Subgroups — C₁₃×#60807 #15747146

Order 3328.

2030 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3223	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3221	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3005	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	2	yes	—
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₁₃×#542	C₂²	1	4	yes	complemented
22	C₁₃×#541	C₂²	1	2	yes	complemented
23	C₁₃×#540	C₂²	1	2	yes	complemented
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#538	—	2	2	no	—
26	C₁₃×#536	—	2	4	no	—
27	C₁₃×#536	C₂²	1	4	yes	—
28	C₁₃×#536	C₂²	1	4	yes	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×#529	—	2	4	no	—
34	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₁₃×#525	C₂²	1	2	yes	—
37	C₂×C₁₃×#123	—	2	2	no	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
39	C₄×C₁₃×#41	C₂²	1	2	yes	—
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
41	C₁₃×#497	C₂²	1	4	yes	complemented
42	C₁₃×#497	C₂²	1	2	yes	complemented
43	C₁₃×#496	C₂²	1	2	yes	complemented
44	C₁₃×#495	C₂²	1	4	yes	complemented
45	C₁₃×#494	C₂²	1	2	yes	complemented
46	C₁₃×#492	C₂²	1	2	yes	complemented
47	C₁₃×#491	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#487	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#463	C₂²	1	8	yes	complemented
53	C₁₃×#462	C₂²	1	8	yes	complemented
54	C₁₃×#461	C₂²	1	8	yes	complemented
55	C₁₃×#452	C₂²	1	8	yes	—
56	C₁₃×#451	C₂²	1	8	yes	complemented
57	C₁₃×#449	C₂²	1	8	yes	—
58	C₁₃×#448	C₂²	1	8	yes	complemented
59	C₁₃×#433	C₂²	1	4	yes	complemented
60	C₁₃×#433	C₂²	1	4	yes	complemented
61	C₁₃×#423	C₂²	1	2	yes	—
62	C₁₃×#419	C₂²	1	2	yes	—
63	C₁₃×#419	C₂²	1	2	yes	—
64	C₁₃×#419	C₂²	1	2	yes	—
65	C₁₃×#418	C₂²	1	2	yes	—
66	C₁₃×#407	C₂²	1	2	yes	—
67	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	4	4	no	—
71	C₂×C₁₃×#41	C₂³	1	2	yes	—
72	C₂×C₁₃×#41	C₂³	1	4	yes	—
73	C₂²×Q₈×C₁₃	—	2	1	no	—
74	C₂²×Q₈×C₁₃	—	2	2	no	—
75	C₂²×Q₈×C₁₃	—	4	4	no	—
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#137	—	4	4	no	—
86	C₁₃×#137	—	4	4	no	—
87	C₁₃×#137	—	4	4	no	—
88	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
89	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×D₈	C₂³	1	4	yes	—
97	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
99	C₁₃×C₄⋊Q₈	—	2	2	no	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
103	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₃×#127	C₂³	1	1	yes	characteristic
107	C₁₃×#126	—	2	4	no	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#125	—	2	4	no	—
110	C₁₃×#125	C₂³	1	2	yes	—
111	C₁₃×#124	—	2	4	no	—
112	C₁₃×#124	—	2	2	no	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	C₂³	1	4	yes	—
115	C₁₃×#124	C₂³	1	2	yes	—
116	C₁₃×#124	C₂³	1	2	yes	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	8	no	—
121	C₁₃×#123	—	2	8	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	8	no	—
125	C₁₃×C₂²⋊Q₈	—	2	8	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₁₃×#120	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×D₄×C₁₃	—	2	4	no	—
135	C₄×D₄×C₁₃	—	2	4	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	C₂³	1	4	yes	—
138	C₁₃×#117	—	2	2	no	—
139	C₁₃×#117	D₄	1	4	yes	—
140	C₁₃×#117	C₂³	1	2	yes	—
141	C₁₃×#117	C₂³	1	2	yes	—
142	C₁₃×#117	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
149	C₂×C₄²×C₁₃	—	2	2	no	—
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
153	C₁₃×#103	C₂³	1	8	yes	—
154	C₁₃×#103	C₂³	1	8	yes	—
155	C₁₃×#103	C₂³	1	8	yes	—
156	C₁₃×#102	C₂³	1	8	yes	—
157	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
158	C₁₃×#97	C₂³	1	2	yes	—
159	C₁₃×#97	C₂³	1	2	yes	—
160	C₄×C₈×C₁₃	C₂³	1	2	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	#60807	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₁₃×#41	—	2	4	no	—
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	4	8	no	—
168	C₁₃×#41	—	4	8	no	—
169	C₂×Q₈×C₁₃	—	2	4	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	2	no	—
174	C₂×Q₈×C₁₃	—	2	4	no	—
175	C₂×Q₈×C₁₃	—	2	4	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	—	4	8	no	—
178	C₂×Q₈×C₁₃	—	4	4	no	—
179	C₂×Q₈×C₁₃	—	4	8	no	—
180	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
181	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
182	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
183	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
184	C₂×D₄×C₁₃	—	2	2	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	4	4	no	—
191	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	4	4	no	—
202	C₂²×C₄×C₁₃	—	4	4	no	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₁₃×Q₁₆	—	4	4	no	—
210	C₁₃×Q₁₆	—	4	4	no	—
211	C₁₃×Q₁₆	—	4	4	no	—
212	C₁₃×SD₁₆	—	4	4	no	—
213	C₁₃×SD₁₆	—	4	4	no	—
214	C₁₃×SD₁₆	—	4	4	no	—
215	C₁₃×SD₁₆	—	4	4	no	—
216	C₁₃×D₈	—	4	4	no	—
217	C₁₃×M₁₆	—	2	4	no	—
218	C₁₃×M₁₆	—	2	4	no	—
219	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
220	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	2	4	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
230	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	8	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
241	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	C₂×D₄	1	2	yes	—
245	C₄²×C₁₃	C₂×D₄	1	2	yes	—
246	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₄²×C₁₃	C₂⁴	1	2	yes	—
249	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3225	C₂×C₁₃	1	8	yes	complemented
252	#3223	C₂×C₁₃	1	4	yes	complemented
253	#3221	C₂×C₁₃	1	4	yes	complemented
254	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3040	C₂×C₁₃	1	2	yes	complemented
259	#3039	C₂×C₁₃	1	2	yes	complemented
260	#3005	C₂×C₁₃	1	2	yes	complemented
261	#3004	C₂×C₁₃	1	2	yes	complemented
262	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	4	2	no	—
267	C₂³×C₁₃	—	4	4	no	—
268	C₂³×C₁₃	—	4	2	no	—
269	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₁₃	—	2	2	no	—
272	Q₈×C₁₃	—	2	4	no	—
273	Q₈×C₁₃	—	2	4	no	—
274	Q₈×C₁₃	—	2	4	no	—
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	4	8	no	—
277	Q₈×C₁₃	—	4	2	no	—
278	Q₈×C₁₃	—	4	2	no	—
279	Q₈×C₁₃	—	4	2	no	—
280	Q₈×C₁₃	—	8	2	no	—
281	D₄×C₁₃	—	2	2	no	—
282	D₄×C₁₃	—	2	4	no	—
283	D₄×C₁₃	—	2	2	no	—
284	D₄×C₁₃	—	4	8	no	—
285	D₄×C₁₃	—	4	4	no	—
286	D₄×C₁₃	—	4	2	no	—
287	D₄×C₁₃	—	8	2	no	—
288	D₄×C₁₃	—	8	4	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	4	2	no	—
298	C₂×C₄×C₁₃	—	4	2	no	—
299	C₂×C₄×C₁₃	—	4	8	no	—
300	C₂×C₄×C₁₃	—	4	8	no	—
301	C₂×C₄×C₁₃	—	4	2	no	—
302	C₂×C₄×C₁₃	—	4	2	no	—
303	C₂×C₄×C₁₃	—	4	2	no	—
304	C₂×C₄×C₁₃	—	4	4	no	—
305	C₂×C₄×C₁₃	—	8	4	no	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
307	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
312	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
313	C₈×C₁₃	—	2	4	no	—
314	C₈×C₁₃	—	2	4	no	—
315	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
316	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#137	C₂²×C₁₃	1	2	yes	—
318	C₂×#137	C₂²×C₁₃	1	2	yes	—
319	C₂×#137	C₂²×C₁₃	1	2	yes	—
320	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
321	#542	C₂²×C₁₃	1	4	yes	complemented
322	#541	C₂²×C₁₃	1	2	yes	complemented
323	#540	C₂²×C₁₃	1	2	yes	complemented
324	#539	—	2	2	no	—
325	#538	—	2	2	no	—
326	#536	—	2	4	no	—
327	#536	C₂²×C₁₃	1	4	yes	—
328	#536	C₂²×C₁₃	1	4	yes	—
329	#533	C₂²×C₁₃	1	1	yes	characteristic
330	#532	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
333	#529	—	2	4	no	—
334	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
336	#525	C₂²×C₁₃	1	2	yes	—
337	C₂×#123	—	2	2	no	—
338	C₂×C₂²⋊Q₈	—	2	2	no	—
339	C₄×#41	C₂²×C₁₃	1	2	yes	—
340	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
341	#497	C₂²×C₁₃	1	4	yes	complemented
342	#497	C₂²×C₁₃	1	2	yes	complemented
343	#496	C₂²×C₁₃	1	2	yes	complemented
344	#495	C₂²×C₁₃	1	4	yes	complemented
345	#494	C₂²×C₁₃	1	2	yes	complemented
346	#492	C₂²×C₁₃	1	2	yes	complemented
347	#491	C₂²×C₁₃	1	4	yes	complemented
348	#489	C₂²×C₁₃	1	4	yes	complemented
349	#488	C₂²×C₁₃	1	4	yes	complemented
350	#487	C₂²×C₁₃	1	4	yes	complemented
351	#464	C₂²×C₁₃	1	8	yes	complemented
352	#463	C₂²×C₁₃	1	8	yes	complemented
353	#462	C₂²×C₁₃	1	8	yes	complemented
354	#461	C₂²×C₁₃	1	8	yes	complemented
355	#452	C₂²×C₁₃	1	8	yes	—
356	#451	C₂²×C₁₃	1	8	yes	complemented
357	#449	C₂²×C₁₃	1	8	yes	—
358	#448	C₂²×C₁₃	1	8	yes	complemented
359	#433	C₂²×C₁₃	1	4	yes	complemented
360	#433	C₂²×C₁₃	1	4	yes	complemented
361	#423	C₂²×C₁₃	1	2	yes	—
362	#419	C₂²×C₁₃	1	2	yes	—
363	#419	C₂²×C₁₃	1	2	yes	—
364	#419	C₂²×C₁₃	1	2	yes	—
365	#418	C₂²×C₁₃	1	2	yes	—
366	#407	C₂²×C₁₃	1	2	yes	—
367	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
368	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₁₃	—	2	2	no	—
370	C₂²×C₁₃	—	2	4	no	—
371	C₂²×C₁₃	—	2	2	no	—
372	C₂²×C₁₃	—	4	4	no	—
373	C₂²×C₁₃	—	4	4	no	—
374	C₂²×C₁₃	—	4	4	no	—
375	C₂²×C₁₃	—	4	2	no	—
376	C₂²×C₁₃	—	4	2	no	—
377	C₂²×C₁₃	—	8	4	no	—
378	C₂²×C₁₃	#535	1	2	yes	—
379	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₁₃	—	2	4	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	4	4	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	—	4	2	no	—
389	C₄×C₁₃	#535	1	2	yes	—
390	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
391	C₂×#41	—	2	2	no	—
392	C₂×#41	—	4	4	no	—
393	C₂×#41	C₂³×C₁₃	1	2	yes	—
394	C₂×#41	C₂³×C₁₃	1	4	yes	—
395	C₂²×Q₈	—	2	1	no	—
396	C₂²×Q₈	—	2	2	no	—
397	C₂²×Q₈	—	4	4	no	—
398	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
407	#137	—	4	4	no	—
408	#137	—	4	4	no	—
409	#137	—	4	4	no	—
410	AGL(1,ℤ/8)	—	4	4	no	—
411	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
412	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
413	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
414	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
415	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
416	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
417	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
418	C₂×D₈	C₂³×C₁₃	1	4	yes	—
419	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
420	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
421	C₄⋊Q₈	—	2	2	no	—
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
424	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
425	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
426	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
428	#127	C₂³×C₁₃	1	1	yes	characteristic
429	#126	—	2	4	no	—
430	#126	—	2	4	no	—
431	#125	—	2	4	no	—
432	#125	C₂³×C₁₃	1	2	yes	—
433	#124	—	2	4	no	—
434	#124	—	2	2	no	—
435	#124	—	2	2	no	—
436	#124	C₂³×C₁₃	1	4	yes	—
437	#124	C₂³×C₁₃	1	2	yes	—
438	#124	C₂³×C₁₃	1	2	yes	—
439	#124	C₂³×C₁₃	1	2	yes	—
440	#123	—	2	2	no	—
441	#123	—	2	4	no	—
442	#123	—	2	8	no	—
443	#123	—	2	8	no	—
444	#123	—	2	4	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	C₂²⋊Q₈	—	2	8	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
450	#121	—	2	2	no	—
451	#121	—	2	4	no	—
452	#121	C₂³×C₁₃	1	4	yes	—
453	#120	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	C₂³×C₁₃	1	4	yes	—
460	#117	—	2	2	no	—
461	#117	D₄×C₁₃	1	4	yes	—
462	#117	C₂³×C₁₃	1	2	yes	—
463	#117	C₂³×C₁₃	1	2	yes	—
464	#117	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	2	no	—
467	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
468	C₂×C₂²⋊C₄	—	2	2	no	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
471	C₂×C₄²	—	2	2	no	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
475	#103	C₂³×C₁₃	1	8	yes	—
476	#103	C₂³×C₁₃	1	8	yes	—
477	#103	C₂³×C₁₃	1	8	yes	—
478	#102	C₂³×C₁₃	1	8	yes	—
479	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
480	#97	C₂³×C₁₃	1	2	yes	—
481	#97	C₂³×C₁₃	1	2	yes	—
482	C₄×C₈	C₂³×C₁₃	1	2	yes	—
483	C₄×C₈	C₂³×C₁₃	1	2	yes	—
484	C₂×C₁₃	—	2	2	no	—
485	C₂×C₁₃	—	4	2	no	—
486	C₂×C₁₃	—	8	2	no	—
487	C₂×C₁₃	—	8	2	no	—
488	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
489	C₂×C₁₃	#3586	1	2	yes	—
490	C₂⁴	—	2	1	no	—
491	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
492	#41	—	2	4	no	—
493	#41	—	2	4	no	—
494	#41	—	4	8	no	—
495	#41	—	4	8	no	—
496	C₂×Q₈	—	2	4	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	4	8	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	8	no	—
507	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
508	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
509	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
510	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
519	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	Q₁₆	—	4	4	no	—
537	Q₁₆	—	4	4	no	—
538	Q₁₆	—	4	4	no	—
539	SD₁₆	—	4	4	no	—
540	SD₁₆	—	4	4	no	—
541	SD₁₆	—	4	4	no	—
542	SD₁₆	—	4	4	no	—
543	D₈	—	4	4	no	—
544	M₁₆	—	2	4	no	—
545	M₁₆	—	2	4	no	—
546	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
547	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
548	C₄⋊C₄	—	2	8	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
557	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
558	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
568	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	4	no	—
571	C₄²	C₂×D₄×C₁₃	1	2	yes	—
572	C₄²	C₂×D₄×C₁₃	1	2	yes	—
573	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
575	C₄²	C₂⁴×C₁₃	1	2	yes	—
576	C₁₃	#60807	1	1	yes	characteristic, direct product factor, Sylow
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	2	no	—
583	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
584	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	4	no	—
587	Q₈	—	2	4	no	—
588	Q₈	—	2	4	no	—
589	Q₈	—	2	2	no	—
590	Q₈	—	4	8	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	2	no	—
593	Q₈	—	4	2	no	—
594	Q₈	—	8	2	no	—
595	D₄	—	2	2	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	—	4	8	no	—
599	D₄	—	4	4	no	—
600	D₄	—	4	2	no	—
601	D₄	—	8	2	no	—
602	D₄	—	8	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	8	4	no	—
620	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
626	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
627	C₈	—	2	4	no	—
628	C₈	—	2	4	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	4	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	8	4	no	—
638	C₂²	C₁₃×#535	1	2	yes	—
639	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
640	C₄	—	2	4	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	4	4	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	C₁₃×#535	1	2	yes	—
650	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	2	no	—
653	C₂	—	8	2	no	—
654	C₂	—	8	2	no	—
655	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
656	C₂	C₁₃×#3586	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. C₁₃×#3455	C₂	semidirect
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3223	C₂	semidirect
5. C₁₃×#3221	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₁₃×#3152	C₂	semidirect
8. C₁₃×#3140	C₂	semidirect
9. C₁₃×#3139	C₂	semidirect
10. C₁₃×#3040	C₂	semidirect
11. C₁₃×#3039	C₂	semidirect
12. C₁₃×#3005	C₂	semidirect
13. C₁₃×#3004	C₂	semidirect
14. C₁₃×#2921	C₂	semidirect
21. C₁₃×#542	C₂²	semidirect
22. C₁₃×#541	C₂²	semidirect
23. C₁₃×#540	C₂²	semidirect
41. C₁₃×#497	C₂²	semidirect
42. C₁₃×#497	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#494	C₂²	semidirect
46. C₁₃×#492	C₂²	semidirect
47. C₁₃×#491	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#487	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#462	C₂²	semidirect
54. C₁₃×#461	C₂²	semidirect
56. C₁₃×#451	C₂²	semidirect
58. C₁₃×#448	C₂²	semidirect
59. C₁₃×#433	C₂²	semidirect
60. C₁₃×#433	C₂²	semidirect
162. #60807	C₁₃	direct (N × H)
249. #3455	C₂×C₁₃	semidirect
250. C₂×#536	C₂×C₁₃	semidirect
251. #3225	C₂×C₁₃	semidirect
252. #3223	C₂×C₁₃	semidirect
253. #3221	C₂×C₁₃	semidirect
254. #3153	C₂×C₁₃	semidirect
255. #3152	C₂×C₁₃	semidirect
256. #3140	C₂×C₁₃	semidirect
257. #3139	C₂×C₁₃	semidirect
258. #3040	C₂×C₁₃	semidirect
259. #3039	C₂×C₁₃	semidirect
260. #3005	C₂×C₁₃	semidirect
261. #3004	C₂×C₁₃	semidirect
262. #2921	C₂×C₁₃	semidirect
321. #542	C₂²×C₁₃	semidirect
322. #541	C₂²×C₁₃	semidirect
323. #540	C₂²×C₁₃	semidirect
341. #497	C₂²×C₁₃	semidirect
342. #497	C₂²×C₁₃	semidirect
343. #496	C₂²×C₁₃	semidirect
344. #495	C₂²×C₁₃	semidirect
345. #494	C₂²×C₁₃	semidirect
346. #492	C₂²×C₁₃	semidirect
347. #491	C₂²×C₁₃	semidirect
348. #489	C₂²×C₁₃	semidirect
349. #488	C₂²×C₁₃	semidirect
350. #487	C₂²×C₁₃	semidirect
351. #464	C₂²×C₁₃	semidirect
352. #463	C₂²×C₁₃	semidirect
353. #462	C₂²×C₁₃	semidirect
354. #461	C₂²×C₁₃	semidirect
356. #451	C₂²×C₁₃	semidirect
358. #448	C₂²×C₁₃	semidirect
359. #433	C₂²×C₁₃	semidirect
360. #433	C₂²×C₁₃	semidirect
576. C₁₃	#60807	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×#3455	2
C₂×C₁₃×#536	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3221	2
C₁₃×#3153	2
C₁₃×#3152	2
C₁₃×#3140	2
C₁₃×#3139	2
C₁₃×#3040	2
C₁₃×#3039	2
C₁₃×#3005	2
C₁₃×#3004	2
C₁₃×#2921	2
#60807	13

Subgroups — C13×#60807 #15747146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60807 #15747146