Subgroups — C₁₃×#61853 #15748192

Order 3328.

1648 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
5	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3121	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	—	2	2	no	—
17	C₁₃×#559	C₂²	1	2	yes	—
18	Q₈²×C₁₃	—	2	1	no	—
19	Q₈²×C₁₃	C₂²	1	2	yes	—
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	2	no	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	4	yes	—
25	C₁₃×#556	—	2	1	no	—
26	C₁₃×#556	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#544	—	2	2	no	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#542	—	2	2	no	—
32	C₁₃×#542	C₂²	1	4	yes	—
33	C₁₃×#536	—	2	2	no	—
34	C₁₃×#533	—	2	2	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#519	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#501	C₂²	1	4	yes	—
42	C₁₃×#501	C₂²	1	2	yes	—
43	C₁₃×#500	C₂²	1	1	yes	characteristic
44	C₁₃×#498	C₂²	1	1	yes	characteristic
45	C₁₃×#498	C₂²	1	4	yes	—
46	C₁₃×#490	C₂²	1	2	yes	—
47	C₁₃×#489	C₂²	1	4	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	1	yes	characteristic
50	C₁₃×#487	C₂²	1	1	yes	characteristic
51	C₁₃×#485	C₂²	1	4	yes	—
52	C₁₃×#483	C₂²	1	2	yes	—
53	C₁₃×#482	C₂²	1	4	yes	—
54	C₁₃×#481	C₂²	1	2	yes	—
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	4	yes	—
59	C₁₃×#476	C₂²	1	2	yes	—
60	C₁₃×#476	C₂²	1	4	yes	—
61	C₁₃×#475	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	4	yes	—
64	C₁₃×#475	C₂²	1	4	yes	—
65	C₁₃×#474	C₂²	1	2	yes	—
66	C₁₃×#464	C₂²	1	4	yes	—
67	C₁₃×#464	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#460	C₂²	1	2	yes	—
70	C₁₃×#451	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×#441	C₂²	1	4	yes	—
76	C₁₃×#441	C₂²	1	4	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	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	1	no	—
86	C₂²×Q₈×C₁₃	—	2	2	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
90	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	—	2	2	no	—
92	C₁₃×C₄⋊Q₈	—	2	4	no	—
93	C₁₃×C₄⋊Q₈	—	2	2	no	—
94	C₁₃×C₄⋊Q₈	—	2	4	no	—
95	C₁₃×C₄⋊Q₈	—	2	2	no	—
96	C₁₃×C₄⋊Q₈	—	2	4	no	—
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
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	1	yes	characteristic
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₁₃×C₄⋊Q₈	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	4	no	—
111	C₁₃×#125	—	2	4	no	—
112	C₁₃×#125	—	2	4	no	—
113	C₁₃×#125	—	2	2	no	—
114	C₁₃×#125	—	2	1	no	—
115	C₁₃×#125	D₄	1	2	yes	—
116	C₁₃×#125	C₂³	1	4	yes	—
117	C₁₃×#125	C₂³	1	2	yes	—
118	C₁₃×#124	—	2	2	no	—
119	C₁₃×#124	—	2	4	no	—
120	C₁₃×#124	—	2	1	no	—
121	C₁₃×#124	C₂³	1	4	yes	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	C₂³	1	2	yes	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	4	no	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	1	no	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	C₂³	1	4	yes	—
160	C₁₃×#117	—	2	1	no	—
161	C₁₃×#117	—	2	2	no	—
162	C₁₃×#117	—	2	4	no	—
163	C₁₃×#117	C₂³	1	2	yes	—
164	C₁₃×#117	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	4	yes	—
171	C₁₃×#106	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	4	yes	—
173	C₁₃×#106	C₂³	1	2	yes	—
174	C₁₃×#106	C₂³	1	4	yes	—
175	C₁₃×#106	C₂³	1	4	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	4	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#103	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	2	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	#61853	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃×#41	—	8	2	no	—
199	C₂×Q₈×C₁₃	—	2	4	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	4	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	—	8	4	no	—
208	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×Q₁₆	—	2	8	no	—
224	C₁₃×SD₁₆	—	2	4	no	—
225	C₁₃×SD₁₆	—	2	4	no	—
226	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
228	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
251	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
252	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
254	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	—	2	2	no	—
269	C₄²×C₁₃	—	2	2	no	—
270	C₄²×C₁₃	—	2	2	no	—
271	C₄²×C₁₃	—	2	4	no	—
272	C₄²×C₁₃	—	2	4	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	2	no	—
275	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₄²×C₁₃	C₂⁴	1	4	yes	—
279	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
280	#3550	C₂×C₁₃	1	1	yes	characteristic
281	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#3387	C₂×C₁₃	1	4	yes	complemented
283	#3386	C₂×C₁₃	1	2	yes	complemented
284	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
285	#3371	C₂×C₁₃	1	4	yes	complemented
286	#3369	C₂×C₁₃	1	2	yes	complemented
287	#3364	C₂×C₁₃	1	2	yes	complemented
288	#3244	C₂×C₁₃	1	4	yes	complemented
289	#3235	C₂×C₁₃	1	1	yes	characteristic
290	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3121	C₂×C₁₃	1	4	yes	complemented
292	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3103	C₂×C₁₃	1	1	yes	characteristic
294	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	Q₈×C₁₃	—	2	4	no	—
298	Q₈×C₁₃	—	2	4	no	—
299	Q₈×C₁₃	—	2	2	no	—
300	Q₈×C₁₃	—	2	4	no	—
301	Q₈×C₁₃	—	4	2	no	—
302	Q₈×C₁₃	—	4	2	no	—
303	Q₈×C₁₃	—	4	2	no	—
304	Q₈×C₁₃	—	8	1	no	—
305	Q₈×C₁₃	—	8	4	no	—
306	Q₈×C₁₃	—	8	4	no	—
307	Q₈×C₁₃	—	8	1	no	—
308	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
309	D₄×C₁₃	—	2	2	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	4	2	no	—
312	D₄×C₁₃	—	8	1	no	—
313	D₄×C₁₃	—	8	2	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	4	no	—
326	C₂×C₄×C₁₃	—	8	4	no	—
327	C₂×C₄×C₁₃	—	8	1	no	—
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
336	C₈×C₁₃	—	2	2	no	—
337	C₈×C₁₃	—	2	2	no	—
338	C₈×C₁₃	—	2	4	no	—
339	#563	—	2	2	no	—
340	#559	C₂²×C₁₃	1	2	yes	—
341	Q₈²	—	2	1	no	—
342	Q₈²	C₂²×C₁₃	1	2	yes	—
343	Q₈²	C₂²×C₁₃	1	2	yes	—
344	#557	—	2	1	no	—
345	#557	—	2	2	no	—
346	#557	C₂²×C₁₃	1	2	yes	—
347	#557	C₂²×C₁₃	1	4	yes	—
348	#556	—	2	1	no	—
349	#556	C₂²×C₁₃	1	2	yes	—
350	D₄×Q₈	—	2	1	no	—
351	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
352	#544	—	2	2	no	—
353	#544	C₂²×C₁₃	1	2	yes	—
354	#542	—	2	2	no	—
355	#542	C₂²×C₁₃	1	4	yes	—
356	#536	—	2	2	no	—
357	#533	—	2	2	no	—
358	#533	C₂²×C₁₃	1	1	yes	characteristic
359	#533	C₂²×C₁₃	1	1	yes	characteristic
360	#533	C₂²×C₁₃	1	1	yes	characteristic
361	#532	C₂²×C₁₃	1	1	yes	characteristic
362	#519	C₂²×C₁₃	1	2	yes	—
363	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
364	#501	C₂²×C₁₃	1	4	yes	—
365	#501	C₂²×C₁₃	1	2	yes	—
366	#500	C₂²×C₁₃	1	1	yes	characteristic
367	#498	C₂²×C₁₃	1	1	yes	characteristic
368	#498	C₂²×C₁₃	1	4	yes	—
369	#490	C₂²×C₁₃	1	2	yes	—
370	#489	C₂²×C₁₃	1	4	yes	—
371	#488	C₂²×C₁₃	1	4	yes	—
372	#487	C₂²×C₁₃	1	1	yes	characteristic
373	#487	C₂²×C₁₃	1	1	yes	characteristic
374	#485	C₂²×C₁₃	1	4	yes	—
375	#483	C₂²×C₁₃	1	2	yes	—
376	#482	C₂²×C₁₃	1	4	yes	—
377	#481	C₂²×C₁₃	1	2	yes	—
378	#479	C₂²×C₁₃	1	4	yes	—
379	#479	C₂²×C₁₃	1	4	yes	—
380	#478	C₂²×C₁₃	1	4	yes	—
381	#477	C₂²×C₁₃	1	4	yes	—
382	#476	C₂²×C₁₃	1	2	yes	—
383	#476	C₂²×C₁₃	1	4	yes	—
384	#475	C₂²×C₁₃	1	2	yes	—
385	#475	C₂²×C₁₃	1	2	yes	—
386	#475	C₂²×C₁₃	1	4	yes	—
387	#475	C₂²×C₁₃	1	4	yes	—
388	#474	C₂²×C₁₃	1	2	yes	—
389	#464	C₂²×C₁₃	1	4	yes	—
390	#464	C₂²×C₁₃	1	4	yes	—
391	#462	C₂²×C₁₃	1	2	yes	—
392	#460	C₂²×C₁₃	1	2	yes	—
393	#451	C₂²×C₁₃	1	2	yes	—
394	#448	C₂²×C₁₃	1	2	yes	—
395	#446	C₂²×C₁₃	1	2	yes	—
396	#446	C₂²×C₁₃	1	4	yes	—
397	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
398	#441	C₂²×C₁₃	1	4	yes	—
399	#441	C₂²×C₁₃	1	4	yes	—
400	#440	C₂²×C₁₃	1	4	yes	—
401	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
402	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
403	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
404	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
405	#433	C₂²×C₁₃	1	4	yes	—
406	#432	C₂²×C₁₃	1	1	yes	characteristic
407	#431	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₁₃	—	2	1	no	—
416	C₄×C₁₃	—	2	1	no	—
417	C₄×C₁₃	—	2	4	no	—
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	1	no	—
420	C₄×C₁₃	—	2	1	no	—
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	#577	1	2	yes	—
429	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
430	C₂×#41	—	2	1	no	—
431	C₂²×Q₈	—	2	2	no	—
432	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
434	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
435	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
436	C₄⋊Q₈	—	2	2	no	—
437	C₄⋊Q₈	—	2	4	no	—
438	C₄⋊Q₈	—	2	2	no	—
439	C₄⋊Q₈	—	2	4	no	—
440	C₄⋊Q₈	—	2	2	no	—
441	C₄⋊Q₈	—	2	4	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
444	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
445	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
451	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
452	#127	C₂³×C₁₃	1	1	yes	characteristic
453	#126	—	2	4	no	—
454	#126	—	2	4	no	—
455	#125	—	2	4	no	—
456	#125	—	2	4	no	—
457	#125	—	2	4	no	—
458	#125	—	2	2	no	—
459	#125	—	2	1	no	—
460	#125	D₄×C₁₃	1	2	yes	—
461	#125	C₂³×C₁₃	1	2	yes	—
462	#125	C₂³×C₁₃	1	4	yes	—
463	#124	—	2	2	no	—
464	#124	—	2	4	no	—
465	#124	—	2	1	no	—
466	#124	C₂³×C₁₃	1	4	yes	—
467	#123	—	2	4	no	—
468	#123	—	2	4	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	2	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
478	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
479	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
480	#121	—	2	1	no	—
481	#121	C₂³×C₁₃	1	2	yes	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	—	2	1	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
494	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
495	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
496	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
497	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
498	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
499	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
500	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	C₂³×C₁₃	1	2	yes	—
504	C₄×D₄	C₂³×C₁₃	1	4	yes	—
505	#117	—	2	1	no	—
506	#117	—	2	2	no	—
507	#117	—	2	4	no	—
508	#117	C₂³×C₁₃	1	2	yes	—
509	#117	C₂³×C₁₃	1	2	yes	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
514	#107	C₂³×C₁₃	1	4	yes	—
515	#107	C₂³×C₁₃	1	4	yes	—
516	#106	C₂³×C₁₃	1	2	yes	—
517	#106	C₂³×C₁₃	1	4	yes	—
518	#106	C₂³×C₁₃	1	2	yes	—
519	#106	C₂³×C₁₃	1	4	yes	—
520	#106	C₂³×C₁₃	1	4	yes	—
521	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
522	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
523	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
524	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
525	#103	C₂³×C₁₃	1	2	yes	—
526	#103	C₂³×C₁₃	1	4	yes	—
527	#103	C₂³×C₁₃	1	2	yes	—
528	#103	C₂³×C₁₃	1	4	yes	—
529	#103	C₂³×C₁₃	1	4	yes	—
530	#103	C₂³×C₁₃	1	4	yes	—
531	#102	C₂³×C₁₃	1	2	yes	—
532	#102	C₂³×C₁₃	1	2	yes	—
533	#102	C₂³×C₁₃	1	4	yes	—
534	#102	C₂³×C₁₃	1	4	yes	—
535	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
536	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
537	#97	C₂³×C₁₃	1	2	yes	—
538	#97	C₂³×C₁₃	1	4	yes	—
539	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₄×C₈	C₂³×C₁₃	1	4	yes	—
542	C₂×C₁₃	—	4	1	no	—
543	C₂×C₁₃	—	8	2	no	—
544	C₂×C₁₃	#3486	1	1	yes	characteristic
545	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
546	C₂×C₁₃	#3586	1	1	yes	characteristic
547	#41	—	8	2	no	—
548	C₂×Q₈	—	2	4	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	8	4	no	—
557	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
558	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
559	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
560	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	Q₁₆	—	2	8	no	—
573	SD₁₆	—	2	4	no	—
574	SD₁₆	—	2	4	no	—
575	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
576	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
577	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
599	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
600	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
602	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
603	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
604	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
607	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
608	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	2	no	—
624	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₄²	C₂⁴×C₁₃	1	4	yes	—
628	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
629	C₁₃	#61853	1	1	yes	characteristic, direct product factor, Sylow
630	C₂³	—	2	2	no	—
631	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
632	Q₈	—	2	4	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	8	4	no	—
640	Q₈	—	8	1	no	—
641	Q₈	—	8	1	no	—
642	Q₈	—	8	4	no	—
643	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	8	1	no	—
648	D₄	—	8	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
671	C₈	—	2	2	no	—
672	C₈	—	2	2	no	—
673	C₈	—	2	4	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	C₁₃×#577	1	2	yes	—
695	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
696	C₂	—	4	1	no	—
697	C₂	—	8	2	no	—
698	C₂	C₁₃×#3486	1	1	yes	characteristic
699	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
700	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#532	C₂²
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
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. Q₈×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3371	C₂	semidirect
7. C₁₃×#3369	C₂	semidirect
8. C₁₃×#3364	C₂	semidirect
9. C₁₃×#3244	C₂	semidirect
11. C₁₃×#3231	C₂	semidirect
12. C₁₃×#3121	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
15. C₁₃×#2985	C₂	semidirect
197. #61853	C₁₃	direct (N × H)
281. #3502	C₂×C₁₃	semidirect
282. #3387	C₂×C₁₃	semidirect
283. #3386	C₂×C₁₃	semidirect
284. Q₈×SD₁₆	C₂×C₁₃	semidirect
285. #3371	C₂×C₁₃	semidirect
286. #3369	C₂×C₁₃	semidirect
287. #3364	C₂×C₁₃	semidirect
288. #3244	C₂×C₁₃	semidirect
290. #3231	C₂×C₁₃	semidirect
291. #3121	C₂×C₁₃	semidirect
292. #3113	C₂×C₁₃	semidirect
294. #2985	C₂×C₁₃	semidirect
629. C₁₃	#61853	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×#3550	2
C₁₃×#3502	2
C₁₃×#3387	2
C₁₃×#3386	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3371	2
C₁₃×#3369	2
C₁₃×#3364	2
C₁₃×#3244	2
C₁₃×#3235	2
C₁₃×#3231	2
C₁₃×#3121	2
C₁₃×#3113	2
C₁₃×#3103	2
C₁₃×#2985	2
#61853	13

Subgroups — C13×#61853 #15748192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61853 #15748192