Subgroups — C₁₃×#61401 #15747740

Order 3328.

1938 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3403	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3150	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3035	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3035	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2943	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	4	yes	—
20	C₁₃×#559	C₂²	1	2	yes	—
21	C₁₃×#559	C₂²	1	4	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	C₂²	1	2	yes	—
24	C₁₃×#556	C₂²	1	4	yes	—
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#553	—	2	4	no	—
27	C₁₃×#550	C₂²	1	2	yes	—
28	C₁₃×#548	—	2	2	no	—
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₁₃×#532	C₂²	1	4	yes	—
31	C₁₃×#529	—	2	2	no	—
32	C₁₃×#529	—	2	4	no	—
33	C₄×C₁₃×#41	—	2	2	no	—
34	C₄×C₁₃×#41	C₂²	1	2	yes	—
35	C₄×C₁₃×#41	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	4	yes	—
38	C₁₃×#497	C₂²	1	4	yes	—
39	C₁₃×#496	C₂²	1	4	yes	—
40	C₁₃×#496	C₂²	1	4	yes	—
41	C₁₃×#495	C₂²	1	2	yes	—
42	C₁₃×#495	C₂²	1	2	yes	—
43	C₁₃×#494	C₂²	1	1	yes	characteristic
44	C₁₃×#493	C₂²	1	1	yes	characteristic
45	C₁₃×#492	C₂²	1	2	yes	—
46	C₁₃×#464	C₂²	1	4	yes	—
47	C₁₃×#464	C₂²	1	4	yes	—
48	C₁₃×#464	C₂²	1	4	yes	—
49	C₁₃×#463	C₂²	1	4	yes	—
50	C₁₃×#463	C₂²	1	4	yes	—
51	C₁₃×#463	C₂²	1	4	yes	—
52	C₁₃×#462	C₂²	1	2	yes	—
53	C₁₃×#462	C₂²	1	4	yes	—
54	C₁₃×#461	C₂²	1	2	yes	—
55	C₁₃×#461	C₂²	1	4	yes	—
56	C₁₃×#460	C₂²	1	4	yes	—
57	C₁₃×#460	C₂²	1	2	yes	—
58	C₁₃×#459	C₂²	1	2	yes	—
59	C₁₃×#459	C₂²	1	4	yes	—
60	C₁₃×#446	C₂²	1	2	yes	—
61	C₁₃×#446	C₂²	1	2	yes	—
62	C₁₃×#446	C₂²	1	2	yes	—
63	C₁₃×#446	C₂²	1	2	yes	—
64	C₁₃×#442	C₂²	1	4	yes	—
65	C₁₃×#441	C₂²	1	4	yes	—
66	C₁₃×#440	C₂²	1	4	yes	—
67	C₁₃×#440	C₂²	1	4	yes	—
68	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
71	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
72	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
74	C₁₃×#427	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
77	C₁₃×#416	C₂²	1	2	yes	—
78	C₁₃×#416	C₂²	1	4	yes	—
79	C₂×C₁₃×#97	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	C₂³	1	2	yes	—
83	C₂×C₁₃×#41	C₂³	1	4	yes	—
84	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
85	C₁₃×#135	—	2	8	no	—
86	C₁₃×#135	—	2	4	no	—
87	C₁₃×#135	—	4	4	no	—
88	C₁₃×#135	—	4	8	no	—
89	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
91	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
92	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×D₈	C₂³	1	2	yes	—
100	C₂×C₁₃×D₈	C₂³	1	2	yes	—
101	C₂×C₁₃×D₈	C₂³	1	4	yes	—
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×#127	C₂³	1	2	yes	—
108	C₁₃×#127	C₂³	1	4	yes	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	4	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#124	C₂³	1	4	yes	—
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	4	no	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	4	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	D₄	1	2	yes	—
132	C₄×Q₈×C₁₃	D₄	1	2	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
137	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
138	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	2	4	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₄×D₄×C₁₃	C₂³	1	4	yes	—
153	C₁₃×#117	—	2	2	no	—
154	C₁₃×#117	—	2	4	no	—
155	C₁₃×#117	—	2	4	no	—
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
160	C₂×C₄²×C₁₃	—	2	2	no	—
161	C₂×C₄²×C₁₃	—	2	4	no	—
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₁₃×#107	C₂³	1	1	yes	characteristic
165	C₁₃×#107	C₂³	1	1	yes	characteristic
166	C₁₃×#106	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
169	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
171	C₁₃×#103	C₂³	1	2	yes	—
172	C₁₃×#103	C₂³	1	2	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	2	yes	—
176	C₁₃×#102	C₂³	1	2	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	C₂³	1	4	yes	—
179	C₁₃×#97	C₂³	1	4	yes	—
180	C₁₃×#97	C₂³	1	4	yes	—
181	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
185	#61401	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃×#41	—	2	8	no	—
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	2	8	no	—
189	C₁₃×#41	—	2	4	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₂×Q₈×C₁₃	—	4	2	no	—
192	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×Q₁₆	—	2	4	no	—
216	C₁₃×Q₁₆	—	2	2	no	—
217	C₁₃×Q₁₆	—	4	2	no	—
218	C₁₃×Q₁₆	—	4	4	no	—
219	C₁₃×SD₁₆	—	2	4	no	—
220	C₁₃×SD₁₆	—	2	8	no	—
221	C₁₃×SD₁₆	—	4	4	no	—
222	C₁₃×SD₁₆	—	4	4	no	—
223	C₁₃×SD₁₆	—	4	4	no	—
224	C₁₃×D₈	—	2	4	no	—
225	C₁₃×D₈	—	2	2	no	—
226	C₁₃×D₈	—	4	2	no	—
227	C₁₃×D₈	—	4	4	no	—
228	C₂×C₈×C₁₃	—	2	2	no	—
229	C₂×C₈×C₁₃	—	2	4	no	—
230	C₂×C₈×C₁₃	#41	1	4	yes	complemented
231	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
234	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
245	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
246	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
247	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
249	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₄²×C₁₃	—	2	2	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	2	no	—
265	C₄²×C₁₃	—	2	2	no	—
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₄²×C₁₃	C₂⁴	1	4	yes	—
272	#3480	C₂×C₁₃	1	2	yes	complemented
273	#3403	C₂×C₁₃	1	2	yes	complemented
274	#3402	C₂×C₁₃	1	2	yes	complemented
275	#3401	C₂×C₁₃	1	4	yes	complemented
276	#3400	C₂×C₁₃	1	2	yes	complemented
277	#3399	C₂×C₁₃	1	2	yes	complemented
278	#3398	C₂×C₁₃	1	2	yes	complemented
279	#3397	C₂×C₁₃	1	2	yes	complemented
280	#3150	C₂×C₁₃	1	2	yes	complemented
281	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#3035	C₂×C₁₃	1	2	yes	complemented
283	#3035	C₂×C₁₃	1	4	yes	complemented
284	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2943	C₂×C₁₃	1	2	yes	complemented
286	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂³×C₁₃	—	2	4	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₁₃	—	2	4	no	—
291	Q₈×C₁₃	—	2	2	no	—
292	Q₈×C₁₃	—	2	4	no	—
293	Q₈×C₁₃	—	2	2	no	—
294	Q₈×C₁₃	—	2	4	no	—
295	Q₈×C₁₃	—	4	2	no	—
296	D₄×C₁₃	—	2	4	no	—
297	D₄×C₁₃	—	2	2	no	—
298	D₄×C₁₃	—	2	4	no	—
299	D₄×C₁₃	—	2	2	no	—
300	D₄×C₁₃	—	4	8	no	—
301	D₄×C₁₃	—	4	4	no	—
302	D₄×C₁₃	—	4	8	no	—
303	D₄×C₁₃	—	4	4	no	—
304	D₄×C₁₃	—	8	4	no	—
305	D₄×C₁₃	—	8	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	2	no	—
313	C₂×C₄×C₁₃	—	4	2	no	—
314	C₂×C₄×C₁₃	—	4	8	no	—
315	C₂×C₄×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	4	8	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	8	2	no	—
319	C₂×C₄×C₁₃	—	8	4	no	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
328	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
330	C₈×C₁₃	—	2	1	no	—
331	C₈×C₁₃	—	2	4	no	—
332	C₈×C₁₃	—	2	1	no	—
333	C₈×C₁₃	C₂×#41	1	2	yes	—
334	C₈×C₁₃	C₂×#41	1	2	yes	—
335	C₂×#135	C₂²×C₁₃	1	2	yes	—
336	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#135	C₂²×C₁₃	1	2	yes	—
338	C₂×#135	C₂²×C₁₃	1	4	yes	—
339	#559	C₂²×C₁₃	1	2	yes	—
340	#559	C₂²×C₁₃	1	4	yes	—
341	#557	C₂²×C₁₃	1	2	yes	—
342	#556	C₂²×C₁₃	1	2	yes	—
343	#556	C₂²×C₁₃	1	4	yes	—
344	#553	—	2	2	no	—
345	#553	—	2	4	no	—
346	#550	C₂²×C₁₃	1	2	yes	—
347	#548	—	2	2	no	—
348	#532	C₂²×C₁₃	1	2	yes	—
349	#532	C₂²×C₁₃	1	4	yes	—
350	#529	—	2	2	no	—
351	#529	—	2	4	no	—
352	C₄×#41	—	2	2	no	—
353	C₄×#41	C₂²×C₁₃	1	2	yes	—
354	C₄×#41	C₂²×C₁₃	1	4	yes	—
355	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
356	#497	C₂²×C₁₃	1	4	yes	—
357	#497	C₂²×C₁₃	1	4	yes	—
358	#496	C₂²×C₁₃	1	4	yes	—
359	#496	C₂²×C₁₃	1	4	yes	—
360	#495	C₂²×C₁₃	1	2	yes	—
361	#495	C₂²×C₁₃	1	2	yes	—
362	#494	C₂²×C₁₃	1	1	yes	characteristic
363	#493	C₂²×C₁₃	1	1	yes	characteristic
364	#492	C₂²×C₁₃	1	2	yes	—
365	#464	C₂²×C₁₃	1	4	yes	—
366	#464	C₂²×C₁₃	1	4	yes	—
367	#464	C₂²×C₁₃	1	4	yes	—
368	#463	C₂²×C₁₃	1	4	yes	—
369	#463	C₂²×C₁₃	1	4	yes	—
370	#463	C₂²×C₁₃	1	4	yes	—
371	#462	C₂²×C₁₃	1	2	yes	—
372	#462	C₂²×C₁₃	1	4	yes	—
373	#461	C₂²×C₁₃	1	2	yes	—
374	#461	C₂²×C₁₃	1	4	yes	—
375	#460	C₂²×C₁₃	1	4	yes	—
376	#460	C₂²×C₁₃	1	2	yes	—
377	#459	C₂²×C₁₃	1	2	yes	—
378	#459	C₂²×C₁₃	1	4	yes	—
379	#446	C₂²×C₁₃	1	2	yes	—
380	#446	C₂²×C₁₃	1	2	yes	—
381	#446	C₂²×C₁₃	1	2	yes	—
382	#446	C₂²×C₁₃	1	2	yes	—
383	#442	C₂²×C₁₃	1	4	yes	—
384	#441	C₂²×C₁₃	1	4	yes	—
385	#440	C₂²×C₁₃	1	4	yes	—
386	#440	C₂²×C₁₃	1	4	yes	—
387	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
388	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
389	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
390	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
391	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
393	#427	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
396	#416	C₂²×C₁₃	1	2	yes	—
397	#416	C₂²×C₁₃	1	4	yes	—
398	C₂×#97	C₂²×C₁₃	1	2	yes	—
399	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂²×C₁₃	—	2	1	no	—
401	C₂²×C₁₃	—	2	1	no	—
402	C₂²×C₁₃	—	4	2	no	—
403	C₂²×C₁₃	—	4	4	no	—
404	C₂²×C₁₃	—	4	4	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	4	no	—
407	C₂²×C₁₃	—	4	2	no	—
408	C₂²×C₁₃	#550	1	2	yes	—
409	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₁₃	—	2	1	no	—
411	C₄×C₁₃	—	2	4	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	4	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	4	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	#550	1	2	yes	—
420	C₄×C₁₃	#575	1	2	yes	—
421	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
422	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂×#41	—	2	2	no	—
424	C₂×#41	C₂³×C₁₃	1	2	yes	—
425	C₂×#41	C₂³×C₁₃	1	4	yes	—
426	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
427	#135	—	2	8	no	—
428	#135	—	2	4	no	—
429	#135	—	4	4	no	—
430	#135	—	4	8	no	—
431	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
433	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
434	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
435	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
436	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
438	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
440	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×D₈	C₂³×C₁₃	1	2	yes	—
442	C₂×D₈	C₂³×C₁₃	1	2	yes	—
443	C₂×D₈	C₂³×C₁₃	1	4	yes	—
444	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
446	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
448	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	#127	C₂³×C₁₃	1	2	yes	—
450	#127	C₂³×C₁₃	1	4	yes	—
451	#126	—	2	4	no	—
452	#126	—	2	4	no	—
453	#126	—	2	4	no	—
454	#125	—	2	2	no	—
455	#125	—	2	4	no	—
456	#124	—	2	2	no	—
457	#124	—	2	4	no	—
458	#124	C₂³×C₁₃	1	4	yes	—
459	#124	C₂³×C₁₃	1	4	yes	—
460	#124	C₂³×C₁₃	1	4	yes	—
461	#123	—	2	4	no	—
462	#123	—	2	4	no	—
463	#123	—	2	4	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	#121	—	2	2	no	—
467	#121	—	2	4	no	—
468	#121	—	2	2	no	—
469	#121	—	2	4	no	—
470	#121	—	2	2	no	—
471	#121	—	2	4	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	D₄×C₁₃	1	2	yes	—
474	C₄×Q₈	D₄×C₁₃	1	2	yes	—
475	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
476	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
477	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
478	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
479	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
480	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	4	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	4	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	C₂³×C₁₃	1	2	yes	—
492	C₄×D₄	C₂³×C₁₃	1	4	yes	—
493	C₄×D₄	C₂³×C₁₃	1	2	yes	—
494	C₄×D₄	C₂³×C₁₃	1	4	yes	—
495	#117	—	2	2	no	—
496	#117	—	2	4	no	—
497	#117	—	2	4	no	—
498	#117	—	2	2	no	—
499	#117	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
502	C₂×C₄²	—	2	2	no	—
503	C₂×C₄²	—	2	4	no	—
504	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
506	#107	C₂³×C₁₃	1	1	yes	characteristic
507	#107	C₂³×C₁₃	1	1	yes	characteristic
508	#106	C₂³×C₁₃	1	2	yes	—
509	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
510	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
511	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
512	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
513	#103	C₂³×C₁₃	1	2	yes	—
514	#103	C₂³×C₁₃	1	2	yes	—
515	#103	C₂³×C₁₃	1	4	yes	—
516	#103	C₂³×C₁₃	1	4	yes	—
517	#102	C₂³×C₁₃	1	2	yes	—
518	#102	C₂³×C₁₃	1	2	yes	—
519	#102	C₂³×C₁₃	1	4	yes	—
520	#102	C₂³×C₁₃	1	4	yes	—
521	#97	C₂³×C₁₃	1	4	yes	—
522	#97	C₂³×C₁₃	1	4	yes	—
523	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
526	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×C₁₃	—	2	2	no	—
528	C₂×C₁₃	—	8	4	no	—
529	C₂×C₁₃	—	8	2	no	—
530	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
531	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
532	C₂×C₁₃	#3584	1	1	yes	characteristic
533	#41	—	2	8	no	—
534	#41	—	2	4	no	—
535	#41	—	2	8	no	—
536	#41	—	2	4	no	—
537	#41	—	4	8	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
540	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
541	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
542	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
550	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
560	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
562	Q₁₆	—	2	4	no	—
563	Q₁₆	—	2	2	no	—
564	Q₁₆	—	4	2	no	—
565	Q₁₆	—	4	4	no	—
566	SD₁₆	—	2	4	no	—
567	SD₁₆	—	2	8	no	—
568	SD₁₆	—	4	4	no	—
569	SD₁₆	—	4	4	no	—
570	SD₁₆	—	4	4	no	—
571	D₈	—	2	4	no	—
572	D₈	—	2	2	no	—
573	D₈	—	4	2	no	—
574	D₈	—	4	4	no	—
575	C₂×C₈	—	2	2	no	—
576	C₂×C₈	—	2	4	no	—
577	C₂×C₈	C₁₃×#41	1	4	yes	complemented
578	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
579	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
580	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
581	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
582	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
592	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
593	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
594	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	2	2	no	—
613	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₄²	C₂×D₄×C₁₃	1	4	yes	—
615	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₄²	C₂⁴×C₁₃	1	4	yes	—
619	C₁₃	#61401	1	1	yes	characteristic, direct product factor, Sylow
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
623	Q₈	—	2	4	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	2	4	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	4	no	—
628	Q₈	—	4	2	no	—
629	D₄	—	2	4	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	2	no	—
633	D₄	—	4	8	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	8	no	—
636	D₄	—	4	4	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	8	2	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
660	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
661	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
662	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
663	C₈	—	2	1	no	—
664	C₈	—	2	4	no	—
665	C₈	—	2	1	no	—
666	C₈	C₂×C₁₃×#41	1	2	yes	—
667	C₈	C₂×C₁₃×#41	1	2	yes	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	4	4	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	2	no	—
676	C₂²	C₁₃×#550	1	2	yes	—
677	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	4	no	—
687	C₄	C₁₃×#550	1	2	yes	—
688	C₄	C₁₃×#575	1	2	yes	—
689	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
690	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂	—	2	2	no	—
692	C₂	—	8	4	no	—
693	C₂	—	8	2	no	—
694	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
695	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
696	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₁₃×#3403	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3400	C₂	semidirect
6. C₁₃×#3399	C₂	semidirect
7. C₁₃×#3398	C₂	semidirect
8. C₁₃×#3397	C₂	semidirect
9. C₁₃×#3150	C₂	semidirect
10. C₁₃×#3147	C₂	semidirect
11. C₁₃×#3035	C₂	semidirect
12. C₁₃×#3035	C₂	semidirect
13. C₂×C₁₃×#446	C₂	semidirect
14. C₁₃×#2943	C₂	semidirect
15. C₄×C₁₃×#135	C₂	semidirect
185. #61401	C₁₃	direct (N × H)
230. C₂×C₈×C₁₃	#41	semidirect
272. #3480	C₂×C₁₃	semidirect
273. #3403	C₂×C₁₃	semidirect
274. #3402	C₂×C₁₃	semidirect
275. #3401	C₂×C₁₃	semidirect
276. #3400	C₂×C₁₃	semidirect
277. #3399	C₂×C₁₃	semidirect
278. #3398	C₂×C₁₃	semidirect
279. #3397	C₂×C₁₃	semidirect
280. #3150	C₂×C₁₃	semidirect
281. #3147	C₂×C₁₃	semidirect
282. #3035	C₂×C₁₃	semidirect
283. #3035	C₂×C₁₃	semidirect
284. C₂×#446	C₂×C₁₃	semidirect
285. #2943	C₂×C₁₃	semidirect
286. C₄×#135	C₂×C₁₃	semidirect
577. C₂×C₈	C₁₃×#41	semidirect
619. C₁₃	#61401	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×#3480	2
C₁₃×#3403	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3399	2
C₁₃×#3398	2
C₁₃×#3397	2
C₁₃×#3150	2
C₁₃×#3147	2
C₁₃×#3035	2
C₂×C₁₃×#446	2
C₁₃×#2943	2
C₄×C₁₃×#135	2
#61401	13

Subgroups — C13×#61401 #15747740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61401 #15747740