Subgroups — C₁₃×#60644 #15746983

Order 3328.

3350 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3155	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3154	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3153	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3151	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#575	—	2	16	no	—
14	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
15	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
24	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
25	C₁₃×#537	—	2	2	no	—
26	C₁₃×#536	C₂²	1	4	yes	complemented
27	C₁₃×#535	—	2	4	no	—
28	C₁₃×#535	C₂²	1	8	yes	complemented
29	C₁₃×#535	C₂²	1	4	yes	complemented
30	C₁₃×#534	—	2	2	no	—
31	C₁₃×#532	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
34	C₁₃×#525	—	2	4	no	—
35	C₂×C₁₃×#121	—	2	2	no	—
36	C₂×C₁₃×#120	—	2	2	no	—
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₁₃×#497	C₂²	1	8	yes	complemented
39	C₁₃×#496	C₂²	1	8	yes	complemented
40	C₁₃×#496	C₂²	1	16	yes	complemented
41	C₁₃×#495	C₂²	1	16	yes	complemented
42	C₁₃×#493	C₂²	1	8	yes	complemented
43	C₁₃×#492	C₂²	1	8	yes	complemented
44	C₁₃×#405	C₂²	1	8	yes	complemented
45	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
46	C₂⁵×C₁₃	—	2	1	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	2	8	no	—
51	C₂×C₁₃×#41	—	2	8	no	—
52	C₂×C₁₃×#41	—	2	8	no	—
53	C₂×C₁₃×#41	C₂³	1	4	yes	—
54	C₂×C₁₃×#41	C₂³	1	4	yes	—
55	C₂×C₁₃×#41	C₂³	1	4	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	2	no	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#137	—	2	16	no	—
72	C₁₃×#137	—	2	16	no	—
73	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
77	C₁₃×#135	—	2	32	no	—
78	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
79	C₂×C₁₃×SD₁₆	—	2	16	no	—
80	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
82	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
83	C₂×C₁₃×D₈	—	2	16	no	—
84	C₂×C₁₃×D₈	C₂³	1	16	yes	—
85	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
86	C₂×C₁₃×M₁₆	D₄	1	16	yes	complemented
87	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
89	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
91	C₁₃×#127	—	2	4	no	—
92	C₁₃×#127	C₂³	1	8	yes	—
93	C₁₃×#127	C₂³	1	4	yes	complemented
94	C₁₃×#124	—	2	4	no	—
95	C₁₃×#124	C₂³	1	8	yes	—
96	C₁₃×#124	C₂³	1	8	yes	complemented
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	8	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#121	—	2	16	no	—
101	C₁₃×#121	—	2	8	no	—
102	C₁₃×#120	—	2	16	no	—
103	C₁₃×#120	—	2	8	no	—
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₁₃×#117	D₄	1	4	yes	—
106	C₁₃×#117	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₁₃×#97	C₂³	1	8	yes	complemented
112	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
113	#60644	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	2	1	no	—
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	4	4	no	—
119	C₂⁴×C₁₃	—	8	4	no	—
120	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₁₃×#41	—	2	8	no	—
122	C₁₃×#41	—	2	8	no	—
123	C₁₃×#41	—	2	8	no	—
124	C₁₃×#41	—	2	8	no	—
125	C₁₃×#41	—	2	8	no	—
126	C₁₃×#41	—	2	8	no	—
127	C₁₃×#41	—	4	8	no	—
128	C₁₃×#41	—	4	8	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	2	4	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	2	16	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	8	8	no	—
157	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	4	8	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₁₃×Q₁₆	—	2	16	no	—
174	C₁₃×SD₁₆	—	2	32	no	—
175	C₁₃×SD₁₆	—	2	16	no	—
176	C₁₃×SD₁₆	—	2	16	no	—
177	C₁₃×D₈	—	2	32	no	—
178	C₁₃×D₈	—	2	16	no	—
179	C₁₃×M₁₆	C₂×D₄	1	16	yes	—
180	C₁₃×M₁₆	C₂×D₄	1	16	yes	complemented
181	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	complemented
182	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
185	C₁₃×C₂²⋊C₄	—	2	16	no	—
186	C₁₃×C₂²⋊C₄	—	2	16	no	—
187	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
188	C₄²×C₁₃	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	C₂⁴	1	4	yes	—
190	C₂×#575	C₂×C₁₃	1	2	yes	complemented
191	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
192	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3155	C₂×C₁₃	1	8	yes	complemented
195	#3154	C₂×C₁₃	1	8	yes	complemented
196	#3153	C₂×C₁₃	1	4	yes	complemented
197	#3151	C₂×C₁₃	1	4	yes	complemented
198	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	4	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	4	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	8	no	—
209	C₂³×C₁₃	—	8	4	no	—
210	C₂³×C₁₃	—	8	8	no	—
211	C₂³×C₁₃	—	8	16	no	—
212	C₂³×C₁₃	#127	1	4	yes	—
213	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	2	4	no	—
221	D₄×C₁₃	—	2	8	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	4	8	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	4	8	no	—
227	D₄×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	4	no	—
229	D₄×C₁₃	—	4	4	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	8	8	no	—
232	D₄×C₁₃	—	8	16	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	8	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	#127	1	4	yes	—
242	C₂×C₄×C₁₃	#127	1	8	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
250	C₈×C₁₃	C₂²×D₄	1	16	yes	—
251	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×#41	C₂²×C₁₃	1	2	yes	—
253	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
254	#575	—	2	16	no	—
255	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
256	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
257	C₂×AGL(1,ℤ/8)	—	2	16	no	—
258	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
259	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
261	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
262	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
263	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
264	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
265	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
266	#537	—	2	2	no	—
267	#536	C₂²×C₁₃	1	4	yes	complemented
268	#535	—	2	4	no	—
269	#535	C₂²×C₁₃	1	8	yes	complemented
270	#535	C₂²×C₁₃	1	4	yes	complemented
271	#534	—	2	2	no	—
272	#532	C₂²×C₁₃	1	4	yes	complemented
273	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
274	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
275	#525	—	2	4	no	—
276	C₂×#121	—	2	2	no	—
277	C₂×#120	—	2	2	no	—
278	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
279	#497	C₂²×C₁₃	1	8	yes	complemented
280	#496	C₂²×C₁₃	1	8	yes	complemented
281	#496	C₂²×C₁₃	1	16	yes	complemented
282	#495	C₂²×C₁₃	1	16	yes	complemented
283	#493	C₂²×C₁₃	1	8	yes	complemented
284	#492	C₂²×C₁₃	1	8	yes	complemented
285	#405	C₂²×C₁₃	1	8	yes	complemented
286	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	4	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	4	8	no	—
292	C₂²×C₁₃	—	4	8	no	—
293	C₂²×C₁₃	—	4	4	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	8	4	no	—
297	C₂²×C₁₃	—	8	8	no	—
298	C₂²×C₁₃	—	8	8	no	—
299	C₂²×C₁₃	—	8	16	no	—
300	C₂²×C₁₃	C₂×#127	1	4	yes	—
301	C₂²×C₁₃	C₂×#127	1	2	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₃	—	2	8	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	C₂×#127	1	2	yes	—
307	C₄×C₁₃	C₂×#127	1	4	yes	—
308	C₄×C₁₃	C₂³×D₄	1	2	yes	—
309	C₂⁵	—	2	1	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	8	no	—
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	C₂³×C₁₃	1	4	yes	—
317	C₂×#41	C₂³×C₁₃	1	4	yes	—
318	C₂×#41	C₂³×C₁₃	1	4	yes	—
319	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	8	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
328	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
330	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	#137	—	2	16	no	—
335	#137	—	2	16	no	—
336	AGL(1,ℤ/8)	—	2	32	no	—
337	AGL(1,ℤ/8)	—	2	16	no	—
338	AGL(1,ℤ/8)	—	2	32	no	—
339	AGL(1,ℤ/8)	—	2	16	no	—
340	#135	—	2	32	no	—
341	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
342	C₂×SD₁₆	—	2	16	no	—
343	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
344	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
345	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
346	C₂×D₈	—	2	16	no	—
347	C₂×D₈	C₂³×C₁₃	1	16	yes	—
348	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
349	C₂×M₁₆	D₄×C₁₃	1	16	yes	complemented
350	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
351	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
352	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
353	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
354	#127	—	2	4	no	—
355	#127	C₂³×C₁₃	1	8	yes	—
356	#127	C₂³×C₁₃	1	4	yes	complemented
357	#124	—	2	4	no	—
358	#124	C₂³×C₁₃	1	8	yes	—
359	#124	C₂³×C₁₃	1	8	yes	complemented
360	#123	—	2	8	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	#121	—	2	8	no	—
363	#121	—	2	16	no	—
364	#121	—	2	8	no	—
365	#120	—	2	16	no	—
366	#120	—	2	8	no	—
367	C₄×D₄	—	2	8	no	—
368	#117	D₄×C₁₃	1	4	yes	—
369	#117	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
371	C₂×C₂²⋊C₄	—	2	4	no	—
372	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
373	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
374	#97	C₂³×C₁₃	1	8	yes	complemented
375	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
376	C₂×C₁₃	—	2	2	no	—
377	C₂×C₁₃	—	2	4	no	—
378	C₂×C₁₃	—	8	2	no	—
379	C₂×C₁₃	—	8	4	no	—
380	C₂×C₁₃	—	8	4	no	—
381	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
382	C₂×C₁₃	#3585	1	2	yes	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	—	2	1	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	—	8	4	no	—
389	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
390	#41	—	2	8	no	—
391	#41	—	2	8	no	—
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	#41	—	4	8	no	—
397	#41	—	4	8	no	—
398	#41	—	4	8	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
405	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	16	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	—	4	8	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	8	no	—
425	C₂×D₄	—	8	8	no	—
426	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	Q₁₆	—	2	16	no	—
443	SD₁₆	—	2	32	no	—
444	SD₁₆	—	2	16	no	—
445	SD₁₆	—	2	16	no	—
446	D₈	—	2	32	no	—
447	D₈	—	2	16	no	—
448	M₁₆	C₂×D₄×C₁₃	1	16	yes	—
449	M₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
450	C₂×C₈	C₂×D₄×C₁₃	1	16	yes	complemented
451	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
454	C₂²⋊C₄	—	2	16	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
457	C₄²	C₂×D₄×C₁₃	1	4	yes	—
458	C₄²	C₂⁴×C₁₃	1	4	yes	—
459	C₁₃	#60644	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	8	8	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	16	no	—
473	C₂³	C₁₃×#127	1	4	yes	—
474	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
475	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	8	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	16	no	—
493	D₄	—	8	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	C₁₃×#127	1	4	yes	—
503	C₂×C₄	C₁₃×#127	1	8	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
507	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
510	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
511	C₈	C₂²×D₄×C₁₃	1	16	yes	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	4	8	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	8	4	no	—
522	C₂²	—	8	8	no	—
523	C₂²	—	8	8	no	—
524	C₂²	—	8	16	no	—
525	C₂²	C₂×C₁₃×#127	1	4	yes	—
526	C₂²	C₂×C₁₃×#127	1	2	yes	—
527	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
528	C₄	—	2	8	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	4	no	—
531	C₄	C₂×C₁₃×#127	1	2	yes	—
532	C₄	C₂×C₁₃×#127	1	4	yes	—
533	C₄	C₂³×D₄×C₁₃	1	2	yes	—
534	C₂	—	2	2	no	—
535	C₂	—	2	4	no	—
536	C₂	—	8	4	no	—
537	C₂	—	8	2	no	—
538	C₂	—	8	4	no	—
539	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
540	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#575	C₂	semidirect
2. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₁₃×#3449	C₂	semidirect
4. C₂×C₁₃×#535	C₂	semidirect
5. C₁₃×#3155	C₂	semidirect
6. C₁₃×#3154	C₂	semidirect
7. C₁₃×#3153	C₂	semidirect
8. C₁₃×#3151	C₂	semidirect
9. C₁₃×#2873	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
15. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂²×C₁₃×D₈	C₂²	semidirect
26. C₁₃×#536	C₂²	semidirect
28. C₁₃×#535	C₂²	semidirect
29. C₁₃×#535	C₂²	semidirect
31. C₁₃×#532	C₂²	semidirect
32. C₂×C₁₃×#127	C₂²	semidirect
33. C₂×C₁₃×#124	C₂²	semidirect
38. C₁₃×#497	C₂²	semidirect
39. C₁₃×#496	C₂²	semidirect
40. C₁₃×#496	C₂²	semidirect
41. C₁₃×#495	C₂²	semidirect
42. C₁₃×#493	C₂²	semidirect
43. C₁₃×#492	C₂²	semidirect
44. C₁₃×#405	C₂²	semidirect
45. C₄×C₁₃×M₁₆	C₂²	semidirect
78. C₂×C₁₃×Q₁₆	C₂³	semidirect
81. C₂×C₁₃×SD₁₆	C₂³	semidirect
82. C₂×C₁₃×SD₁₆	C₂³	semidirect
85. C₂×C₁₃×D₈	C₂³	semidirect
86. C₂×C₁₃×M₁₆	D₄	semidirect
90. C₁₃×C₄⋊Q₈	C₂³	semidirect
93. C₁₃×#127	C₂³	semidirect
96. C₁₃×#124	C₂³	semidirect
111. C₁₃×#97	C₂³	semidirect
112. C₄×C₈×C₁₃	C₂³	semidirect
113. #60644	C₁₃	direct (N × H)
180. C₁₃×M₁₆	C₂×D₄	semidirect
181. C₂×C₈×C₁₃	C₂×D₄	semidirect
190. C₂×#575	C₂×C₁₃	semidirect
191. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
192. #3449	C₂×C₁₃	semidirect
193. C₂×#535	C₂×C₁₃	semidirect
194. #3155	C₂×C₁₃	semidirect
195. #3154	C₂×C₁₃	semidirect
196. #3153	C₂×C₁₃	semidirect
197. #3151	C₂×C₁₃	semidirect
198. #2873	C₂×C₁₃	semidirect
255. C₂×#137	C₂²×C₁₃	semidirect
256. C₂×#137	C₂²×C₁₃	semidirect
258. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
259. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
260. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
261. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
262. C₂×#135	C₂²×C₁₃	semidirect
263. C₂²×SD₁₆	C₂²×C₁₃	semidirect
264. C₂²×D₈	C₂²×C₁₃	semidirect
267. #536	C₂²×C₁₃	semidirect
269. #535	C₂²×C₁₃	semidirect
270. #535	C₂²×C₁₃	semidirect
272. #532	C₂²×C₁₃	semidirect
273. C₂×#127	C₂²×C₁₃	semidirect
274. C₂×#124	C₂²×C₁₃	semidirect
279. #497	C₂²×C₁₃	semidirect
280. #496	C₂²×C₁₃	semidirect
281. #496	C₂²×C₁₃	semidirect
282. #495	C₂²×C₁₃	semidirect
283. #493	C₂²×C₁₃	semidirect
284. #492	C₂²×C₁₃	semidirect
285. #405	C₂²×C₁₃	semidirect
286. C₄×M₁₆	C₂²×C₁₃	semidirect
341. C₂×Q₁₆	C₂³×C₁₃	semidirect
344. C₂×SD₁₆	C₂³×C₁₃	semidirect
345. C₂×SD₁₆	C₂³×C₁₃	semidirect
348. C₂×D₈	C₂³×C₁₃	semidirect
349. C₂×M₁₆	D₄×C₁₃	semidirect
353. C₄⋊Q₈	C₂³×C₁₃	semidirect
356. #127	C₂³×C₁₃	semidirect
359. #124	C₂³×C₁₃	semidirect
374. #97	C₂³×C₁₃	semidirect
375. C₄×C₈	C₂³×C₁₃	semidirect
449. M₁₆	C₂×D₄×C₁₃	semidirect
450. C₂×C₈	C₂×D₄×C₁₃	semidirect
459. C₁₃	#60644	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×#575	2
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#3449	2
C₂×C₁₃×#535	2
C₁₃×#3155	2
C₁₃×#3154	2
C₁₃×#3153	2
C₁₃×#3151	2
C₁₃×#2873	2
#60644	13

Subgroups — C13×#60644 #15746983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60644 #15746983