₃×SD₁₆	—	4	4	no	—
171	C₁₃×SD₁₆	—	4	4	no	—
172	C₁₃×D₈	—	4	4	no	—
173	C₁₃×M₁₆	—	2	4	no	—
174	C₁₃×M₁₆	—	2	8	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	4	no	—
177	C₁₃×M₁₆	—	2	8	no	—
178	C₁₃×M₁₆	—	2	4	no	—
179	C₁₃×M₁₆	—	2	2	no	—
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	2	no	—
182	C₁₃×M₁₆	—	2	2	no	—
183	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₁₃	—	2	4	no	—
185	C₂×C₈×C₁₃	—	2	8	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	2	8	no	—
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	—	2	2	no	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#471	C₂×C₁₃	1	2	yes	complemented
206	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3006	C₂×C₁₃	1	1	yes	characteristic
209	#1908	C₂×C₁₃	1	2	yes	complemented
210	#1907	C₂×C₁₃	1	2	yes	complemented
211	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1816	C₂×C₁₃	1	2	yes	complemented
214	#1811	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	2	no	—
222	C₂³×C₁₃	—	8	1	no	—
223	C₂³×C₁₃	—	8	1	no	—
224	C₂³×C₁₃	—	8	1	no	—
225	C₂³×C₁₃	—	8	1	no	—
226	C₂³×C₁₃	#121	1	1	yes	characteristic
227	C₂³×C₁₃	#121	1	1	yes	characteristic
228	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	4	no	—
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	#121	1	4	yes	—
235	D₄×C₁₃	—	2	8	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	8	2	no	—
244	D₄×C₁₃	—	8	2	no	—
245	D₄×C₁₃	#121	1	4	yes	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	8	1	no	—
263	C₂×C₄×C₁₃	—	8	1	no	—
264	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
270	C₈×C₁₃	—	2	4	no	—
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₈×C₁₃	—	4	2	no	—
274	C₈×C₁₃	#120	1	4	yes	—
275	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#137	C₂²×C₁₃	1	2	yes	—
277	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
279	#568	—	2	8	no	—
280	C₂×#131	—	2	2	no	—
281	C₂×#131	C₂²×C₁₃	1	2	yes	—
282	C₂×#131	C₂²×C₁₃	1	2	yes	—
283	C₂²×M₁₆	—	2	2	no	—
284	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
285	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
288	#471	—	2	8	no	—
289	#468	—	2	2	no	—
290	#468	—	2	2	no	—
291	#452	—	2	2	no	—
292	#451	—	2	1	no	—
293	#450	—	2	1	no	—
294	#449	—	2	2	no	—
295	#448	—	2	1	no	—
296	#447	—	2	1	no	—
297	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	#417	C₂²×C₁₃	1	2	yes	—
300	#417	C₂²×C₁₃	1	2	yes	—
301	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
304	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
305	#407	C₂²×C₁₃	1	1	yes	characteristic
306	#407	C₂²×C₁₃	1	1	yes	characteristic
307	#343	C₂²×C₁₃	1	2	yes	complemented
308	#343	C₂²×C₁₃	1	2	yes	complemented
309	#341	C₂²×C₁₃	1	2	yes	complemented
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	4	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	8	2	no	—
322	C₂²×C₁₃	—	8	4	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	—	8	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	16	2	no	—
327	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
328	C₂²×C₁₃	#525	1	2	yes	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	4	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	8	1	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
336	C₄×C₁₃	C₂×#121	1	2	yes	—
337	C₄×C₁₃	#525	1	1	yes	characteristic
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	D₄×C₁₃	1	2	yes	—
343	C₂×#41	C₂³×C₁₃	1	2	yes	—
344	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
345	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	#137	—	2	4	no	—
353	#137	—	2	4	no	—
354	AGL(1,ℤ/8)	—	2	4	no	—
355	AGL(1,ℤ/8)	—	2	4	no	—
356	C₂×Q₁₆	—	2	2	no	—
357	C₂×SD₁₆	—	2	2	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	2	4	no	—
361	C₂×D₈	—	2	2	no	—
362	#131	—	2	16	no	—
363	#131	—	2	4	no	—
364	#131	—	2	4	no	—
365	#131	—	2	4	no	—
366	#131	D₄×C₁₃	1	8	yes	complemented
367	C₂×M₁₆	—	2	16	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	4	no	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	4	no	—
373	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
374	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
375	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
376	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
377	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	2	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	#108	—	2	4	no	—
397	#107	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#101	—	2	4	no	—
405	#100	—	2	4	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂×C₁₃	—	2	2	no	—
411	C₂×C₁₃	—	4	1	no	—
412	C₂×C₁₃	—	4	1	no	—
413	C₂×C₁₃	—	4	4	no	—
414	C₂×C₁₃	—	16	1	no	—
415	C₂×C₁₃	#2847	1	1	yes	characteristic
416	C₂×C₁₃	#3068	1	1	yes	characteristic
417	C₂×C₁₃	#3069	1	1	yes	characteristic
418	C₂⁴	—	2	1	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	C₁₃×#41	1	1	yes	characteristic
421	#41	—	2	4	no	—
422	#41	—	2	8	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	C₂×D₄×C₁₃	1	4	yes	—
429	#41	C₁₃×#41	1	4	yes	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	8	2	no	—
449	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
466	Q₁₆	—	4	4	no	—
467	SD₁₆	—	4	4	no	—
468	SD₁₆	—	4	4	no	—
469	SD₁₆	—	4	4	no	—
470	D₈	—	4	4	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	—	2	8	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	4	no	—
475	M₁₆	—	2	8	no	—
476	M₁₆	—	2	4	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
482	C₂×C₈	—	2	4	no	—
483	C₂×C₈	—	2	8	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	8	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
490	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
491	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₁₃	#32944	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³	—	2	4	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	8	1	no	—
511	C₂³	—	8	1	no	—
512	C₂³	—	8	1	no	—
513	C₂³	—	8	1	no	—
514	C₂³	C₁₃×#121	1	1	yes	characteristic
515	C₂³	C₁₃×#121	1	1	yes	characteristic
516	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
517	Q₈	—	2	4	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	4	1	no	—
522	Q₈	C₁₃×#121	1	4	yes	—
523	D₄	—	2	8	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	1	no	—
531	D₄	—	8	2	no	—
532	D₄	—	8	2	no	—
533	D₄	C₁₃×#121	1	4	yes	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	—	8	1	no	—
552	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
553	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
558	C₈	—	2	4	no	—
559	C₈	—	2	2	no	—
560	C₈	—	4	2	no	—
561	C₈	—	4	2	no	—
562	C₈	C₁₃×#120	1	4	yes	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	4	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	16	2	no	—
580	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
581	C₂²	C₁₃×#525	1	2	yes	—
582	C₄	—	2	1	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
589	C₄	C₂×C₁₃×#121	1	2	yes	—
590	C₄	C₁₃×#525	1	1	yes	characteristic
591	C₂	—	2	2	no	—
592	C₂	—	4	1	no	—
593	C₂	—	4	1	no	—
594	C₂	—	4	4	no	—
595	C₂	—	16	1	no	—
596	C₂	C₁₃×#2847	1	1	yes	characteristic
597	C₂	C₁₃×#3068	1	1	yes	characteristic
598	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	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. C₂×C₁₃×#568	C₂	semidirect
2. C₂×C₁₃×#471	C₂	semidirect
3. C₂×C₁₃×#468	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×#1816	C₂	semidirect
11. C₁₃×#1811	C₂	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
34. C₂×C₁₃×#108	C₂²	semidirect
35. C₂×C₁₃×#107	C₂²	semidirect
38. C₂×C₁₃×#103	C₂²	semidirect
39. C₂×C₁₃×#102	C₂²	semidirect
40. C₂×C₁₃×#101	C₂²	semidirect
41. C₂×C₁₃×#100	C₂²	semidirect
44. C₁₃×#343	C₂²	semidirect
45. C₁₃×#343	C₂²	semidirect
46. C₁₃×#341	C₂²	semidirect
75. C₁₃×#131	D₄	semidirect
119. #32944	C₁₃	direct (N × H)
204. C₂×#568	C₂×C₁₃	semidirect
205. C₂×#471	C₂×C₁₃	semidirect
206. C₂×#468	C₂×C₁₃	semidirect
207. #3007	C₂×C₁₃	semidirect
209. #1908	C₂×C₁₃	semidirect
210. #1907	C₂×C₁₃	semidirect
211. #1901	C₂×C₁₃	semidirect
212. #1900	C₂×C₁₃	semidirect
213. #1816	C₂×C₁₃	semidirect
214. #1811	C₂×C₁₃	semidirect
278. C₂²×SD₁₆	C₂²×C₁₃	semidirect
297. C₂×#108	C₂²×C₁₃	semidirect
298. C₂×#107	C₂²×C₁₃	semidirect
301. C₂×#103	C₂²×C₁₃	semidirect
302. C₂×#102	C₂²×C₁₃	semidirect
303. C₂×#101	C₂²×C₁₃	semidirect
304. C₂×#100	C₂²×C₁₃	semidirect
307. #343	C₂²×C₁₃	semidirect
308. #343	C₂²×C₁₃	semidirect
309. #341	C₂²×C₁₃	semidirect
366. #131	D₄×C₁₃	semidirect
502. C₁₃	#32944	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×#568	2
C₂×C₁₃×#471	2
C₂×C₁₃×#468	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1901	2
C₁₃×#1900	2
C₁₃×#1816	2
C₁₃×#1811	2
#32944	13

Subgroups — C13×#32944 #15719283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32944 #15719283