Subgroups — C₁₃×#61914 #15748253

Order 3328.

1752 conjugacy classes of subgroups.

The subgroup lattice has 748 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×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3221	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3119	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#562	—	2	2	no	—
17	C₁₃×#559	C₂²	1	2	yes	—
18	C₁₃×#557	C₂²	1	2	yes	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	C₂²	1	4	yes	—
21	C₁₃×#554	—	2	1	no	—
22	C₁₃×#554	C₂²	1	2	yes	—
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#550	C₂²	1	2	yes	—
26	C₁₃×#550	C₂²	1	2	yes	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#540	C₂²	1	4	yes	—
30	C₁₃×#539	—	2	2	no	—
31	C₁₃×#537	—	2	2	no	—
32	C₁₃×#537	—	2	2	no	—
33	C₁₃×#536	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#529	—	2	2	no	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#496	C₂²	1	2	yes	—
42	C₁₃×#496	C₂²	1	4	yes	—
43	C₁₃×#493	C₂²	1	1	yes	characteristic
44	C₁₃×#492	C₂²	1	1	yes	characteristic
45	C₁₃×#492	C₂²	1	4	yes	—
46	C₁₃×#491	C₂²	1	4	yes	—
47	C₁₃×#489	C₂²	1	2	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	1	yes	characteristic
50	C₁₃×#486	C₂²	1	1	yes	characteristic
51	C₁₃×#481	C₂²	1	2	yes	—
52	C₁₃×#480	C₂²	1	2	yes	—
53	C₁₃×#479	C₂²	1	4	yes	—
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#477	C₂²	1	2	yes	—
56	C₁₃×#475	C₂²	1	2	yes	—
57	C₁₃×#463	C₂²	1	4	yes	—
58	C₁₃×#463	C₂²	1	4	yes	—
59	C₁₃×#463	C₂²	1	4	yes	—
60	C₁₃×#461	C₂²	1	2	yes	—
61	C₁₃×#461	C₂²	1	4	yes	—
62	C₁₃×#461	C₂²	1	4	yes	—
63	C₁₃×#460	C₂²	1	2	yes	—
64	C₁₃×#460	C₂²	1	2	yes	—
65	C₁₃×#460	C₂²	1	4	yes	—
66	C₁₃×#459	C₂²	1	2	yes	—
67	C₁₃×#459	C₂²	1	4	yes	—
68	C₁₃×#449	C₂²	1	4	yes	—
69	C₁₃×#449	C₂²	1	4	yes	—
70	C₁₃×#448	C₂²	1	2	yes	—
71	C₁₃×#448	C₂²	1	2	yes	—
72	C₁₃×#446	C₂²	1	2	yes	—
73	C₁₃×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
75	C₁₃×#442	C₂²	1	4	yes	—
76	C₁₃×#440	C₂²	1	4	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
81	C₄×C₁₃×D₈	C₂²	1	4	yes	—
82	C₁₃×#433	C₂²	1	4	yes	—
83	C₁₃×#432	C₂²	1	1	yes	characteristic
84	C₁₃×#431	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	2	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×D₈	C₂³	1	4	yes	—
98	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×#127	C₂³	1	1	yes	characteristic
105	C₁₃×#127	C₂³	1	4	yes	—
106	C₁₃×#127	C₂³	1	1	yes	characteristic
107	C₁₃×#127	C₂³	1	1	yes	characteristic
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	—	2	4	no	—
112	C₁₃×#125	D₄	1	2	yes	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	1	no	—
116	C₁₃×#124	—	2	1	no	—
117	C₁₃×#124	C₂³	1	4	yes	—
118	C₁₃×#124	C₂³	1	2	yes	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
131	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	4	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	C₂³	1	2	yes	—
143	C₁₃×#121	C₂³	1	2	yes	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	4	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	—	2	1	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	C₂³	1	4	yes	—
159	C₄×D₄×C₁₃	C₂³	1	4	yes	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	C₂³	1	4	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	—	2	4	no	—
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₁₃×#107	C₂³	1	4	yes	—
174	C₁₃×#106	C₂³	1	2	yes	—
175	C₁₃×#106	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	2	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	2	yes	—
188	C₁₃×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₁₃×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	4	yes	—
197	#61914	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃×#41	—	4	4	no	—
199	C₁₃×#41	—	8	2	no	—
200	C₁₃×#41	—	8	2	no	—
201	C₁₃×#41	—	8	4	no	—
202	C₁₃×#41	—	8	4	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×SD₁₆	—	4	2	no	—
237	C₁₃×SD₁₆	—	4	4	no	—
238	C₁₃×SD₁₆	—	4	4	no	—
239	C₁₃×SD₁₆	—	4	2	no	—
240	C₁₃×SD₁₆	—	4	4	no	—
241	C₁₃×D₈	—	4	4	no	—
242	C₁₃×D₈	—	4	4	no	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	4	yes	—
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3399	C₂×C₁₃	1	2	yes	complemented
290	#3397	C₂×C₁₃	1	4	yes	complemented
291	#3392	C₂×C₁₃	1	2	yes	complemented
292	#3376	C₂×C₁₃	1	4	yes	complemented
293	#3372	C₂×C₁₃	1	2	yes	complemented
294	#3361	C₂×C₁₃	1	2	yes	complemented
295	#3221	C₂×C₁₃	1	4	yes	complemented
296	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3119	C₂×C₁₃	1	4	yes	complemented
299	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂³×C₁₃	—	2	2	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₁₃	—	2	4	no	—
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	4	no	—
310	Q₈×C₁₃	—	4	2	no	—
311	Q₈×C₁₃	—	4	2	no	—
312	Q₈×C₁₃	—	8	1	no	—
313	Q₈×C₁₃	—	8	1	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	2	4	no	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	—	4	2	no	—
319	D₄×C₁₃	—	4	4	no	—
320	D₄×C₁₃	—	4	2	no	—
321	D₄×C₁₃	—	4	2	no	—
322	D₄×C₁₃	—	8	1	no	—
323	D₄×C₁₃	—	8	1	no	—
324	D₄×C₁₃	—	8	4	no	—
325	D₄×C₁₃	—	8	1	no	—
326	D₄×C₁₃	—	8	4	no	—
327	D₄×C₁₃	—	8	2	no	—
328	D₄×C₁₃	—	8	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	4	2	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	—	8	4	no	—
343	C₂×C₄×C₁₃	—	8	4	no	—
344	C₂×C₄×C₁₃	—	8	1	no	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
353	C₈×C₁₃	—	2	2	no	—
354	C₈×C₁₃	—	2	4	no	—
355	C₈×C₁₃	—	2	2	no	—
356	#562	—	2	2	no	—
357	#559	C₂²×C₁₃	1	2	yes	—
358	#557	C₂²×C₁₃	1	2	yes	—
359	#556	—	2	1	no	—
360	#556	C₂²×C₁₃	1	4	yes	—
361	#554	—	2	1	no	—
362	#554	C₂²×C₁₃	1	2	yes	—
363	#554	C₂²×C₁₃	1	2	yes	—
364	#552	—	2	2	no	—
365	#550	C₂²×C₁₃	1	2	yes	—
366	#550	C₂²×C₁₃	1	2	yes	—
367	#547	—	2	1	no	—
368	#547	—	2	1	no	—
369	#540	C₂²×C₁₃	1	4	yes	—
370	#539	—	2	2	no	—
371	#537	—	2	2	no	—
372	#537	—	2	2	no	—
373	#536	C₂²×C₁₃	1	2	yes	—
374	#533	C₂²×C₁₃	1	1	yes	characteristic
375	#532	C₂²×C₁₃	1	1	yes	characteristic
376	#532	C₂²×C₁₃	1	1	yes	characteristic
377	#532	C₂²×C₁₃	1	1	yes	characteristic
378	#529	—	2	2	no	—
379	#520	C₂²×C₁₃	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
381	#496	C₂²×C₁₃	1	2	yes	—
382	#496	C₂²×C₁₃	1	4	yes	—
383	#493	C₂²×C₁₃	1	1	yes	characteristic
384	#492	C₂²×C₁₃	1	1	yes	characteristic
385	#492	C₂²×C₁₃	1	4	yes	—
386	#491	C₂²×C₁₃	1	4	yes	—
387	#489	C₂²×C₁₃	1	2	yes	—
388	#488	C₂²×C₁₃	1	4	yes	—
389	#487	C₂²×C₁₃	1	1	yes	characteristic
390	#486	C₂²×C₁₃	1	1	yes	characteristic
391	#481	C₂²×C₁₃	1	2	yes	—
392	#480	C₂²×C₁₃	1	2	yes	—
393	#479	C₂²×C₁₃	1	4	yes	—
394	#478	C₂²×C₁₃	1	4	yes	—
395	#477	C₂²×C₁₃	1	2	yes	—
396	#475	C₂²×C₁₃	1	2	yes	—
397	#463	C₂²×C₁₃	1	4	yes	—
398	#463	C₂²×C₁₃	1	4	yes	—
399	#463	C₂²×C₁₃	1	4	yes	—
400	#461	C₂²×C₁₃	1	2	yes	—
401	#461	C₂²×C₁₃	1	4	yes	—
402	#461	C₂²×C₁₃	1	4	yes	—
403	#460	C₂²×C₁₃	1	2	yes	—
404	#460	C₂²×C₁₃	1	2	yes	—
405	#460	C₂²×C₁₃	1	4	yes	—
406	#459	C₂²×C₁₃	1	2	yes	—
407	#459	C₂²×C₁₃	1	4	yes	—
408	#449	C₂²×C₁₃	1	4	yes	—
409	#449	C₂²×C₁₃	1	4	yes	—
410	#448	C₂²×C₁₃	1	2	yes	—
411	#448	C₂²×C₁₃	1	2	yes	—
412	#446	C₂²×C₁₃	1	2	yes	—
413	#446	C₂²×C₁₃	1	4	yes	—
414	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
415	#442	C₂²×C₁₃	1	4	yes	—
416	#440	C₂²×C₁₃	1	4	yes	—
417	#440	C₂²×C₁₃	1	4	yes	—
418	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
419	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
420	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
421	C₄×D₈	C₂²×C₁₃	1	4	yes	—
422	#433	C₂²×C₁₃	1	4	yes	—
423	#432	C₂²×C₁₃	1	1	yes	characteristic
424	#431	C₂²×C₁₃	1	1	yes	characteristic
425	C₂²×C₁₃	—	2	1	no	—
426	C₂²×C₁₃	—	2	1	no	—
427	C₂²×C₁₃	—	2	1	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
438	C₄×C₁₃	—	2	1	no	—
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	4	no	—
441	C₄×C₁₃	—	2	1	no	—
442	C₄×C₁₃	—	2	1	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	#577	1	2	yes	—
450	C₄×C₁₃	#585	1	2	yes	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	C₂³×C₁₃	1	2	yes	—
456	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
458	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
459	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
460	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
461	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
462	C₂×D₈	C₂³×C₁₃	1	4	yes	—
463	C₂×D₈	C₂³×C₁₃	1	4	yes	—
464	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
465	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
468	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
470	#127	C₂³×C₁₃	1	1	yes	characteristic
471	#127	C₂³×C₁₃	1	1	yes	characteristic
472	#127	C₂³×C₁₃	1	1	yes	characteristic
473	#127	C₂³×C₁₃	1	4	yes	—
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#125	—	2	2	no	—
477	#125	—	2	4	no	—
478	#125	D₄×C₁₃	1	2	yes	—
479	#125	C₂³×C₁₃	1	4	yes	—
480	#124	—	2	2	no	—
481	#124	—	2	1	no	—
482	#124	—	2	1	no	—
483	#124	C₂³×C₁₃	1	2	yes	—
484	#124	C₂³×C₁₃	1	4	yes	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
497	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#121	—	2	4	no	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	C₂³×C₁₃	1	2	yes	—
509	#121	C₂³×C₁₃	1	2	yes	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
516	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
517	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	C₂³×C₁₃	1	2	yes	—
526	C₄×D₄	C₂³×C₁₃	1	2	yes	—
527	C₄×D₄	C₂³×C₁₃	1	4	yes	—
528	C₄×D₄	C₂³×C₁₃	1	4	yes	—
529	#117	—	2	2	no	—
530	#117	—	2	4	no	—
531	#117	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
539	#107	C₂³×C₁₃	1	4	yes	—
540	#106	C₂³×C₁₃	1	2	yes	—
541	#106	C₂³×C₁₃	1	2	yes	—
542	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
543	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
544	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
545	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
546	#103	C₂³×C₁₃	1	2	yes	—
547	#103	C₂³×C₁₃	1	2	yes	—
548	#103	C₂³×C₁₃	1	4	yes	—
549	#103	C₂³×C₁₃	1	4	yes	—
550	#103	C₂³×C₁₃	1	4	yes	—
551	#102	C₂³×C₁₃	1	2	yes	—
552	#102	C₂³×C₁₃	1	4	yes	—
553	#102	C₂³×C₁₃	1	2	yes	—
554	#102	C₂³×C₁₃	1	4	yes	—
555	#102	C₂³×C₁₃	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
558	#97	C₂³×C₁₃	1	2	yes	—
559	#97	C₂³×C₁₃	1	4	yes	—
560	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₁₃	1	4	yes	—
563	C₂×C₁₃	—	4	1	no	—
564	C₂×C₁₃	—	8	2	no	—
565	C₂×C₁₃	—	8	2	no	—
566	C₂×C₁₃	—	8	2	no	—
567	C₂×C₁₃	#3487	1	1	yes	characteristic
568	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
569	C₂×C₁₃	#3585	1	1	yes	characteristic
570	#41	—	4	4	no	—
571	#41	—	8	2	no	—
572	#41	—	8	2	no	—
573	#41	—	8	4	no	—
574	#41	—	8	4	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
580	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
581	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
582	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	SD₁₆	—	4	2	no	—
609	SD₁₆	—	4	4	no	—
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	2	no	—
612	SD₁₆	—	4	4	no	—
613	D₈	—	4	4	no	—
614	D₈	—	4	4	no	—
615	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
617	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₄²	C₂⁴×C₁₃	1	4	yes	—
658	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₁₃	#61914	1	1	yes	characteristic, direct product factor, Sylow
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	Q₈	—	2	4	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	4	no	—
668	Q₈	—	4	2	no	—
669	Q₈	—	4	2	no	—
670	Q₈	—	8	1	no	—
671	Q₈	—	8	1	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	2	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	1	no	—
682	D₄	—	8	4	no	—
683	D₄	—	8	1	no	—
684	D₄	—	8	4	no	—
685	D₄	—	8	2	no	—
686	D₄	—	8	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	1	no	—
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	2	4	no	—
713	C₈	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	C₁₃×#577	1	2	yes	—
739	C₄	C₁₃×#585	1	2	yes	—
740	C₂	—	4	1	no	—
741	C₂	—	8	2	no	—
742	C₂	—	8	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₁₃×#3487	1	1	yes	characteristic
745	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
746	C₂	C₁₃×#3585	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 ◁ 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×#3507	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3392	C₂	semidirect
6. C₁₃×#3376	C₂	semidirect
7. C₁₃×#3372	C₂	semidirect
8. C₁₃×#3361	C₂	semidirect
9. C₁₃×#3221	C₂	semidirect
10. C₁₃×#3214	C₂	semidirect
11. C₁₃×#3207	C₂	semidirect
12. C₁₃×#3119	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3103	C₂	semidirect
15. C₁₃×#2985	C₂	semidirect
197. #61914	C₁₃	direct (N × H)
287. #3548	C₂×C₁₃	semidirect
288. #3507	C₂×C₁₃	semidirect
289. #3399	C₂×C₁₃	semidirect
290. #3397	C₂×C₁₃	semidirect
291. #3392	C₂×C₁₃	semidirect
292. #3376	C₂×C₁₃	semidirect
293. #3372	C₂×C₁₃	semidirect
294. #3361	C₂×C₁₃	semidirect
295. #3221	C₂×C₁₃	semidirect
296. #3214	C₂×C₁₃	semidirect
297. #3207	C₂×C₁₃	semidirect
298. #3119	C₂×C₁₃	semidirect
299. #3112	C₂×C₁₃	semidirect
300. #3103	C₂×C₁₃	semidirect
301. #2985	C₂×C₁₃	semidirect
659. C₁₃	#61914	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×#3507	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3392	2
C₁₃×#3376	2
C₁₃×#3372	2
C₁₃×#3361	2
C₁₃×#3221	2
C₁₃×#3214	2
C₁₃×#3207	2
C₁₃×#3119	2
C₁₃×#3112	2
C₁₃×#3103	2
C₁₃×#2985	2
#61914	13

Subgroups — C13×#61914 #15748253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61914 #15748253