Subgroups — C₁₃×#19024 #15705363

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3558	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1662	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1661	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1659	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1659	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1527	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#562	C₂²	1	2	yes	—
13	C₁₃×H(3,𝔽₄)	C₂²	1	2	yes	—
14	C₁₃×#559	—	2	1	no	—
15	C₁₃×#548	—	2	1	no	—
16	C₁₃×#546	—	2	2	no	—
17	C₁₃×#546	—	2	1	no	—
18	D₄²×C₁₃	—	2	1	no	—
19	C₁₃×#542	—	2	1	no	—
20	C₁₃×#538	—	2	2	no	—
21	C₁₃×#538	—	2	1	no	—
22	C₁₃×#535	—	2	1	no	—
23	C₁₃×#534	—	2	1	no	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#497	C₂²	1	2	yes	complemented
31	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#489	C₂²	1	2	yes	complemented
33	C₁₃×#489	C₂²	1	2	yes	complemented
34	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#489	C₂²	1	2	yes	complemented
36	C₁₃×#488	—	2	2	no	—
37	C₁₃×#470	—	2	1	no	—
38	C₁₃×#468	—	2	1	no	—
39	C₁₃×#462	—	2	1	no	—
40	C₁₃×#460	—	2	1	no	—
41	C₁₃×#452	—	2	2	no	—
42	C₄×C₁₃×Q₁₆	—	2	1	no	—
43	C₄×C₁₃×SD₁₆	—	2	1	no	—
44	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#419	—	2	1	no	—
46	C₁₃×#418	—	2	1	no	—
47	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#330	C₂²	1	2	yes	complemented
50	C₁₃×#329	C₂²	1	2	yes	complemented
51	C₁₃×#329	C₂²	1	2	yes	complemented
52	C₁₃×#329	C₂²	1	2	yes	complemented
53	C₁₃×#329	C₂²	1	2	yes	complemented
54	C₁₃×#329	C₂²	1	2	yes	complemented
55	C₂×C₁₃×#41	—	2	1	no	—
56	C₂×C₁₃×#41	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₁₃×Q₁₆	—	2	1	no	—
62	C₂×C₁₃×Q₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	1	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₃×#127	—	2	1	no	—
71	C₁₃×#127	D₄	1	1	yes	characteristic
72	C₁₃×#126	—	2	2	no	—
73	C₁₃×#126	—	2	1	no	—
74	C₁₃×#125	—	2	1	no	—
75	C₁₃×#125	C₂³	1	1	yes	characteristic
76	C₁₃×#124	—	2	1	no	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#124	—	2	1	no	—
81	C₁₃×#124	—	2	1	no	—
82	C₁₃×#124	D₄	1	2	yes	—
83	C₁₃×#124	C₂³	1	2	yes	—
84	C₁₃×#124	C₂³	1	1	yes	characteristic
85	C₁₃×#124	C₂³	1	2	yes	—
86	C₁₃×#123	—	2	2	no	—
87	C₁₃×#123	—	2	2	no	—
88	C₁₃×#123	—	2	1	no	—
89	C₁₃×#123	—	2	2	no	—
90	C₁₃×#123	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	2	no	—
93	C₁₃×C₂²⋊Q₈	—	2	2	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	2	1	no	—
96	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	2	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	1	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	2	1	no	—
104	C₁₃×#121	—	2	1	no	—
105	C₁₃×#121	D₄	1	1	yes	characteristic
106	C₁₃×#120	—	2	2	no	—
107	C₁₃×#120	—	2	2	no	—
108	C₁₃×#120	—	2	2	no	—
109	C₁₃×#120	—	2	2	no	—
110	C₁₃×#120	—	2	2	no	—
111	C₄×Q₈×C₁₃	—	2	1	no	—
112	C₄×Q₈×C₁₃	—	2	1	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₄×D₄×C₁₃	—	2	1	no	—
118	C₄×D₄×C₁₃	—	2	1	no	—
119	C₄×D₄×C₁₃	—	2	1	no	—
120	C₄×D₄×C₁₃	—	2	1	no	—
121	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
122	C₁₃×#117	—	2	1	no	—
123	C₁₃×#117	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#107	—	2	1	no	—
129	C₁₃×#106	—	2	1	no	—
130	C₁₃×C₄⋊C₈	—	2	1	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×C₂²⋊C₈	—	2	1	no	—
142	C₁₃×#97	C₂³	1	1	yes	characteristic
143	C₁₃×#97	C₂³	1	1	yes	characteristic
144	C₁₃×#97	C₂³	1	2	yes	—
145	C₁₃×#97	C₂³	1	2	yes	—
146	C₄×C₈×C₁₃	—	2	1	no	—
147	C₄×C₈×C₁₃	—	2	1	no	—
148	#19024	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	2	no	—
150	C₂⁴×C₁₃	—	2	1	no	—
151	C₁₃×#41	—	8	2	no	—
152	C₁₃×#41	—	8	2	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	4	2	no	—
157	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	2	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	—	8	2	no	—
172	C₂×D₄×C₁₃	—	8	4	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₁₃×Q₁₆	—	4	2	no	—
185	C₁₃×Q₁₆	—	8	2	no	—
186	C₁₃×SD₁₆	—	4	2	no	—
187	C₁₃×SD₁₆	—	8	2	no	—
188	C₁₃×M₁₆	—	4	2	no	—
189	C₁₃×M₁₆	—	4	2	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	2	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	4	1	no	—
207	C₁₃×C₄⋊C₄	—	4	1	no	—
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×C₂²⋊C₄	—	2	2	no	—
214	C₁₃×C₂²⋊C₄	—	2	2	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	2	2	no	—
217	C₁₃×C₂²⋊C₄	—	2	1	no	—
218	C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	2	no	—
221	C₁₃×C₂²⋊C₄	—	2	2	no	—
222	C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	2	no	—
226	C₁₃×C₂²⋊C₄	—	4	1	no	—
227	C₄²×C₁₃	—	2	2	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	4	1	no	—
230	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
234	#3558	C₂×C₁₃	1	1	yes	characteristic
235	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1662	C₂×C₁₃	1	2	yes	complemented
239	#1661	C₂×C₁₃	1	2	yes	complemented
240	#1659	C₂×C₁₃	1	2	yes	complemented
241	#1659	C₂×C₁₃	1	2	yes	complemented
242	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1527	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	2	no	—
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	4	2	no	—
249	C₂³×C₁₃	—	8	1	no	—
250	C₂³×C₁₃	—	8	1	no	—
251	C₂³×C₁₃	—	8	2	no	—
252	C₂³×C₁₃	—	8	2	no	—
253	C₂³×C₁₃	—	8	2	no	—
254	C₂³×C₁₃	#120	1	1	yes	characteristic
255	Q₈×C₁₃	—	4	1	no	—
256	Q₈×C₁₃	—	4	2	no	—
257	Q₈×C₁₃	—	4	2	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	Q₈×C₁₃	—	4	1	no	—
260	Q₈×C₁₃	—	4	1	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	2	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	2	no	—
265	D₄×C₁₃	—	4	2	no	—
266	D₄×C₁₃	—	4	2	no	—
267	D₄×C₁₃	—	4	4	no	—
268	D₄×C₁₃	—	4	2	no	—
269	D₄×C₁₃	—	4	2	no	—
270	D₄×C₁₃	—	8	1	no	—
271	D₄×C₁₃	—	8	2	no	—
272	D₄×C₁₃	—	8	2	no	—
273	D₄×C₁₃	—	8	2	no	—
274	D₄×C₁₃	—	8	2	no	—
275	D₄×C₁₃	—	8	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	1	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	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	8	2	no	—
288	C₂×C₄×C₁₃	—	8	1	no	—
289	C₂×C₄×C₁₃	—	8	2	no	—
290	C₂×C₄×C₁₃	—	8	2	no	—
291	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
292	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
293	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₈×C₁₃	—	2	2	no	—
298	C₈×C₁₃	—	4	2	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₈×C₁₃	—	4	2	no	—
301	#562	C₂²×C₁₃	1	2	yes	—
302	H(3,𝔽₄)	C₂²×C₁₃	1	2	yes	—
303	#559	—	2	1	no	—
304	#548	—	2	1	no	—
305	#546	—	2	2	no	—
306	#546	—	2	1	no	—
307	D₄²	—	2	1	no	—
308	#542	—	2	1	no	—
309	#538	—	2	2	no	—
310	#538	—	2	1	no	—
311	#535	—	2	1	no	—
312	#534	—	2	1	no	—
313	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#532	C₂²×C₁₃	1	1	yes	characteristic
315	#529	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
317	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	#497	C₂²×C₁₃	1	2	yes	complemented
320	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#489	C₂²×C₁₃	1	2	yes	complemented
322	#489	C₂²×C₁₃	1	2	yes	complemented
323	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	#489	C₂²×C₁₃	1	2	yes	complemented
325	#488	—	2	2	no	—
326	#470	—	2	1	no	—
327	#468	—	2	1	no	—
328	#462	—	2	1	no	—
329	#460	—	2	1	no	—
330	#452	—	2	2	no	—
331	C₄×Q₁₆	—	2	1	no	—
332	C₄×SD₁₆	—	2	1	no	—
333	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
334	#419	—	2	1	no	—
335	#418	—	2	1	no	—
336	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	#330	C₂²×C₁₃	1	2	yes	complemented
339	#329	C₂²×C₁₃	1	2	yes	complemented
340	#329	C₂²×C₁₃	1	2	yes	complemented
341	#329	C₂²×C₁₃	1	2	yes	complemented
342	#329	C₂²×C₁₃	1	2	yes	complemented
343	#329	C₂²×C₁₃	1	2	yes	complemented
344	C₂²×C₁₃	—	2	1	no	—
345	C₂²×C₁₃	—	2	1	no	—
346	C₂²×C₁₃	—	2	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	4	2	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	2	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	2	no	—
355	C₂²×C₁₃	—	4	1	no	—
356	C₂²×C₁₃	—	16	2	no	—
357	C₂²×C₁₃	—	16	4	no	—
358	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	#455	1	2	yes	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	D₄×C₁₃	1	2	yes	—
374	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
375	C₂²×D₄	—	2	2	no	—
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
378	C₂×Q₁₆	—	2	1	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	#127	—	2	1	no	—
388	#127	D₄×C₁₃	1	1	yes	characteristic
389	#126	—	2	2	no	—
390	#126	—	2	1	no	—
391	#125	—	2	1	no	—
392	#125	C₂³×C₁₃	1	1	yes	characteristic
393	#124	—	2	1	no	—
394	#124	—	2	2	no	—
395	#124	—	2	2	no	—
396	#124	—	2	2	no	—
397	#124	—	2	1	no	—
398	#124	—	2	1	no	—
399	#124	D₄×C₁₃	1	2	yes	—
400	#124	C₂³×C₁₃	1	2	yes	—
401	#124	C₂³×C₁₃	1	1	yes	characteristic
402	#124	C₂³×C₁₃	1	2	yes	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	#123	—	2	1	no	—
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
414	#121	—	2	2	no	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	—	2	1	no	—
421	#121	—	2	1	no	—
422	#121	D₄×C₁₃	1	1	yes	characteristic
423	#120	—	2	2	no	—
424	#120	—	2	2	no	—
425	#120	—	2	2	no	—
426	#120	—	2	2	no	—
427	#120	—	2	2	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
439	#117	—	2	1	no	—
440	#117	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	#107	—	2	1	no	—
446	#106	—	2	1	no	—
447	C₄⋊C₈	—	2	1	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	1	no	—
451	#103	—	2	2	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	—	2	1	no	—
457	#102	—	2	2	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	#97	C₂³×C₁₃	1	1	yes	characteristic
460	#97	C₂³×C₁₃	1	1	yes	characteristic
461	#97	C₂³×C₁₃	1	2	yes	—
462	#97	C₂³×C₁₃	1	2	yes	—
463	C₄×C₈	—	2	1	no	—
464	C₄×C₈	—	2	1	no	—
465	C₂×C₁₃	—	4	1	no	—
466	C₂×C₁₃	—	8	2	no	—
467	C₂×C₁₃	—	8	1	no	—
468	C₂×C₁₃	—	8	2	no	—
469	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
470	C₂×C₁₃	#3018	1	1	yes	characteristic
471	C₂×C₁₃	#3019	1	1	yes	characteristic
472	C₂⁴	—	2	2	no	—
473	C₂⁴	—	2	1	no	—
474	#41	—	8	2	no	—
475	#41	—	8	2	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	4	2	no	—
480	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
481	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	8	2	no	—
495	C₂×D₄	—	8	4	no	—
496	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
497	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	Q₁₆	—	4	2	no	—
508	Q₁₆	—	8	2	no	—
509	SD₁₆	—	4	2	no	—
510	SD₁₆	—	8	2	no	—
511	M₁₆	—	4	2	no	—
512	M₁₆	—	4	2	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₄²	—	2	2	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	4	1	no	—
553	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₁₃	#19024	1	1	yes	characteristic, direct product factor, Sylow
558	C₂³	—	2	1	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	8	1	no	—
563	C₂³	—	8	1	no	—
564	C₂³	—	8	2	no	—
565	C₂³	—	8	2	no	—
566	C₂³	—	8	2	no	—
567	C₂³	C₁₃×#120	1	1	yes	characteristic
568	Q₈	—	4	1	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	4	2	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	2	no	—
576	D₄	—	4	1	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	8	1	no	—
584	D₄	—	8	2	no	—
585	D₄	—	8	2	no	—
586	D₄	—	8	2	no	—
587	D₄	—	8	2	no	—
588	D₄	—	8	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	—	8	1	no	—
602	C₂×C₄	—	8	2	no	—
603	C₂×C₄	—	8	2	no	—
604	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
605	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
606	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
610	C₈	—	2	2	no	—
611	C₈	—	4	2	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	2	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	16	2	no	—
627	C₂²	—	16	4	no	—
628	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₁₃×#455	1	2	yes	—
642	C₂	—	4	1	no	—
643	C₂	—	8	1	no	—
644	C₂	—	8	2	no	—
645	C₂	—	8	2	no	—
646	C₂	C₂×C₁₃×#455	1	1	yes	characteristic
647	C₂	C₁₃×#3018	1	1	yes	characteristic
648	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3558	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3216	C₂	semidirect
3. C₁₃×#3172	C₂	semidirect
4. C₁₃×#3140	C₂	semidirect
5. C₁₃×#1662	C₂	semidirect
6. C₁₃×#1661	C₂	semidirect
7. C₁₃×#1659	C₂	semidirect
8. C₁₃×#1659	C₂	semidirect
9. C₁₃×#1529	C₂	semidirect
10. C₁₃×#1527	C₂	semidirect
11. C₁₃×#1525	C₂	semidirect
24. C₁₃×#533	C₂²	semidirect
28. C₁₃×#501	C₂²	semidirect
29. C₁₃×#497	C₂²	semidirect
30. C₁₃×#497	C₂²	semidirect
31. C₁₃×#491	C₂²	semidirect
32. C₁₃×#489	C₂²	semidirect
33. C₁₃×#489	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#489	C₂²	semidirect
44. C₁₃×#432	C₂²	semidirect
47. C₄×C₁₃×M₁₆	C₂²	semidirect
48. C₄×C₁₃×M₁₆	C₂²	semidirect
49. C₁₃×#330	C₂²	semidirect
50. C₁₃×#329	C₂²	semidirect
51. C₁₃×#329	C₂²	semidirect
52. C₁₃×#329	C₂²	semidirect
53. C₁₃×#329	C₂²	semidirect
54. C₁₃×#329	C₂²	semidirect
148. #19024	C₁₃	direct (N × H)
235. #3216	C₂×C₁₃	semidirect
236. #3172	C₂×C₁₃	semidirect
237. #3140	C₂×C₁₃	semidirect
238. #1662	C₂×C₁₃	semidirect
239. #1661	C₂×C₁₃	semidirect
240. #1659	C₂×C₁₃	semidirect
241. #1659	C₂×C₁₃	semidirect
242. #1529	C₂×C₁₃	semidirect
243. #1527	C₂×C₁₃	semidirect
244. #1525	C₂×C₁₃	semidirect
313. #533	C₂²×C₁₃	semidirect
317. #501	C₂²×C₁₃	semidirect
318. #497	C₂²×C₁₃	semidirect
319. #497	C₂²×C₁₃	semidirect
320. #491	C₂²×C₁₃	semidirect
321. #489	C₂²×C₁₃	semidirect
322. #489	C₂²×C₁₃	semidirect
323. #489	C₂²×C₁₃	semidirect
324. #489	C₂²×C₁₃	semidirect
333. #432	C₂²×C₁₃	semidirect
336. C₄×M₁₆	C₂²×C₁₃	semidirect
337. C₄×M₁₆	C₂²×C₁₃	semidirect
338. #330	C₂²×C₁₃	semidirect
339. #329	C₂²×C₁₃	semidirect
340. #329	C₂²×C₁₃	semidirect
341. #329	C₂²×C₁₃	semidirect
342. #329	C₂²×C₁₃	semidirect
343. #329	C₂²×C₁₃	semidirect
557. C₁₃	#19024	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×#3558	2
C₁₃×#3216	2
C₁₃×#3172	2
C₁₃×#3140	2
C₁₃×#1662	2
C₁₃×#1661	2
C₁₃×#1659	2
C₁₃×#1529	2
C₁₃×#1527	2
C₁₃×#1525	2
#19024	13

Subgroups — C13×#19024 #15705363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19024 #15705363