Subgroups — C₁₃×#61909 #15748248

Order 3328.

1710 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3400	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3375	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3369	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3216	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3210	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3116	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	3	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	Q₈²×C₁₃	C₂²	1	3	yes	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	—	2	3	no	—
21	C₁₃×#557	C₂²	1	1	yes	characteristic
22	C₁₃×#557	C₂²	1	1	yes	characteristic
23	C₁₃×#557	C₂²	1	3	yes	—
24	C₁₃×#556	C₂²	1	3	yes	—
25	C₁₃×#553	—	2	3	no	—
26	C₁₃×#550	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	1	no	—
28	C₁₃×#544	—	2	3	no	—
29	C₁₃×#533	C₂²	1	3	yes	—
30	C₁₃×#533	C₂²	1	3	yes	—
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#529	—	2	3	no	—
33	C₁₃×#519	—	2	1	no	—
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	3	yes	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	6	yes	—
38	C₁₃×#494	C₂²	1	3	yes	—
39	C₁₃×#492	C₂²	1	3	yes	—
40	C₁₃×#489	C₂²	1	6	yes	—
41	C₁₃×#487	C₂²	1	3	yes	—
42	C₁₃×#486	C₂²	1	3	yes	—
43	C₁₃×#485	C₂²	1	1	yes	characteristic
44	C₁₃×#485	C₂²	1	3	yes	—
45	C₁₃×#477	C₂²	1	3	yes	—
46	C₁₃×#476	C₂²	1	3	yes	—
47	C₁₃×#475	C₂²	1	3	yes	—
48	C₁₃×#474	C₂²	1	3	yes	—
49	C₁₃×#464	C₂²	1	6	yes	—
50	C₁₃×#464	C₂²	1	6	yes	—
51	C₁₃×#462	C₂²	1	3	yes	—
52	C₁₃×#462	C₂²	1	3	yes	—
53	C₁₃×#462	C₂²	1	3	yes	—
54	C₁₃×#462	C₂²	1	3	yes	—
55	C₁₃×#461	C₂²	1	3	yes	—
56	C₁₃×#461	C₂²	1	3	yes	—
57	C₁₃×#460	C₂²	1	3	yes	—
58	C₁₃×#460	C₂²	1	3	yes	—
59	C₁₃×#452	C₂²	1	3	yes	—
60	C₁₃×#452	C₂²	1	3	yes	—
61	C₁₃×#452	C₂²	1	6	yes	—
62	C₁₃×#446	C₂²	1	3	yes	—
63	C₁₃×#446	C₂²	1	3	yes	—
64	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₁₃×#441	C₂²	1	6	yes	—
67	C₁₃×#440	C₂²	1	6	yes	—
68	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
69	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
70	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
71	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
72	C₁₃×#432	C₂²	1	3	yes	—
73	C₁₃×#431	C₂²	1	3	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
77	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
78	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
79	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
83	C₁₃×C₄⋊Q₈	—	2	3	no	—
84	C₁₃×C₄⋊Q₈	—	2	3	no	—
85	C₁₃×C₄⋊Q₈	—	2	6	no	—
86	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
88	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×#127	C₂³	1	3	yes	—
92	C₁₃×#126	—	2	6	no	—
93	C₁₃×#125	—	2	3	no	—
94	C₁₃×#125	—	2	3	no	—
95	C₁₃×#125	—	2	3	no	—
96	C₁₃×#125	—	2	6	no	—
97	C₁₃×#125	—	2	3	no	—
98	C₁₃×#125	—	2	3	no	—
99	C₁₃×#124	—	2	3	no	—
100	C₁₃×#124	C₂³	1	6	yes	—
101	C₁₃×#123	—	2	6	no	—
102	C₁₃×C₂²⋊Q₈	—	2	3	no	—
103	C₁₃×C₂²⋊Q₈	—	2	3	no	—
104	C₁₃×C₂²⋊Q₈	—	2	3	no	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	3	no	—
109	C₁₃×#121	—	2	3	no	—
110	C₄×Q₈×C₁₃	—	2	1	no	—
111	C₄×Q₈×C₁₃	—	2	3	no	—
112	C₄×Q₈×C₁₃	—	2	1	no	—
113	C₄×Q₈×C₁₃	—	2	3	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	3	no	—
116	C₄×Q₈×C₁₃	—	2	3	no	—
117	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
118	C₄×Q₈×C₁₃	D₄	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	—	2	3	no	—
130	C₄×D₄×C₁₃	—	2	3	no	—
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₁₃×#117	—	2	3	no	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	—	2	3	no	—
137	C₁₃×#117	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
139	C₂×C₄²×C₁₃	—	2	3	no	—
140	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
141	C₁₃×#107	C₂³	1	1	yes	characteristic
142	C₁₃×#107	C₂³	1	3	yes	—
143	C₁₃×#106	C₂³	1	1	yes	characteristic
144	C₁₃×#106	C₂³	1	3	yes	—
145	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
146	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
147	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×#103	C₂³	1	1	yes	characteristic
150	C₁₃×#103	C₂³	1	3	yes	—
151	C₁₃×#103	C₂³	1	1	yes	characteristic
152	C₁₃×#103	C₂³	1	3	yes	—
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#103	C₂³	1	6	yes	—
156	C₁₃×#102	C₂³	1	3	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	6	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
161	C₁₃×#97	C₂³	1	6	yes	—
162	C₄×C₈×C₁₃	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	#61909	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₁₃×#41	—	4	3	no	—
166	C₁₃×#41	—	4	3	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	—	2	3	no	—
170	C₂×Q₈×C₁₃	—	2	3	no	—
171	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
176	C₂×D₄×C₁₃	—	2	3	no	—
177	C₂×D₄×C₁₃	—	2	3	no	—
178	C₂×D₄×C₁₃	—	2	3	no	—
179	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₁₃	—	2	3	no	—
181	C₂²×C₄×C₁₃	—	2	3	no	—
182	C₂²×C₄×C₁₃	—	2	3	no	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×Q₁₆	—	4	3	no	—
187	C₁₃×Q₁₆	—	4	6	no	—
188	C₁₃×Q₁₆	—	4	3	no	—
189	C₁₃×SD₁₆	—	4	3	no	—
190	C₁₃×SD₁₆	—	4	6	no	—
191	C₁₃×SD₁₆	—	4	3	no	—
192	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
196	C₁₃×C₄⋊C₄	—	2	3	no	—
197	C₁₃×C₄⋊C₄	—	2	3	no	—
198	C₁₃×C₄⋊C₄	—	2	3	no	—
199	C₁₃×C₄⋊C₄	—	2	3	no	—
200	C₁₃×C₄⋊C₄	—	2	3	no	—
201	C₁₃×C₄⋊C₄	—	2	3	no	—
202	C₁₃×C₄⋊C₄	—	2	3	no	—
203	C₁₃×C₄⋊C₄	—	2	3	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	3	no	—
206	C₁₃×C₄⋊C₄	—	2	3	no	—
207	C₁₃×C₄⋊C₄	—	2	3	no	—
208	C₁₃×C₄⋊C₄	—	2	6	no	—
209	C₁₃×C₄⋊C₄	—	2	3	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
212	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
216	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
218	C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₁₃×C₂²⋊C₄	—	2	3	no	—
220	C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₁₃×C₂²⋊C₄	—	2	6	no	—
222	C₁₃×C₂²⋊C₄	—	2	3	no	—
223	C₁₃×C₂²⋊C₄	—	2	3	no	—
224	C₁₃×C₂²⋊C₄	—	2	6	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	3	no	—
227	C₄²×C₁₃	—	2	3	no	—
228	C₄²×C₁₃	—	2	6	no	—
229	C₄²×C₁₃	—	2	3	no	—
230	C₄²×C₁₃	—	2	3	no	—
231	C₄²×C₁₃	C₂×D₄	1	3	yes	—
232	C₄²×C₁₃	C₂×D₄	1	3	yes	—
233	C₄²×C₁₃	C₂⁴	1	3	yes	—
234	C₄²×C₁₃	C₂⁴	1	3	yes	—
235	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#3480	C₂×C₁₃	1	1	yes	characteristic
237	#3400	C₂×C₁₃	1	3	yes	complemented
238	#3398	C₂×C₁₃	1	3	yes	complemented
239	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3375	C₂×C₁₃	1	3	yes	complemented
242	#3369	C₂×C₁₃	1	3	yes	complemented
243	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3216	C₂×C₁₃	1	3	yes	complemented
246	#3210	C₂×C₁₃	1	3	yes	complemented
247	#3116	C₂×C₁₃	1	3	yes	complemented
248	#3107	C₂×C₁₃	1	3	yes	complemented
249	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂³×C₁₃	—	2	3	no	—
251	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₁₃	—	2	6	no	—
253	Q₈×C₁₃	—	2	1	no	—
254	Q₈×C₁₃	—	2	3	no	—
255	Q₈×C₁₃	—	2	3	no	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	3	no	—
258	Q₈×C₁₃	—	2	3	no	—
259	Q₈×C₁₃	—	8	3	no	—
260	Q₈×C₁₃	—	8	3	no	—
261	Q₈×C₁₃	#137	1	4	yes	—
262	D₄×C₁₃	—	2	3	no	—
263	D₄×C₁₃	—	2	3	no	—
264	D₄×C₁₃	—	4	6	no	—
265	D₄×C₁₃	—	4	6	no	—
266	D₄×C₁₃	—	8	3	no	—
267	C₂×C₄×C₁₃	—	2	6	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	3	no	—
274	C₂×C₄×C₁₃	—	2	3	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	3	no	—
277	C₂×C₄×C₁₃	—	4	3	no	—
278	C₂×C₄×C₁₃	—	4	6	no	—
279	C₂×C₄×C₁₃	—	4	6	no	—
280	C₂×C₄×C₁₃	—	8	3	no	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
287	C₈×C₁₃	—	2	1	no	—
288	C₈×C₁₃	—	2	3	no	—
289	C₈×C₁₃	—	2	3	no	—
290	C₈×C₁₃	—	2	1	no	—
291	#559	C₂²×C₁₃	1	3	yes	—
292	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
293	Q₈²	C₂²×C₁₃	1	3	yes	—
294	#557	—	2	1	no	—
295	#557	—	2	3	no	—
296	#557	C₂²×C₁₃	1	1	yes	characteristic
297	#557	C₂²×C₁₃	1	1	yes	characteristic
298	#557	C₂²×C₁₃	1	3	yes	—
299	#556	C₂²×C₁₃	1	3	yes	—
300	#553	—	2	3	no	—
301	#550	C₂²×C₁₃	1	1	yes	characteristic
302	#548	—	2	1	no	—
303	#544	—	2	3	no	—
304	#533	C₂²×C₁₃	1	3	yes	—
305	#533	C₂²×C₁₃	1	3	yes	—
306	#532	C₂²×C₁₃	1	3	yes	—
307	#529	—	2	3	no	—
308	#519	—	2	1	no	—
309	C₄×#41	—	2	1	no	—
310	C₄×#41	C₂²×C₁₃	1	3	yes	—
311	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	#497	C₂²×C₁₃	1	6	yes	—
313	#494	C₂²×C₁₃	1	3	yes	—
314	#492	C₂²×C₁₃	1	3	yes	—
315	#489	C₂²×C₁₃	1	6	yes	—
316	#487	C₂²×C₁₃	1	3	yes	—
317	#486	C₂²×C₁₃	1	3	yes	—
318	#485	C₂²×C₁₃	1	1	yes	characteristic
319	#485	C₂²×C₁₃	1	3	yes	—
320	#477	C₂²×C₁₃	1	3	yes	—
321	#476	C₂²×C₁₃	1	3	yes	—
322	#475	C₂²×C₁₃	1	3	yes	—
323	#474	C₂²×C₁₃	1	3	yes	—
324	#464	C₂²×C₁₃	1	6	yes	—
325	#464	C₂²×C₁₃	1	6	yes	—
326	#462	C₂²×C₁₃	1	3	yes	—
327	#462	C₂²×C₁₃	1	3	yes	—
328	#462	C₂²×C₁₃	1	3	yes	—
329	#462	C₂²×C₁₃	1	3	yes	—
330	#461	C₂²×C₁₃	1	3	yes	—
331	#461	C₂²×C₁₃	1	3	yes	—
332	#460	C₂²×C₁₃	1	3	yes	—
333	#460	C₂²×C₁₃	1	3	yes	—
334	#452	C₂²×C₁₃	1	3	yes	—
335	#452	C₂²×C₁₃	1	3	yes	—
336	#452	C₂²×C₁₃	1	6	yes	—
337	#446	C₂²×C₁₃	1	3	yes	—
338	#446	C₂²×C₁₃	1	3	yes	—
339	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
340	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
341	#441	C₂²×C₁₃	1	6	yes	—
342	#440	C₂²×C₁₃	1	6	yes	—
343	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
344	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
345	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
346	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
347	#432	C₂²×C₁₃	1	3	yes	—
348	#431	C₂²×C₁₃	1	3	yes	—
349	C₂²×C₁₃	—	2	1	no	—
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	1	no	—
352	C₂²×C₁₃	—	4	3	no	—
353	C₂²×C₁₃	—	4	3	no	—
354	C₂²×C₁₃	—	4	3	no	—
355	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₃	—	2	3	no	—
357	C₄×C₁₃	—	2	3	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	3	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	3	no	—
363	C₄×C₁₃	—	4	3	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	3	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	C₂×#137	1	6	yes	—
368	C₄×C₁₃	#585	1	1	yes	characteristic
369	C₄×C₁₃	#585	1	1	yes	characteristic
370	C₂×#41	—	2	1	no	—
371	C₂×#41	C₂³×C₁₃	1	3	yes	—
372	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
373	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
374	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
375	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
376	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
377	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
378	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
379	C₄⋊Q₈	—	2	3	no	—
380	C₄⋊Q₈	—	2	3	no	—
381	C₄⋊Q₈	—	2	6	no	—
382	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
383	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
384	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
385	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
386	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
387	#127	C₂³×C₁₃	1	3	yes	—
388	#126	—	2	6	no	—
389	#125	—	2	3	no	—
390	#125	—	2	3	no	—
391	#125	—	2	3	no	—
392	#125	—	2	6	no	—
393	#125	—	2	3	no	—
394	#125	—	2	3	no	—
395	#124	—	2	3	no	—
396	#124	C₂³×C₁₃	1	6	yes	—
397	#123	—	2	6	no	—
398	C₂²⋊Q₈	—	2	3	no	—
399	C₂²⋊Q₈	—	2	3	no	—
400	C₂²⋊Q₈	—	2	3	no	—
401	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
403	#121	—	2	3	no	—
404	#121	—	2	3	no	—
405	#121	—	2	3	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	3	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	3	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	3	no	—
412	C₄×Q₈	—	2	3	no	—
413	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₃	1	3	yes	—
415	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
416	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
417	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
418	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
419	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
422	C₄×D₄	—	2	3	no	—
423	C₄×D₄	—	2	3	no	—
424	C₄×D₄	—	2	3	no	—
425	C₄×D₄	—	2	3	no	—
426	C₄×D₄	—	2	3	no	—
427	C₄×D₄	C₂³×C₁₃	1	3	yes	—
428	C₄×D₄	C₂³×C₁₃	1	3	yes	—
429	#117	—	2	3	no	—
430	#117	—	2	3	no	—
431	#117	—	2	3	no	—
432	#117	—	2	3	no	—
433	#117	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
435	C₂×C₄²	—	2	3	no	—
436	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
437	#107	C₂³×C₁₃	1	1	yes	characteristic
438	#107	C₂³×C₁₃	1	3	yes	—
439	#106	C₂³×C₁₃	1	1	yes	characteristic
440	#106	C₂³×C₁₃	1	3	yes	—
441	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
442	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
443	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
444	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
445	#103	C₂³×C₁₃	1	1	yes	characteristic
446	#103	C₂³×C₁₃	1	3	yes	—
447	#103	C₂³×C₁₃	1	1	yes	characteristic
448	#103	C₂³×C₁₃	1	3	yes	—
449	#103	C₂³×C₁₃	1	3	yes	—
450	#103	C₂³×C₁₃	1	3	yes	—
451	#103	C₂³×C₁₃	1	6	yes	—
452	#102	C₂³×C₁₃	1	3	yes	—
453	#102	C₂³×C₁₃	1	3	yes	—
454	#102	C₂³×C₁₃	1	6	yes	—
455	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
457	#97	C₂³×C₁₃	1	6	yes	—
458	C₄×C₈	C₂³×C₁₃	1	3	yes	—
459	C₄×C₈	C₂³×C₁₃	1	3	yes	—
460	C₂×C₁₃	—	4	1	no	—
461	C₂×C₁₃	—	8	3	no	—
462	C₂×C₁₃	#3487	1	1	yes	characteristic
463	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
464	C₂×C₁₃	#3584	1	1	yes	characteristic
465	#41	—	4	3	no	—
466	#41	—	4	3	no	—
467	#41	—	4	4	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	3	no	—
470	C₂×Q₈	—	2	3	no	—
471	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
472	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
474	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
476	C₂×D₄	—	2	3	no	—
477	C₂×D₄	—	2	3	no	—
478	C₂×D₄	—	2	3	no	—
479	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
480	C₂²×C₄	—	2	3	no	—
481	C₂²×C₄	—	2	3	no	—
482	C₂²×C₄	—	2	3	no	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	Q₁₆	—	4	3	no	—
487	Q₁₆	—	4	6	no	—
488	Q₁₆	—	4	3	no	—
489	SD₁₆	—	4	3	no	—
490	SD₁₆	—	4	6	no	—
491	SD₁₆	—	4	3	no	—
492	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
494	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
495	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
496	C₄⋊C₄	—	2	3	no	—
497	C₄⋊C₄	—	2	3	no	—
498	C₄⋊C₄	—	2	3	no	—
499	C₄⋊C₄	—	2	3	no	—
500	C₄⋊C₄	—	2	3	no	—
501	C₄⋊C₄	—	2	3	no	—
502	C₄⋊C₄	—	2	3	no	—
503	C₄⋊C₄	—	2	3	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	3	no	—
506	C₄⋊C₄	—	2	3	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	6	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
514	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
516	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	3	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	6	no	—
522	C₂²⋊C₄	—	2	3	no	—
523	C₂²⋊C₄	—	2	3	no	—
524	C₂²⋊C₄	—	2	6	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	3	no	—
527	C₄²	—	2	3	no	—
528	C₄²	—	2	6	no	—
529	C₄²	—	2	3	no	—
530	C₄²	—	2	3	no	—
531	C₄²	C₂×D₄×C₁₃	1	3	yes	—
532	C₄²	C₂×D₄×C₁₃	1	3	yes	—
533	C₄²	C₂⁴×C₁₃	1	3	yes	—
534	C₄²	C₂⁴×C₁₃	1	3	yes	—
535	C₁₃	#61909	1	1	yes	characteristic, direct product factor, Sylow
536	C₂³	—	2	3	no	—
537	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	Q₈	—	2	6	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	2	3	no	—
541	Q₈	—	2	3	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	2	3	no	—
544	Q₈	—	2	3	no	—
545	Q₈	—	8	3	no	—
546	Q₈	—	8	3	no	—
547	Q₈	C₁₃×#137	1	4	yes	—
548	D₄	—	2	3	no	—
549	D₄	—	2	3	no	—
550	D₄	—	4	6	no	—
551	D₄	—	4	6	no	—
552	D₄	—	8	3	no	—
553	C₂×C₄	—	2	6	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	3	no	—
560	C₂×C₄	—	2	3	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	3	no	—
563	C₂×C₄	—	4	3	no	—
564	C₂×C₄	—	4	6	no	—
565	C₂×C₄	—	4	6	no	—
566	C₂×C₄	—	8	3	no	—
567	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
570	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
571	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
572	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
573	C₈	—	2	1	no	—
574	C₈	—	2	3	no	—
575	C₈	—	2	3	no	—
576	C₈	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	3	no	—
581	C₂²	—	4	3	no	—
582	C₂²	—	4	3	no	—
583	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
584	C₄	—	2	3	no	—
585	C₄	—	2	3	no	—
586	C₄	—	2	3	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	3	no	—
592	C₄	—	4	3	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	3	no	—
595	C₄	C₂×C₁₃×#137	1	6	yes	—
596	C₄	C₁₃×#585	1	1	yes	characteristic
597	C₄	C₁₃×#585	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	8	3	no	—
600	C₂	C₁₃×#3487	1	1	yes	characteristic
601	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
602	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3395	C₂	semidirect
6. C₁₃×#3392	C₂	semidirect
7. C₁₃×#3375	C₂	semidirect
8. C₁₃×#3369	C₂	semidirect
9. C₁₃×#3363	C₂	semidirect
10. C₁₃×#3362	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3210	C₂	semidirect
13. C₁₃×#3116	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#2984	C₂	semidirect
164. #61909	C₁₃	direct (N × H)
235. #3502	C₂×C₁₃	semidirect
237. #3400	C₂×C₁₃	semidirect
238. #3398	C₂×C₁₃	semidirect
239. #3395	C₂×C₁₃	semidirect
240. #3392	C₂×C₁₃	semidirect
241. #3375	C₂×C₁₃	semidirect
242. #3369	C₂×C₁₃	semidirect
243. #3363	C₂×C₁₃	semidirect
244. #3362	C₂×C₁₃	semidirect
245. #3216	C₂×C₁₃	semidirect
246. #3210	C₂×C₁₃	semidirect
247. #3116	C₂×C₁₃	semidirect
248. #3107	C₂×C₁₃	semidirect
249. #2984	C₂×C₁₃	semidirect
535. C₁₃	#61909	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×#3502	2
C₁₃×#3480	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3392	2
C₁₃×#3375	2
C₁₃×#3369	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3216	2
C₁₃×#3210	2
C₁₃×#3116	2
C₁₃×#3107	2
C₁₃×#2984	2
#61909	13

Subgroups — C13×#61909 #15748248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61909 #15748248