Subgroups — C₁₃×#61410 #15747749

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3394	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3392	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₁₃×#559	C₂²	1	4	yes	—
22	C₁₃×#557	C₂²	1	4	yes	complemented
23	C₁₃×#556	C₂²	1	4	yes	complemented
24	C₁₃×#552	—	2	4	no	—
25	C₁₃×#550	C₂²	1	4	yes	—
26	C₁₃×#546	—	2	4	no	—
27	C₁₃×#541	—	2	2	no	—
28	C₁₃×#540	—	2	2	no	—
29	C₁₃×#536	C₂²	1	2	yes	—
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#533	—	2	2	no	—
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#532	—	2	2	no	—
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
36	C₁₃×#519	C₂²	1	2	yes	—
37	C₁₃×#518	C₂²	1	2	yes	—
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
40	C₁₃×#497	C₂²	1	4	yes	complemented
41	C₁₃×#496	C₂²	1	4	yes	complemented
42	C₁₃×#495	C₂²	1	4	yes	complemented
43	C₁₃×#492	C₂²	1	4	yes	—
44	C₁₃×#492	C₂²	1	4	yes	—
45	C₁₃×#492	C₂²	1	4	yes	complemented
46	C₁₃×#464	C₂²	1	8	yes	complemented
47	C₁₃×#463	C₂²	1	8	yes	complemented
48	C₁₃×#462	C₂²	1	4	yes	complemented
49	C₁₃×#461	C₂²	1	4	yes	complemented
50	C₁₃×#461	C₂²	1	8	yes	complemented
51	C₁₃×#460	C₂²	1	4	yes	—
52	C₁₃×#460	C₂²	1	8	yes	complemented
53	C₁₃×#459	C₂²	1	4	yes	—
54	C₁₃×#446	C₂²	1	4	yes	complemented
55	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
56	C₁₃×#440	C₂²	1	8	yes	complemented
57	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
58	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
59	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
60	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
61	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
62	C₁₃×#427	C₂²	1	1	yes	characteristic
63	C₁₃×#424	C₂²	1	2	yes	—
64	C₁₃×#423	C₂²	1	1	yes	characteristic
65	C₁₃×#419	C₂²	1	2	yes	—
66	C₁₃×#418	C₂²	1	2	yes	—
67	C₁₃×#416	C₂²	1	1	yes	characteristic
68	C₁₃×#416	C₂²	1	1	yes	characteristic
69	C₁₃×#405	C₂²	1	2	yes	—
70	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	—	2	4	no	—
72	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#137	—	4	4	no	—
78	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
79	C₁₃×#135	—	2	4	no	—
80	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×SD₁₆	—	2	8	no	—
83	C₂×C₁₃×SD₁₆	—	4	4	no	—
84	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
90	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
91	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×D₈	C₂³	1	4	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×C₄⋊Q₈	—	2	1	no	—
98	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#127	—	2	1	no	—
102	C₁₃×#127	—	2	1	no	—
103	C₁₃×#127	C₂³	1	4	yes	—
104	C₁₃×#127	C₂³	1	4	yes	—
105	C₁₃×#126	—	2	8	no	—
106	C₁₃×#125	—	2	4	no	—
107	C₁₃×#125	—	2	8	no	—
108	C₁₃×#125	D₄	1	2	yes	—
109	C₁₃×#124	—	2	4	no	—
110	C₁₃×#124	C₂³	1	4	yes	—
111	C₁₃×#124	C₂³	1	4	yes	—
112	C₁₃×#123	—	2	8	no	—
113	C₁₃×#123	—	2	4	no	—
114	C₁₃×C₂²⋊Q₈	—	2	4	no	—
115	C₁₃×C₂²⋊Q₈	—	2	4	no	—
116	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
117	C₁₃×#121	—	2	4	no	—
118	C₁₃×#121	—	2	4	no	—
119	C₁₃×#121	—	2	8	no	—
120	C₁₃×#120	—	2	4	no	—
121	C₄×Q₈×C₁₃	—	2	4	no	—
122	C₄×Q₈×C₁₃	—	2	4	no	—
123	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
126	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
127	C₄×D₄×C₁₃	—	2	2	no	—
128	C₄×D₄×C₁₃	—	2	2	no	—
129	C₄×D₄×C₁₃	—	2	4	no	—
130	C₄×D₄×C₁₃	—	2	4	no	—
131	C₄×D₄×C₁₃	C₂³	1	2	yes	—
132	C₄×D₄×C₁₃	C₂³	1	2	yes	—
133	C₄×D₄×C₁₃	C₂³	1	8	yes	—
134	C₁₃×#117	—	2	4	no	—
135	C₁₃×#117	—	2	4	no	—
136	C₁₃×#117	—	2	1	no	—
137	C₁₃×#117	—	2	1	no	—
138	C₁₃×#117	C₂³	1	1	yes	characteristic
139	C₁₃×#117	C₂³	1	1	yes	characteristic
140	C₁₃×#117	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₄²×C₁₃	—	2	1	no	—
144	C₂×C₄²×C₁₃	—	2	1	no	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#107	C₂³	1	2	yes	—
147	C₁₃×#106	C₂³	1	2	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
150	C₁₃×#103	C₂³	1	2	yes	—
151	C₁₃×#103	C₂³	1	2	yes	—
152	C₁₃×#103	C₂³	1	8	yes	—
153	C₁₃×#102	C₂³	1	2	yes	—
154	C₁₃×#102	C₂³	1	2	yes	—
155	C₁₃×#102	C₂³	1	8	yes	—
156	C₁₃×#97	C₂³	1	4	yes	—
157	C₄×C₈×C₁₃	C₂³	1	2	yes	—
158	C₄×C₈×C₁₃	C₂³	1	2	yes	—
159	C₄×C₈×C₁₃	C₂³	1	4	yes	—
160	#61410	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₃	—	2	2	no	—
162	C₁₃×#41	—	2	2	no	—
163	C₁₃×#41	—	2	2	no	—
164	C₁₃×#41	—	2	2	no	—
165	C₁₃×#41	—	2	2	no	—
166	C₁₃×#41	—	8	8	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	—	2	4	no	—
170	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
171	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
173	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	8	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	8	4	no	—
183	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	8	no	—
192	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×Q₁₆	—	2	2	no	—
195	C₁₃×Q₁₆	—	4	4	no	—
196	C₁₃×SD₁₆	—	2	8	no	—
197	C₁₃×SD₁₆	—	2	8	no	—
198	C₁₃×SD₁₆	—	2	2	no	—
199	C₁₃×SD₁₆	—	2	2	no	—
200	C₁₃×SD₁₆	—	4	8	no	—
201	C₁₃×SD₁₆	—	4	4	no	—
202	C₁₃×SD₁₆	—	4	4	no	—
203	C₁₃×D₈	—	2	2	no	—
204	C₁₃×D₈	—	4	4	no	—
205	C₁₃×M₁₆	—	2	4	no	—
206	C₂×C₈×C₁₃	—	2	2	no	—
207	C₂×C₈×C₁₃	#41	1	4	yes	complemented
208	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
210	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	8	no	—
217	C₁₃×C₄⋊C₄	—	2	8	no	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
219	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	2	no	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	2	no	—
235	C₄²×C₁₃	—	2	8	no	—
236	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₃	C₂⁴	1	2	yes	—
239	C₄²×C₁₃	C₂⁴	1	4	yes	—
240	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3400	C₂×C₁₃	1	4	yes	complemented
243	#3397	C₂×C₁₃	1	4	yes	complemented
244	#3394	C₂×C₁₃	1	4	yes	complemented
245	#3392	C₂×C₁₃	1	4	yes	complemented
246	#3154	C₂×C₁₃	1	2	yes	complemented
247	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#3043	C₂×C₁₃	1	2	yes	complemented
249	#3042	C₂×C₁₃	1	2	yes	complemented
250	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2949	C₂×C₁₃	1	2	yes	complemented
254	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	4	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	4	4	no	—
259	C₂³×C₁₃	—	8	4	no	—
260	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	Q₈×C₁₃	—	2	8	no	—
262	Q₈×C₁₃	—	2	4	no	—
263	Q₈×C₁₃	—	2	1	no	—
264	Q₈×C₁₃	—	2	1	no	—
265	Q₈×C₁₃	—	2	1	no	—
266	Q₈×C₁₃	—	2	4	no	—
267	Q₈×C₁₃	—	2	1	no	—
268	Q₈×C₁₃	—	4	4	no	—
269	D₄×C₁₃	—	2	1	no	—
270	D₄×C₁₃	—	2	1	no	—
271	D₄×C₁₃	—	2	4	no	—
272	D₄×C₁₃	—	2	1	no	—
273	D₄×C₁₃	—	2	4	no	—
274	D₄×C₁₃	—	2	1	no	—
275	D₄×C₁₃	—	4	2	no	—
276	D₄×C₁₃	—	4	2	no	—
277	D₄×C₁₃	—	4	4	no	—
278	D₄×C₁₃	—	4	8	no	—
279	D₄×C₁₃	—	8	4	no	—
280	D₄×C₁₃	—	8	8	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	4	4	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	2	no	—
290	C₂×C₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	4	4	no	—
292	C₂×C₄×C₁₃	—	8	8	no	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
298	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
300	C₈×C₁₃	—	2	2	no	—
301	C₈×C₁₃	—	2	4	no	—
302	C₈×C₁₃	C₂×#41	1	2	yes	—
303	C₈×C₁₃	C₂×#41	1	2	yes	—
304	C₂×#137	C₂²×C₁₃	1	2	yes	—
305	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
306	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
308	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
309	#559	C₂²×C₁₃	1	4	yes	—
310	#557	C₂²×C₁₃	1	4	yes	complemented
311	#556	C₂²×C₁₃	1	4	yes	complemented
312	#552	—	2	4	no	—
313	#550	C₂²×C₁₃	1	4	yes	—
314	#546	—	2	4	no	—
315	#541	—	2	2	no	—
316	#540	—	2	2	no	—
317	#536	C₂²×C₁₃	1	2	yes	—
318	#535	C₂²×C₁₃	1	2	yes	—
319	#533	—	2	2	no	—
320	#533	C₂²×C₁₃	1	1	yes	characteristic
321	#532	—	2	2	no	—
322	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
324	#519	C₂²×C₁₃	1	2	yes	—
325	#518	C₂²×C₁₃	1	2	yes	—
326	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
328	#497	C₂²×C₁₃	1	4	yes	complemented
329	#496	C₂²×C₁₃	1	4	yes	complemented
330	#495	C₂²×C₁₃	1	4	yes	complemented
331	#492	C₂²×C₁₃	1	4	yes	—
332	#492	C₂²×C₁₃	1	4	yes	—
333	#492	C₂²×C₁₃	1	4	yes	complemented
334	#464	C₂²×C₁₃	1	8	yes	complemented
335	#463	C₂²×C₁₃	1	8	yes	complemented
336	#462	C₂²×C₁₃	1	4	yes	complemented
337	#461	C₂²×C₁₃	1	4	yes	complemented
338	#461	C₂²×C₁₃	1	8	yes	complemented
339	#460	C₂²×C₁₃	1	4	yes	—
340	#460	C₂²×C₁₃	1	8	yes	complemented
341	#459	C₂²×C₁₃	1	4	yes	—
342	#446	C₂²×C₁₃	1	4	yes	complemented
343	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
344	#440	C₂²×C₁₃	1	8	yes	complemented
345	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
346	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
347	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
348	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
349	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
350	#427	C₂²×C₁₃	1	1	yes	characteristic
351	#424	C₂²×C₁₃	1	2	yes	—
352	#423	C₂²×C₁₃	1	1	yes	characteristic
353	#419	C₂²×C₁₃	1	2	yes	—
354	#418	C₂²×C₁₃	1	2	yes	—
355	#416	C₂²×C₁₃	1	1	yes	characteristic
356	#416	C₂²×C₁₃	1	1	yes	characteristic
357	#405	C₂²×C₁₃	1	2	yes	—
358	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	4	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	8	no	—
366	C₂²×C₁₃	—	16	4	no	—
367	C₂²×C₁₃	#550	1	2	yes	—
368	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	8	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	4	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	#550	1	2	yes	—
377	C₄×C₁₃	#577	1	4	yes	—
378	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
379	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×#41	—	2	4	no	—
381	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
384	C₂²×D₄	—	2	2	no	—
385	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
386	#137	—	4	4	no	—
387	AGL(1,ℤ/8)	—	4	4	no	—
388	#135	—	2	4	no	—
389	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
391	C₂×SD₁₆	—	2	8	no	—
392	C₂×SD₁₆	—	4	4	no	—
393	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
394	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
395	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
398	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
399	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
400	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×D₈	C₂³×C₁₃	1	4	yes	—
402	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
403	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	—	2	1	no	—
407	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
408	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
409	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
410	#127	—	2	1	no	—
411	#127	—	2	1	no	—
412	#127	C₂³×C₁₃	1	4	yes	—
413	#127	C₂³×C₁₃	1	4	yes	—
414	#126	—	2	8	no	—
415	#125	—	2	4	no	—
416	#125	—	2	8	no	—
417	#125	D₄×C₁₃	1	2	yes	—
418	#124	—	2	4	no	—
419	#124	C₂³×C₁₃	1	4	yes	—
420	#124	C₂³×C₁₃	1	4	yes	—
421	#123	—	2	8	no	—
422	#123	—	2	4	no	—
423	C₂²⋊Q₈	—	2	4	no	—
424	C₂²⋊Q₈	—	2	4	no	—
425	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
426	#121	—	2	4	no	—
427	#121	—	2	4	no	—
428	#121	—	2	8	no	—
429	#120	—	2	4	no	—
430	C₄×Q₈	—	2	4	no	—
431	C₄×Q₈	—	2	4	no	—
432	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
433	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
434	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
435	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	4	no	—
440	C₄×D₄	C₂³×C₁₃	1	2	yes	—
441	C₄×D₄	C₂³×C₁₃	1	2	yes	—
442	C₄×D₄	C₂³×C₁₃	1	8	yes	—
443	#117	—	2	4	no	—
444	#117	—	2	4	no	—
445	#117	—	2	1	no	—
446	#117	—	2	1	no	—
447	#117	C₂³×C₁₃	1	1	yes	characteristic
448	#117	C₂³×C₁₃	1	1	yes	characteristic
449	#117	C₂³×C₁₃	1	2	yes	—
450	C₂×C₄⋊C₄	—	2	2	no	—
451	C₂×C₂²⋊C₄	—	2	4	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
455	#107	C₂³×C₁₃	1	2	yes	—
456	#106	C₂³×C₁₃	1	2	yes	—
457	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
458	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
459	#103	C₂³×C₁₃	1	2	yes	—
460	#103	C₂³×C₁₃	1	2	yes	—
461	#103	C₂³×C₁₃	1	8	yes	—
462	#102	C₂³×C₁₃	1	2	yes	—
463	#102	C₂³×C₁₃	1	2	yes	—
464	#102	C₂³×C₁₃	1	8	yes	—
465	#97	C₂³×C₁₃	1	4	yes	—
466	C₄×C₈	C₂³×C₁₃	1	2	yes	—
467	C₄×C₈	C₂³×C₁₃	1	2	yes	—
468	C₄×C₈	C₂³×C₁₃	1	4	yes	—
469	C₂×C₁₃	—	2	2	no	—
470	C₂×C₁₃	—	8	1	no	—
471	C₂×C₁₃	—	8	1	no	—
472	C₂×C₁₃	—	8	4	no	—
473	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
474	C₂×C₁₃	C₂×#577	1	2	yes	—
475	C₂⁴	—	2	2	no	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	8	8	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
485	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
487	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	8	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	8	4	no	—
497	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
499	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
508	Q₁₆	—	2	2	no	—
509	Q₁₆	—	4	4	no	—
510	SD₁₆	—	2	8	no	—
511	SD₁₆	—	2	8	no	—
512	SD₁₆	—	2	2	no	—
513	SD₁₆	—	2	2	no	—
514	SD₁₆	—	4	8	no	—
515	SD₁₆	—	4	4	no	—
516	SD₁₆	—	4	4	no	—
517	D₈	—	2	2	no	—
518	D₈	—	4	4	no	—
519	M₁₆	—	2	4	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	C₁₃×#41	1	4	yes	complemented
522	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
523	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
524	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	8	no	—
531	C₄⋊C₄	—	2	8	no	—
532	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
534	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	8	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	8	no	—
550	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄²	C₂⁴×C₁₃	1	2	yes	—
553	C₄²	C₂⁴×C₁₃	1	4	yes	—
554	C₁₃	#61410	1	1	yes	characteristic, direct product factor, Sylow
555	C₂³	—	2	1	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	4	4	no	—
559	C₂³	—	8	4	no	—
560	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	Q₈	—	2	8	no	—
562	Q₈	—	2	4	no	—
563	Q₈	—	2	1	no	—
564	Q₈	—	2	1	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	2	4	no	—
567	Q₈	—	2	1	no	—
568	Q₈	—	4	4	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	4	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	4	no	—
574	D₄	—	2	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	8	no	—
579	D₄	—	8	4	no	—
580	D₄	—	8	8	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	8	8	no	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
598	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
599	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
600	C₈	—	2	2	no	—
601	C₈	—	2	4	no	—
602	C₈	C₂×C₁₃×#41	1	2	yes	—
603	C₈	C₂×C₁₃×#41	1	2	yes	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	8	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	16	4	no	—
612	C₂²	C₁₃×#550	1	2	yes	—
613	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	—	2	2	no	—
615	C₄	—	2	8	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	4	no	—
621	C₄	C₁₃×#550	1	2	yes	—
622	C₄	C₁₃×#577	1	4	yes	—
623	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
624	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂	—	2	2	no	—
626	C₂	—	8	4	no	—
627	C₂	—	8	1	no	—
628	C₂	—	8	1	no	—
629	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
630	C₂	C₂×C₁₃×#577	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3394	C₂	semidirect
6. C₁₃×#3392	C₂	semidirect
7. C₁₃×#3154	C₂	semidirect
8. C₂×C₁₃×#492	C₂	semidirect
9. C₁₃×#3043	C₂	semidirect
10. C₁₃×#3042	C₂	semidirect
11. C₁₃×#3039	C₂	semidirect
12. C₁₃×#3038	C₂	semidirect
13. C₁₃×#2960	C₂	semidirect
14. C₁₃×#2949	C₂	semidirect
15. C₄×C₁₃×#135	C₂	semidirect
22. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
40. C₁₃×#497	C₂²	semidirect
41. C₁₃×#496	C₂²	semidirect
42. C₁₃×#495	C₂²	semidirect
45. C₁₃×#492	C₂²	semidirect
46. C₁₃×#464	C₂²	semidirect
47. C₁₃×#463	C₂²	semidirect
48. C₁₃×#462	C₂²	semidirect
49. C₁₃×#461	C₂²	semidirect
50. C₁₃×#461	C₂²	semidirect
52. C₁₃×#460	C₂²	semidirect
54. C₁₃×#446	C₂²	semidirect
55. C₈×Q₈×C₁₃	C₂²	semidirect
56. C₁₃×#440	C₂²	semidirect
57. C₄×C₁₃×Q₁₆	C₂²	semidirect
58. C₄×C₁₃×SD₁₆	C₂²	semidirect
59. C₄×C₁₃×SD₁₆	C₂²	semidirect
60. C₄×C₁₃×SD₁₆	C₂²	semidirect
61. C₄×C₁₃×D₈	C₂²	semidirect
160. #61410	C₁₃	direct (N × H)
207. C₂×C₈×C₁₃	#41	semidirect
240. #3509	C₂×C₁₃	semidirect
241. #3508	C₂×C₁₃	semidirect
242. #3400	C₂×C₁₃	semidirect
243. #3397	C₂×C₁₃	semidirect
244. #3394	C₂×C₁₃	semidirect
245. #3392	C₂×C₁₃	semidirect
246. #3154	C₂×C₁₃	semidirect
247. C₂×#492	C₂×C₁₃	semidirect
248. #3043	C₂×C₁₃	semidirect
249. #3042	C₂×C₁₃	semidirect
250. #3039	C₂×C₁₃	semidirect
251. #3038	C₂×C₁₃	semidirect
252. #2960	C₂×C₁₃	semidirect
253. #2949	C₂×C₁₃	semidirect
254. C₄×#135	C₂×C₁₃	semidirect
310. #557	C₂²×C₁₃	semidirect
311. #556	C₂²×C₁₃	semidirect
328. #497	C₂²×C₁₃	semidirect
329. #496	C₂²×C₁₃	semidirect
330. #495	C₂²×C₁₃	semidirect
333. #492	C₂²×C₁₃	semidirect
334. #464	C₂²×C₁₃	semidirect
335. #463	C₂²×C₁₃	semidirect
336. #462	C₂²×C₁₃	semidirect
337. #461	C₂²×C₁₃	semidirect
338. #461	C₂²×C₁₃	semidirect
340. #460	C₂²×C₁₃	semidirect
342. #446	C₂²×C₁₃	semidirect
343. C₈×Q₈	C₂²×C₁₃	semidirect
344. #440	C₂²×C₁₃	semidirect
345. C₄×Q₁₆	C₂²×C₁₃	semidirect
346. C₄×SD₁₆	C₂²×C₁₃	semidirect
347. C₄×SD₁₆	C₂²×C₁₃	semidirect
348. C₄×SD₁₆	C₂²×C₁₃	semidirect
349. C₄×D₈	C₂²×C₁₃	semidirect
521. C₂×C₈	C₁₃×#41	semidirect
554. C₁₃	#61410	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×#3509	2
C₁₃×#3508	2
C₁₃×#3400	2
C₁₃×#3397	2
C₁₃×#3394	2
C₁₃×#3392	2
C₁₃×#3154	2
C₂×C₁₃×#492	2
C₁₃×#3043	2
C₁₃×#3042	2
C₁₃×#3039	2
C₁₃×#3038	2
C₁₃×#2960	2
C₁₃×#2949	2
C₄×C₁₃×#135	2
#61410	13

Subgroups — C13×#61410 #15747749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61410 #15747749