Subgroups — C₁₃×#61942 #15748281

Order 3328.

1762 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#562	—	2	2	no	—
15	C₁₃×#559	C₂²	1	4	yes	—
16	C₁₃×#556	C₂²	1	4	yes	—
17	C₁₃×#554	C₂²	1	4	yes	complemented
18	C₁₃×#551	—	2	4	no	—
19	C₁₃×#550	C₂²	1	4	yes	complemented
20	C₁₃×#547	—	2	2	no	—
21	C₁₃×#542	—	2	2	no	—
22	C₁₃×#540	C₂²	1	2	yes	—
23	C₁₃×#540	C₂²	1	2	yes	—
24	C₁₃×#537	—	2	4	no	—
25	C₁₃×#536	C₂²	1	1	yes	characteristic
26	C₁₃×#535	C₂²	1	1	yes	characteristic
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₁₃×#529	—	2	2	no	—
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₁₃×#519	C₂²	1	1	yes	characteristic
32	C₁₃×#518	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
34	C₁₃×#496	C₂²	1	2	yes	—
35	C₁₃×#496	C₂²	1	4	yes	—
36	C₁₃×#496	C₂²	1	2	yes	complemented
37	C₁₃×#493	C₂²	1	2	yes	—
38	C₁₃×#492	C₂²	1	2	yes	complemented
39	C₁₃×#491	C₂²	1	2	yes	complemented
40	C₁₃×#490	C₂²	1	2	yes	—
41	C₁₃×#489	C₂²	1	4	yes	—
42	C₁₃×#488	C₂²	1	2	yes	—
43	C₁₃×#488	C₂²	1	2	yes	complemented
44	C₁₃×#482	C₂²	1	4	yes	—
45	C₁₃×#479	C₂²	1	4	yes	complemented
46	C₁₃×#478	C₂²	1	4	yes	—
47	C₁₃×#475	C₂²	1	2	yes	complemented
48	C₁₃×#474	C₂²	1	2	yes	complemented
49	C₁₃×#463	C₂²	1	4	yes	—
50	C₁₃×#463	C₂²	1	4	yes	—
51	C₁₃×#463	C₂²	1	4	yes	—
52	C₁₃×#463	C₂²	1	4	yes	complemented
53	C₁₃×#461	C₂²	1	4	yes	complemented
54	C₁₃×#460	C₂²	1	2	yes	complemented
55	C₁₃×#460	C₂²	1	4	yes	complemented
56	C₁₃×#459	C₂²	1	4	yes	—
57	C₁₃×#459	C₂²	1	4	yes	—
58	C₁₃×#459	C₂²	1	2	yes	complemented
59	C₁₃×#449	C₂²	1	4	yes	—
60	C₁₃×#448	C₂²	1	4	yes	—
61	C₁₃×#447	C₂²	1	4	yes	—
62	C₁₃×#446	C₂²	1	4	yes	complemented
63	C₁₃×#446	C₂²	1	4	yes	complemented
64	C₁₃×#442	C₂²	1	4	yes	—
65	C₁₃×#442	C₂²	1	4	yes	complemented
66	C₁₃×#440	C₂²	1	4	yes	complemented
67	C₁₃×#440	C₂²	1	4	yes	complemented
68	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
69	C₄×C₁₃×D₈	C₂²	1	4	yes	—
70	C₁₃×#433	C₂²	1	2	yes	—
71	C₁₃×#433	C₂²	1	2	yes	—
72	C₁₃×#432	C₂²	1	2	yes	—
73	C₂×C₁₃×#41	—	2	4	no	—
74	C₂×C₁₃×#41	—	2	2	no	—
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
81	C₂×C₁₃×D₈	C₂³	1	4	yes	—
82	C₂×C₁₃×D₈	C₂³	1	4	yes	—
83	C₂×C₁₃×D₈	C₂³	1	4	yes	—
84	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#127	C₂³	1	2	yes	—
90	C₁₃×#127	C₂³	1	2	yes	—
91	C₁₃×#126	—	2	4	no	—
92	C₁₃×#126	—	2	4	no	—
93	C₁₃×#125	D₄	1	2	yes	—
94	C₁₃×#125	C₂³	1	2	yes	—
95	C₁₃×#125	C₂³	1	2	yes	—
96	C₁₃×#124	—	2	4	no	—
97	C₁₃×#124	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	C₂³	1	2	yes	—
101	C₁₃×#124	C₂³	1	4	yes	—
102	C₁₃×#124	C₂³	1	2	yes	—
103	C₁₃×#123	—	2	4	no	—
104	C₁₃×#123	—	2	4	no	—
105	C₁₃×#123	—	2	4	no	—
106	C₁₃×#123	—	2	4	no	—
107	C₁₃×#123	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	—	2	4	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	4	no	—
112	C₁₃×C₂²⋊Q₈	—	2	4	no	—
113	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	2	no	—
116	C₁₃×#121	—	2	4	no	—
117	C₁₃×#121	—	2	4	no	—
118	C₁₃×#121	—	2	4	no	—
119	C₁₃×#121	—	2	4	no	—
120	C₁₃×#121	—	2	4	no	—
121	C₁₃×#121	C₂³	1	4	yes	—
122	C₁₃×#120	—	2	2	no	—
123	C₄×Q₈×C₁₃	—	2	2	no	—
124	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
125	C₄×Q₈×C₁₃	C₂³	1	2	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	2	no	—
131	C₄×D₄×C₁₃	C₂³	1	4	yes	—
132	C₄×D₄×C₁₃	C₂³	1	4	yes	—
133	C₄×D₄×C₁₃	C₂³	1	4	yes	—
134	C₄×D₄×C₁₃	C₂³	1	4	yes	—
135	C₄×D₄×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#117	—	2	4	no	—
137	C₁₃×#117	—	2	2	no	—
138	C₁₃×#117	—	2	1	no	—
139	C₁₃×#117	C₂³	1	1	yes	characteristic
140	C₁₃×#117	C₂³	1	1	yes	characteristic
141	C₁₃×#117	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
145	C₂×C₄²×C₁₃	—	2	1	no	—
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₁₃×#107	C₂³	1	4	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
152	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	4	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	4	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×#102	C₂³	1	4	yes	—
159	C₁₃×#102	C₂³	1	4	yes	—
160	C₁₃×#102	C₂³	1	4	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
162	C₁₃×#97	C₂³	1	4	yes	—
163	C₁₃×#97	C₂³	1	2	yes	—
164	C₁₃×#97	C₂³	1	2	yes	—
165	C₄×C₈×C₁₃	C₂³	1	2	yes	—
166	C₄×C₈×C₁₃	C₂³	1	2	yes	—
167	#61942	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂⁴×C₁₃	—	2	1	no	—
169	C₁₃×#41	—	4	2	no	—
170	C₁₃×#41	—	8	4	no	—
171	C₁₃×#41	—	8	8	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	2	no	—
174	C₂×Q₈×C₁₃	—	4	2	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	2	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₁₃×SD₁₆	—	4	4	no	—
200	C₁₃×SD₁₆	—	4	4	no	—
201	C₁₃×SD₁₆	—	4	4	no	—
202	C₁₃×D₈	—	4	4	no	—
203	C₁₃×D₈	—	4	4	no	—
204	C₁₃×D₈	—	4	4	no	—
205	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
206	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
214	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
215	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
220	C₁₃×C₂²⋊C₄	—	2	1	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	2	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	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
232	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	4	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	2	yes	—
240	C₄²×C₁₃	C₂⁴	1	2	yes	—
241	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3399	C₂×C₁₃	1	4	yes	complemented
244	#3397	C₂×C₁₃	1	4	yes	complemented
245	#3376	C₂×C₁₃	1	4	yes	complemented
246	#3370	C₂×C₁₃	1	4	yes	complemented
247	#3221	C₂×C₁₃	1	2	yes	complemented
248	#3220	C₂×C₁₃	1	2	yes	complemented
249	#3213	C₂×C₁₃	1	2	yes	complemented
250	#3126	C₂×C₁₃	1	2	yes	complemented
251	#3122	C₂×C₁₃	1	2	yes	complemented
252	#3115	C₂×C₁₃	1	2	yes	complemented
253	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	4	no	—
257	C₂³×C₁₃	—	4	2	no	—
258	C₂³×C₁₃	—	8	2	no	—
259	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₃	—	2	4	no	—
261	Q₈×C₁₃	—	2	2	no	—
262	Q₈×C₁₃	—	4	4	no	—
263	Q₈×C₁₃	—	4	2	no	—
264	Q₈×C₁₃	—	8	2	no	—
265	D₄×C₁₃	—	2	4	no	—
266	D₄×C₁₃	—	2	4	no	—
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	2	4	no	—
269	D₄×C₁₃	—	4	2	no	—
270	D₄×C₁₃	—	4	4	no	—
271	D₄×C₁₃	—	4	2	no	—
272	D₄×C₁₃	—	8	4	no	—
273	D₄×C₁₃	—	8	2	no	—
274	D₄×C₁₃	—	8	4	no	—
275	D₄×C₁₃	—	8	4	no	—
276	D₄×C₁₃	—	8	4	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	—	8	2	no	—
287	C₂×C₄×C₁₃	—	8	4	no	—
288	C₂×C₄×C₁₃	—	8	4	no	—
289	C₂×C₄×C₁₃	—	8	4	no	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
296	C₈×C₁₃	—	2	4	no	—
297	C₈×C₁₃	—	2	4	no	—
298	#562	—	2	2	no	—
299	#559	C₂²×C₁₃	1	4	yes	—
300	#556	C₂²×C₁₃	1	4	yes	—
301	#554	C₂²×C₁₃	1	4	yes	complemented
302	#551	—	2	4	no	—
303	#550	C₂²×C₁₃	1	4	yes	complemented
304	#547	—	2	2	no	—
305	#542	—	2	2	no	—
306	#540	C₂²×C₁₃	1	2	yes	—
307	#540	C₂²×C₁₃	1	2	yes	—
308	#537	—	2	4	no	—
309	#536	C₂²×C₁₃	1	1	yes	characteristic
310	#535	C₂²×C₁₃	1	1	yes	characteristic
311	#533	C₂²×C₁₃	1	1	yes	characteristic
312	#532	C₂²×C₁₃	1	2	yes	—
313	#529	—	2	2	no	—
314	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
315	#519	C₂²×C₁₃	1	1	yes	characteristic
316	#518	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
318	#496	C₂²×C₁₃	1	2	yes	—
319	#496	C₂²×C₁₃	1	4	yes	—
320	#496	C₂²×C₁₃	1	2	yes	complemented
321	#493	C₂²×C₁₃	1	2	yes	—
322	#492	C₂²×C₁₃	1	2	yes	complemented
323	#491	C₂²×C₁₃	1	2	yes	complemented
324	#490	C₂²×C₁₃	1	2	yes	—
325	#489	C₂²×C₁₃	1	4	yes	—
326	#488	C₂²×C₁₃	1	2	yes	—
327	#488	C₂²×C₁₃	1	2	yes	complemented
328	#482	C₂²×C₁₃	1	4	yes	—
329	#479	C₂²×C₁₃	1	4	yes	complemented
330	#478	C₂²×C₁₃	1	4	yes	—
331	#475	C₂²×C₁₃	1	2	yes	complemented
332	#474	C₂²×C₁₃	1	2	yes	complemented
333	#463	C₂²×C₁₃	1	4	yes	—
334	#463	C₂²×C₁₃	1	4	yes	—
335	#463	C₂²×C₁₃	1	4	yes	—
336	#463	C₂²×C₁₃	1	4	yes	complemented
337	#461	C₂²×C₁₃	1	4	yes	complemented
338	#460	C₂²×C₁₃	1	2	yes	complemented
339	#460	C₂²×C₁₃	1	4	yes	complemented
340	#459	C₂²×C₁₃	1	4	yes	—
341	#459	C₂²×C₁₃	1	4	yes	—
342	#459	C₂²×C₁₃	1	2	yes	complemented
343	#449	C₂²×C₁₃	1	4	yes	—
344	#448	C₂²×C₁₃	1	4	yes	—
345	#447	C₂²×C₁₃	1	4	yes	—
346	#446	C₂²×C₁₃	1	4	yes	complemented
347	#446	C₂²×C₁₃	1	4	yes	complemented
348	#442	C₂²×C₁₃	1	4	yes	—
349	#442	C₂²×C₁₃	1	4	yes	complemented
350	#440	C₂²×C₁₃	1	4	yes	complemented
351	#440	C₂²×C₁₃	1	4	yes	complemented
352	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
353	C₄×D₈	C₂²×C₁₃	1	4	yes	—
354	#433	C₂²×C₁₃	1	2	yes	—
355	#433	C₂²×C₁₃	1	2	yes	—
356	#432	C₂²×C₁₃	1	2	yes	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	4	4	no	—
360	C₂²×C₁₃	—	4	4	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	4	4	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	4	no	—
366	C₂²×C₁₃	—	16	2	no	—
367	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₁₃	—	2	2	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	4	no	—
371	C₄×C₁₃	—	2	4	no	—
372	C₄×C₁₃	—	2	1	no	—
373	C₄×C₁₃	—	4	4	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	#585	1	2	yes	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	2	no	—
380	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
384	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
385	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
386	C₂×D₈	C₂³×C₁₃	1	4	yes	—
387	C₂×D₈	C₂³×C₁₃	1	4	yes	—
388	C₂×D₈	C₂³×C₁₃	1	4	yes	—
389	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
390	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
391	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
392	#127	C₂³×C₁₃	1	2	yes	—
393	#127	C₂³×C₁₃	1	2	yes	—
394	#127	C₂³×C₁₃	1	2	yes	—
395	#127	C₂³×C₁₃	1	2	yes	—
396	#126	—	2	4	no	—
397	#126	—	2	4	no	—
398	#125	D₄×C₁₃	1	2	yes	—
399	#125	C₂³×C₁₃	1	2	yes	—
400	#125	C₂³×C₁₃	1	2	yes	—
401	#124	—	2	4	no	—
402	#124	—	2	1	no	—
403	#124	—	2	1	no	—
404	#124	—	2	2	no	—
405	#124	C₂³×C₁₃	1	4	yes	—
406	#124	C₂³×C₁₃	1	2	yes	—
407	#124	C₂³×C₁₃	1	2	yes	—
408	#123	—	2	4	no	—
409	#123	—	2	4	no	—
410	#123	—	2	4	no	—
411	#123	—	2	4	no	—
412	#123	—	2	2	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	—	2	4	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	2	4	no	—
417	C₂²⋊Q₈	—	2	4	no	—
418	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
419	#121	—	2	2	no	—
420	#121	—	2	2	no	—
421	#121	—	2	4	no	—
422	#121	—	2	4	no	—
423	#121	—	2	4	no	—
424	#121	—	2	4	no	—
425	#121	—	2	4	no	—
426	#121	C₂³×C₁₃	1	4	yes	—
427	#120	—	2	2	no	—
428	C₄×Q₈	—	2	2	no	—
429	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
430	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
431	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	4	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	C₂³×C₁₃	1	2	yes	—
437	C₄×D₄	C₂³×C₁₃	1	4	yes	—
438	C₄×D₄	C₂³×C₁₃	1	4	yes	—
439	C₄×D₄	C₂³×C₁₃	1	4	yes	—
440	C₄×D₄	C₂³×C₁₃	1	4	yes	—
441	#117	—	2	4	no	—
442	#117	—	2	2	no	—
443	#117	—	2	1	no	—
444	#117	C₂³×C₁₃	1	1	yes	characteristic
445	#117	C₂³×C₁₃	1	1	yes	characteristic
446	#117	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	2	4	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₂²⋊C₄	—	2	2	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
452	#107	C₂³×C₁₃	1	4	yes	—
453	#106	C₂³×C₁₃	1	4	yes	—
454	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
455	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
456	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
457	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
458	#103	C₂³×C₁₃	1	4	yes	—
459	#103	C₂³×C₁₃	1	4	yes	—
460	#103	C₂³×C₁₃	1	4	yes	—
461	#102	C₂³×C₁₃	1	4	yes	—
462	#102	C₂³×C₁₃	1	4	yes	—
463	#102	C₂³×C₁₃	1	4	yes	—
464	#102	C₂³×C₁₃	1	4	yes	—
465	#102	C₂³×C₁₃	1	4	yes	—
466	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
467	#97	C₂³×C₁₃	1	4	yes	—
468	#97	C₂³×C₁₃	1	2	yes	—
469	#97	C₂³×C₁₃	1	2	yes	—
470	C₄×C₈	C₂³×C₁₃	1	2	yes	—
471	C₄×C₈	C₂³×C₁₃	1	2	yes	—
472	C₂×C₁₃	—	4	1	no	—
473	C₂×C₁₃	—	8	4	no	—
474	C₂×C₁₃	—	8	1	no	—
475	C₂×C₁₃	—	8	2	no	—
476	C₂×C₁₃	#3487	1	1	yes	characteristic
477	C₂×C₁₃	#3585	1	2	yes	—
478	C₂⁴	—	2	1	no	—
479	#41	—	4	2	no	—
480	#41	—	8	4	no	—
481	#41	—	8	8	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	4	2	no	—
485	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
486	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
487	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
498	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
509	SD₁₆	—	4	4	no	—
510	SD₁₆	—	4	4	no	—
511	SD₁₆	—	4	4	no	—
512	D₈	—	4	4	no	—
513	D₈	—	4	4	no	—
514	D₈	—	4	4	no	—
515	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
516	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
525	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
526	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
527	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
528	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
543	C₄²	—	2	2	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	4	no	—
546	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₄²	C₂⁴×C₁₃	1	2	yes	—
549	C₄²	C₂⁴×C₁₃	1	2	yes	—
550	C₄²	C₂⁴×C₁₃	1	2	yes	—
551	C₁₃	#61942	1	1	yes	characteristic, direct product factor, Sylow
552	C₂³	—	2	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	8	2	no	—
557	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	Q₈	—	2	4	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	4	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	8	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	8	4	no	—
571	D₄	—	8	2	no	—
572	D₄	—	8	4	no	—
573	D₄	—	8	4	no	—
574	D₄	—	8	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	8	2	no	—
585	C₂×C₄	—	8	4	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
593	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
594	C₈	—	2	4	no	—
595	C₈	—	2	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	16	2	no	—
606	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	4	no	—
611	C₄	—	2	1	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	C₁₃×#585	1	2	yes	—
617	C₂	—	4	1	no	—
618	C₂	—	8	2	no	—
619	C₂	—	8	4	no	—
620	C₂	—	8	1	no	—
621	C₂	C₁₃×#3487	1	1	yes	characteristic
622	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3548	C₂	semidirect
2. C₁₃×#3510	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3376	C₂	semidirect
6. C₁₃×#3370	C₂	semidirect
7. C₁₃×#3221	C₂	semidirect
8. C₁₃×#3220	C₂	semidirect
9. C₁₃×#3213	C₂	semidirect
10. C₁₃×#3126	C₂	semidirect
11. C₁₃×#3122	C₂	semidirect
12. C₁₃×#3115	C₂	semidirect
13. C₁₃×#2987	C₂	semidirect
17. C₁₃×#554	C₂²	semidirect
19. C₁₃×#550	C₂²	semidirect
36. C₁₃×#496	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#491	C₂²	semidirect
43. C₁₃×#488	C₂²	semidirect
45. C₁₃×#479	C₂²	semidirect
47. C₁₃×#475	C₂²	semidirect
48. C₁₃×#474	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#461	C₂²	semidirect
54. C₁₃×#460	C₂²	semidirect
55. C₁₃×#460	C₂²	semidirect
58. C₁₃×#459	C₂²	semidirect
62. C₁₃×#446	C₂²	semidirect
63. C₁₃×#446	C₂²	semidirect
65. C₁₃×#442	C₂²	semidirect
66. C₁₃×#440	C₂²	semidirect
67. C₁₃×#440	C₂²	semidirect
68. C₄×C₁₃×SD₁₆	C₂²	semidirect
167. #61942	C₁₃	direct (N × H)
241. #3548	C₂×C₁₃	semidirect
242. #3510	C₂×C₁₃	semidirect
243. #3399	C₂×C₁₃	semidirect
244. #3397	C₂×C₁₃	semidirect
245. #3376	C₂×C₁₃	semidirect
246. #3370	C₂×C₁₃	semidirect
247. #3221	C₂×C₁₃	semidirect
248. #3220	C₂×C₁₃	semidirect
249. #3213	C₂×C₁₃	semidirect
250. #3126	C₂×C₁₃	semidirect
251. #3122	C₂×C₁₃	semidirect
252. #3115	C₂×C₁₃	semidirect
253. #2987	C₂×C₁₃	semidirect
301. #554	C₂²×C₁₃	semidirect
303. #550	C₂²×C₁₃	semidirect
320. #496	C₂²×C₁₃	semidirect
322. #492	C₂²×C₁₃	semidirect
323. #491	C₂²×C₁₃	semidirect
327. #488	C₂²×C₁₃	semidirect
329. #479	C₂²×C₁₃	semidirect
331. #475	C₂²×C₁₃	semidirect
332. #474	C₂²×C₁₃	semidirect
336. #463	C₂²×C₁₃	semidirect
337. #461	C₂²×C₁₃	semidirect
338. #460	C₂²×C₁₃	semidirect
339. #460	C₂²×C₁₃	semidirect
342. #459	C₂²×C₁₃	semidirect
346. #446	C₂²×C₁₃	semidirect
347. #446	C₂²×C₁₃	semidirect
349. #442	C₂²×C₁₃	semidirect
350. #440	C₂²×C₁₃	semidirect
351. #440	C₂²×C₁₃	semidirect
352. C₄×SD₁₆	C₂²×C₁₃	semidirect
551. C₁₃	#61942	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×#3548	2
C₁₃×#3510	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3376	2
C₁₃×#3370	2
C₁₃×#3221	2
C₁₃×#3220	2
C₁₃×#3213	2
C₁₃×#3126	2
C₁₃×#3122	2
C₁₃×#3115	2
C₁₃×#2987	2
#61942	13

Subgroups — C13×#61942 #15748281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61942 #15748281