Subgroups — C₁₃×#60810 #15747149

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3224	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3153	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3141	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
15	C₁₃×#542	—	2	4	no	—
16	C₁₃×#542	C₂²	1	8	yes	complemented
17	C₁₃×#537	—	2	1	no	—
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#536	C₂²	1	4	yes	complemented
20	C₁₃×#535	C₂²	1	4	yes	complemented
21	C₁₃×#534	—	2	1	no	—
22	C₁₃×#534	—	2	1	no	—
23	C₁₃×#532	C₂²	1	2	yes	—
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#126	—	2	1	no	—
27	C₂×C₁₃×#124	—	2	1	no	—
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#525	—	2	4	no	—
30	C₂×C₁₃×#123	—	2	1	no	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	4	yes	complemented
38	C₁₃×#496	C₂²	1	4	yes	complemented
39	C₁₃×#495	C₂²	1	8	yes	complemented
40	C₁₃×#489	C₂²	1	8	yes	complemented
41	C₁₃×#487	C₂²	1	4	yes	complemented
42	C₁₃×#486	C₂²	1	4	yes	complemented
43	C₁₃×#464	C₂²	1	8	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#462	C₂²	1	4	yes	complemented
46	C₁₃×#461	C₂²	1	4	yes	complemented
47	C₁₃×#460	C₂²	1	4	yes	complemented
48	C₁₃×#459	C₂²	1	4	yes	complemented
49	C₁₃×#452	C₂²	1	8	yes	complemented
50	C₁₃×#451	C₂²	1	4	yes	complemented
51	C₁₃×#450	C₂²	1	4	yes	complemented
52	C₁₃×#449	C₂²	1	8	yes	—
53	C₁₃×#448	C₂²	1	4	yes	complemented
54	C₁₃×#447	C₂²	1	4	yes	complemented
55	C₁₃×#433	C₂²	1	8	yes	complemented
56	C₁₃×#423	C₂²	1	2	yes	complemented
57	C₁₃×#417	C₂²	1	4	yes	complemented
58	C₁₃×#417	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	—
60	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
61	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	4	8	no	—
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₃	—	2	1	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	—	2	2	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	—	2	2	no	—
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#137	—	4	8	no	—
77	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
78	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×D₈	C₂³	1	8	yes	—
82	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#126	—	2	8	no	—
90	C₁₃×#124	—	2	8	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×C₂²⋊Q₈	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	—	2	4	no	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	—	2	2	no	—
107	C₁₃×#121	—	2	2	no	—
108	C₁₃×#121	—	2	4	no	—
109	C₁₃×#121	—	2	4	no	—
110	C₁₃×#121	C₂³	1	4	yes	—
111	C₁₃×#120	—	2	4	no	—
112	C₁₃×#120	—	2	4	no	—
113	C₄×Q₈×C₁₃	—	2	2	no	—
114	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	—	2	2	no	—
120	C₄×D₄×C₁₃	C₂³	1	4	yes	—
121	C₁₃×#117	D₄	1	4	yes	—
122	C₁₃×#117	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	—	2	1	no	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
141	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
142	C₁₃×#103	C₂³	1	8	yes	—
143	C₁₃×#103	C₂³	1	8	yes	—
144	C₁₃×#102	C₂³	1	8	yes	—
145	C₁₃×#102	C₂³	1	8	yes	—
146	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
147	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
148	C₁₃×#97	C₂³	1	4	yes	—
149	C₄×C₈×C₁₃	C₂³	1	4	yes	—
150	#60810	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	—	2	2	no	—
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₁₃×#41	—	2	8	no	—
155	C₁₃×#41	—	2	8	no	—
156	C₁₃×#41	—	4	4	no	—
157	C₁₃×#41	—	4	4	no	—
158	C₁₃×#41	—	4	8	no	—
159	C₁₃×#41	—	4	8	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	2	no	—
162	C₂×Q₈×C₁₃	—	2	4	no	—
163	C₂×Q₈×C₁₃	—	2	4	no	—
164	C₂×Q₈×C₁₃	—	4	4	no	—
165	C₂×Q₈×C₁₃	—	8	2	no	—
166	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
168	C₂×D₄×C₁₃	—	2	4	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	—	2	2	no	—
174	C₂×D₄×C₁₃	—	2	2	no	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	4	4	no	—
179	C₂×D₄×C₁₃	—	4	8	no	—
180	C₂×D₄×C₁₃	—	8	2	no	—
181	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	4	8	no	—
192	C₂²×C₄×C₁₃	—	8	2	no	—
193	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₁₃×Q₁₆	—	4	8	no	—
202	C₁₃×SD₁₆	—	4	8	no	—
203	C₁₃×SD₁₆	—	4	8	no	—
204	C₁₃×D₈	—	4	8	no	—
205	C₁₃×M₁₆	—	2	8	no	—
206	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	4	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
230	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
231	C₄²×C₁₃	—	2	4	no	—
232	C₄²×C₁₃	C₂×D₄	1	2	yes	—
233	C₄²×C₁₃	C₂×D₄	1	2	yes	—
234	C₄²×C₁₃	C₂⁴	1	2	yes	—
235	C₄²×C₁₃	C₂⁴	1	2	yes	—
236	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3225	C₂×C₁₃	1	8	yes	complemented
239	#3224	C₂×C₁₃	1	8	yes	complemented
240	#3153	C₂×C₁₃	1	2	yes	complemented
241	#3141	C₂×C₁₃	1	2	yes	complemented
242	#3037	C₂×C₁₃	1	2	yes	complemented
243	#3036	C₂×C₁₃	1	2	yes	complemented
244	#3007	C₂×C₁₃	1	2	yes	complemented
245	#3006	C₂×C₁₃	1	2	yes	complemented
246	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	2	2	no	—
249	C₂³×C₁₃	—	2	4	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	4	no	—
253	C₂³×C₁₃	—	4	2	no	—
254	C₂³×C₁₃	—	4	2	no	—
255	C₂³×C₁₃	—	4	2	no	—
256	C₂³×C₁₃	—	8	2	no	—
257	C₂³×C₁₃	—	8	2	no	—
258	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₃	—	2	4	no	—
261	Q₈×C₁₃	—	2	4	no	—
262	Q₈×C₁₃	—	2	4	no	—
263	Q₈×C₁₃	—	4	4	no	—
264	Q₈×C₁₃	—	4	2	no	—
265	Q₈×C₁₃	—	8	4	no	—
266	D₄×C₁₃	—	2	4	no	—
267	D₄×C₁₃	—	2	4	no	—
268	D₄×C₁₃	—	2	4	no	—
269	D₄×C₁₃	—	4	4	no	—
270	D₄×C₁₃	—	4	8	no	—
271	D₄×C₁₃	—	4	8	no	—
272	D₄×C₁₃	—	4	2	no	—
273	D₄×C₁₃	—	8	2	no	—
274	D₄×C₁₃	—	8	2	no	—
275	D₄×C₁₃	—	8	2	no	—
276	D₄×C₁₃	—	8	2	no	—
277	D₄×C₁₃	—	8	4	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	8	no	—
290	C₂×C₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	4	2	no	—
292	C₂×C₄×C₁₃	—	4	2	no	—
293	C₂×C₄×C₁₃	—	4	2	no	—
294	C₂×C₄×C₁₃	—	4	8	no	—
295	C₂×C₄×C₁₃	—	8	4	no	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
303	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
304	C₈×C₁₃	—	2	8	no	—
305	C₂²×#41	C₂²×C₁₃	1	2	yes	—
306	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
307	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
308	#542	—	2	4	no	—
309	#542	C₂²×C₁₃	1	8	yes	complemented
310	#537	—	2	1	no	—
311	#537	—	2	1	no	—
312	#536	C₂²×C₁₃	1	4	yes	complemented
313	#535	C₂²×C₁₃	1	4	yes	complemented
314	#534	—	2	1	no	—
315	#534	—	2	1	no	—
316	#532	C₂²×C₁₃	1	2	yes	—
317	#532	C₂²×C₁₃	1	2	yes	—
318	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#126	—	2	1	no	—
320	C₂×#124	—	2	1	no	—
321	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#525	—	2	4	no	—
323	C₂×#123	—	2	1	no	—
324	C₂×C₂²⋊Q₈	—	2	1	no	—
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
330	#497	C₂²×C₁₃	1	4	yes	complemented
331	#496	C₂²×C₁₃	1	4	yes	complemented
332	#495	C₂²×C₁₃	1	8	yes	complemented
333	#489	C₂²×C₁₃	1	8	yes	complemented
334	#487	C₂²×C₁₃	1	4	yes	complemented
335	#486	C₂²×C₁₃	1	4	yes	complemented
336	#464	C₂²×C₁₃	1	8	yes	complemented
337	#463	C₂²×C₁₃	1	8	yes	complemented
338	#462	C₂²×C₁₃	1	4	yes	complemented
339	#461	C₂²×C₁₃	1	4	yes	complemented
340	#460	C₂²×C₁₃	1	4	yes	complemented
341	#459	C₂²×C₁₃	1	4	yes	complemented
342	#452	C₂²×C₁₃	1	8	yes	complemented
343	#451	C₂²×C₁₃	1	4	yes	complemented
344	#450	C₂²×C₁₃	1	4	yes	complemented
345	#449	C₂²×C₁₃	1	8	yes	—
346	#448	C₂²×C₁₃	1	4	yes	complemented
347	#447	C₂²×C₁₃	1	4	yes	complemented
348	#433	C₂²×C₁₃	1	8	yes	complemented
349	#423	C₂²×C₁₃	1	2	yes	complemented
350	#417	C₂²×C₁₃	1	4	yes	complemented
351	#417	C₂²×C₁₃	1	4	yes	complemented
352	#407	C₂²×C₁₃	1	2	yes	—
353	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
354	C₂²×C₁₃	—	2	1	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	4	no	—
361	C₂²×C₁₃	—	4	4	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	4	4	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	8	2	no	—
366	C₂²×C₁₃	—	8	4	no	—
367	C₂²×C₁₃	—	8	8	no	—
368	C₂²×C₁₃	#535	1	2	yes	—
369	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₁₃	—	2	2	no	—
371	C₄×C₁₃	—	2	2	no	—
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	2	2	no	—
374	C₄×C₁₃	—	2	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₄×C₁₃	—	4	2	no	—
379	C₄×C₁₃	#535	1	2	yes	—
380	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	2	no	—
383	C₂×#41	—	4	8	no	—
384	C₂×#41	C₂³×C₁₃	1	4	yes	—
385	C₂×#41	C₂³×C₁₃	1	4	yes	—
386	C₂²×Q₈	—	2	1	no	—
387	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
393	C₂³×C₄	—	2	2	no	—
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
396	#137	—	4	8	no	—
397	AGL(1,ℤ/8)	—	4	8	no	—
398	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
399	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
400	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
401	C₂×D₈	C₂³×C₁₃	1	8	yes	—
402	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
405	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
406	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
407	#127	C₂³×C₁₃	1	2	yes	—
408	#127	C₂³×C₁₃	1	2	yes	—
409	#126	—	2	8	no	—
410	#124	—	2	8	no	—
411	#124	—	2	2	no	—
412	#124	C₂³×C₁₃	1	4	yes	—
413	#124	C₂³×C₁₃	1	4	yes	—
414	#124	C₂³×C₁₃	1	4	yes	—
415	#123	—	2	8	no	—
416	#123	—	2	4	no	—
417	#123	—	2	4	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	8	no	—
420	C₂²⋊Q₈	—	2	4	no	—
421	C₂²⋊Q₈	—	2	4	no	—
422	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
423	#121	—	2	2	no	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	#121	—	2	2	no	—
427	#121	—	2	2	no	—
428	#121	—	2	4	no	—
429	#121	—	2	4	no	—
430	#121	C₂³×C₁₃	1	4	yes	—
431	#120	—	2	4	no	—
432	#120	—	2	4	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	C₂³×C₁₃	1	4	yes	—
441	#117	D₄×C₁₃	1	4	yes	—
442	#117	C₂³×C₁₃	1	4	yes	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
460	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
461	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
462	#103	C₂³×C₁₃	1	8	yes	—
463	#103	C₂³×C₁₃	1	8	yes	—
464	#102	C₂³×C₁₃	1	8	yes	—
465	#102	C₂³×C₁₃	1	8	yes	—
466	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
467	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
468	#97	C₂³×C₁₃	1	4	yes	—
469	C₄×C₈	C₂³×C₁₃	1	4	yes	—
470	C₂×C₁₃	—	2	2	no	—
471	C₂×C₁₃	—	4	2	no	—
472	C₂×C₁₃	—	8	2	no	—
473	C₂×C₁₃	—	8	4	no	—
474	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
475	C₂×C₁₃	#3585	1	1	yes	characteristic
476	C₂×C₁₃	#3586	1	1	yes	characteristic
477	C₂⁴	—	2	1	no	—
478	C₂⁴	—	2	2	no	—
479	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
480	#41	—	2	8	no	—
481	#41	—	2	8	no	—
482	#41	—	4	4	no	—
483	#41	—	4	4	no	—
484	#41	—	4	8	no	—
485	#41	—	4	8	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	—	8	2	no	—
492	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
493	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	4	8	no	—
506	C₂×D₄	—	8	2	no	—
507	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
508	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	4	8	no	—
518	C₂²×C₄	—	8	2	no	—
519	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	Q₁₆	—	4	8	no	—
528	SD₁₆	—	4	8	no	—
529	SD₁₆	—	4	8	no	—
530	D₈	—	4	8	no	—
531	M₁₆	—	2	8	no	—
532	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
543	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
544	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
556	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
557	C₄²	—	2	4	no	—
558	C₄²	C₂×D₄×C₁₃	1	2	yes	—
559	C₄²	C₂×D₄×C₁₃	1	2	yes	—
560	C₄²	C₂⁴×C₁₃	1	2	yes	—
561	C₄²	C₂⁴×C₁₃	1	2	yes	—
562	C₁₃	#60810	1	1	yes	characteristic, direct product factor, Sylow
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	8	2	no	—
573	C₂³	—	8	2	no	—
574	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
575	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
576	Q₈	—	2	4	no	—
577	Q₈	—	2	4	no	—
578	Q₈	—	2	4	no	—
579	Q₈	—	4	4	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	8	4	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	4	4	no	—
586	D₄	—	4	8	no	—
587	D₄	—	4	8	no	—
588	D₄	—	4	2	no	—
589	D₄	—	8	2	no	—
590	D₄	—	8	2	no	—
591	D₄	—	8	2	no	—
592	D₄	—	8	2	no	—
593	D₄	—	8	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	8	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	8	4	no	—
612	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
614	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
616	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
617	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
619	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
620	C₈	—	2	8	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	8	2	no	—
633	C₂²	—	8	4	no	—
634	C₂²	—	8	8	no	—
635	C₂²	C₁₃×#535	1	2	yes	—
636	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	4	no	—
645	C₄	—	4	2	no	—
646	C₄	C₁₃×#535	1	2	yes	—
647	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
648	C₂	—	2	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	8	2	no	—
651	C₂	—	8	4	no	—
652	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
653	C₂	C₁₃×#3585	1	1	yes	characteristic
654	C₂	C₁₃×#3586	1	1	yes	characteristic

	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×#542	C₂	semidirect
2. C₁₃×#3449	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3224	C₂	semidirect
5. C₁₃×#3153	C₂	semidirect
6. C₁₃×#3141	C₂	semidirect
7. C₁₃×#3037	C₂	semidirect
8. C₁₃×#3036	C₂	semidirect
9. C₁₃×#3007	C₂	semidirect
10. C₁₃×#3006	C₂	semidirect
11. C₁₃×#2921	C₂	semidirect
13. C₂×C₁₃×#137	C₂²	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
16. C₁₃×#542	C₂²	semidirect
19. C₁₃×#536	C₂²	semidirect
20. C₁₃×#535	C₂²	semidirect
25. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#124	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
38. C₁₃×#496	C₂²	semidirect
39. C₁₃×#495	C₂²	semidirect
40. C₁₃×#489	C₂²	semidirect
41. C₁₃×#487	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
43. C₁₃×#464	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#462	C₂²	semidirect
46. C₁₃×#461	C₂²	semidirect
47. C₁₃×#460	C₂²	semidirect
48. C₁₃×#459	C₂²	semidirect
49. C₁₃×#452	C₂²	semidirect
50. C₁₃×#451	C₂²	semidirect
51. C₁₃×#450	C₂²	semidirect
53. C₁₃×#448	C₂²	semidirect
54. C₁₃×#447	C₂²	semidirect
55. C₁₃×#433	C₂²	semidirect
56. C₁₃×#423	C₂²	semidirect
57. C₁₃×#417	C₂²	semidirect
58. C₁₃×#417	C₂²	semidirect
60. C₄×C₁₃×M₁₆	C₂²	semidirect
150. #60810	C₁₃	direct (N × H)
236. C₂×#542	C₂×C₁₃	semidirect
237. #3449	C₂×C₁₃	semidirect
238. #3225	C₂×C₁₃	semidirect
239. #3224	C₂×C₁₃	semidirect
240. #3153	C₂×C₁₃	semidirect
241. #3141	C₂×C₁₃	semidirect
242. #3037	C₂×C₁₃	semidirect
243. #3036	C₂×C₁₃	semidirect
244. #3007	C₂×C₁₃	semidirect
245. #3006	C₂×C₁₃	semidirect
246. #2921	C₂×C₁₃	semidirect
306. C₂×#137	C₂²×C₁₃	semidirect
307. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
309. #542	C₂²×C₁₃	semidirect
312. #536	C₂²×C₁₃	semidirect
313. #535	C₂²×C₁₃	semidirect
318. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
321. C₂×#124	C₂²×C₁₃	semidirect
327. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
328. C₂×C₄×D₄	C₂²×C₁₃	semidirect
330. #497	C₂²×C₁₃	semidirect
331. #496	C₂²×C₁₃	semidirect
332. #495	C₂²×C₁₃	semidirect
333. #489	C₂²×C₁₃	semidirect
334. #487	C₂²×C₁₃	semidirect
335. #486	C₂²×C₁₃	semidirect
336. #464	C₂²×C₁₃	semidirect
337. #463	C₂²×C₁₃	semidirect
338. #462	C₂²×C₁₃	semidirect
339. #461	C₂²×C₁₃	semidirect
340. #460	C₂²×C₁₃	semidirect
341. #459	C₂²×C₁₃	semidirect
342. #452	C₂²×C₁₃	semidirect
343. #451	C₂²×C₁₃	semidirect
344. #450	C₂²×C₁₃	semidirect
346. #448	C₂²×C₁₃	semidirect
347. #447	C₂²×C₁₃	semidirect
348. #433	C₂²×C₁₃	semidirect
349. #423	C₂²×C₁₃	semidirect
350. #417	C₂²×C₁₃	semidirect
351. #417	C₂²×C₁₃	semidirect
353. C₄×M₁₆	C₂²×C₁₃	semidirect
562. C₁₃	#60810	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×#542	2
C₁₃×#3449	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3153	2
C₁₃×#3141	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#2921	2
#60810	13

Subgroups — C13×#60810 #15747149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60810 #15747149