Subgroups — C₁₃×#19418 #15705757

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1674	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1671	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₁₃×#500	C₂²	1	1	yes	characteristic
20	C₁₃×#498	C₂²	1	1	yes	characteristic
21	C₁₃×#487	C₂²	1	1	yes	characteristic
22	C₁₃×#487	C₂²	1	1	yes	characteristic
23	C₁₃×#485	—	2	1	no	—
24	C₁₃×#485	—	2	1	no	—
25	C₁₃×#485	—	2	1	no	—
26	C₁₃×#485	—	2	1	no	—
27	C₁₃×#479	—	2	1	no	—
28	C₁₃×#479	—	2	1	no	—
29	C₁₃×#477	C₂²	1	1	yes	characteristic
30	C₁₃×#476	C₂²	1	1	yes	characteristic
31	C₁₃×#475	C₂²	1	1	yes	characteristic
32	C₁₃×#474	C₂²	1	1	yes	characteristic
33	C₁₃×#462	C₂²	1	1	yes	characteristic
34	C₁₃×#462	C₂²	1	1	yes	characteristic
35	C₁₃×#461	C₂²	1	1	yes	characteristic
36	C₁₃×#461	C₂²	1	1	yes	characteristic
37	C₁₃×#452	—	2	1	no	—
38	C₁₃×#452	—	2	1	no	—
39	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#441	—	2	1	no	—
42	C₁₃×#440	—	2	1	no	—
43	C₄×C₁₃×Q₁₆	—	2	1	no	—
44	C₄×C₁₃×SD₁₆	—	2	1	no	—
45	C₈×D₄×C₁₃	—	2	1	no	—
46	C₈×D₄×C₁₃	—	2	1	no	—
47	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#432	C₂²	1	1	yes	characteristic
50	C₁₃×#431	—	2	1	no	—
51	C₁₃×#431	C₂²	1	1	yes	characteristic
52	C₁₃×#431	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₃×#335	C₂²	1	1	yes	characteristic
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#334	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×#332	C₂²	1	1	yes	characteristic
63	C₁₃×#332	C₂²	1	1	yes	characteristic
64	C₁₃×#332	C₂²	1	1	yes	characteristic
65	C₁₃×#332	C₂²	1	1	yes	characteristic
66	C₁₃×#332	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×#125	—	2	1	no	—
80	C₁₃×#125	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₄×Q₈×C₁₃	—	2	1	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	—	2	1	no	—
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#107	—	2	1	no	—
102	C₁₃×#107	—	2	1	no	—
103	C₁₃×#107	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#106	—	2	1	no	—
106	C₁₃×#106	—	2	1	no	—
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	—	2	1	no	—
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×C₂²⋊C₈	—	2	1	no	—
133	C₁₃×C₂²⋊C₈	—	2	1	no	—
134	C₁₃×C₂²⋊C₈	—	2	1	no	—
135	C₁₃×C₂²⋊C₈	—	2	1	no	—
136	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₃×#97	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	—	2	1	no	—
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19418	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	2	2	no	—
146	C₁₃×#41	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	4	2	no	—
161	C₁₃×Q₁₆	—	4	2	no	—
162	C₁₃×SD₁₆	—	4	2	no	—
163	C₁₃×SD₁₆	—	4	2	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	8	1	no	—
171	C₂×C₈×C₁₃	—	8	1	no	—
172	C₂×C₈×C₁₃	—	8	1	no	—
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
193	C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	4	1	no	—
202	C₄²×C₁₃	—	4	1	no	—
203	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₃	#41	1	1	yes	characteristic
206	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
207	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3116	C₂×C₁₃	1	1	yes	characteristic
209	#3107	C₂×C₁₃	1	1	yes	characteristic
210	#2988	C₂×C₁₃	1	1	yes	characteristic
211	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1679	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1674	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1673	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1672	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1671	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1552	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1542	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	#121	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	1	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	Q₈×C₁₃	—	8	1	no	—
232	Q₈×C₁₃	#135	1	2	yes	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	#135	1	2	yes	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	8	1	no	—
252	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₈×C₁₃	—	2	1	no	—
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	4	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	#533	C₂²×C₁₃	1	1	yes	characteristic
269	#533	C₂²×C₁₃	1	1	yes	characteristic
270	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
271	#500	C₂²×C₁₃	1	1	yes	characteristic
272	#498	C₂²×C₁₃	1	1	yes	characteristic
273	#487	C₂²×C₁₃	1	1	yes	characteristic
274	#487	C₂²×C₁₃	1	1	yes	characteristic
275	#485	—	2	1	no	—
276	#485	—	2	1	no	—
277	#485	—	2	1	no	—
278	#485	—	2	1	no	—
279	#479	—	2	1	no	—
280	#479	—	2	1	no	—
281	#477	C₂²×C₁₃	1	1	yes	characteristic
282	#476	C₂²×C₁₃	1	1	yes	characteristic
283	#475	C₂²×C₁₃	1	1	yes	characteristic
284	#474	C₂²×C₁₃	1	1	yes	characteristic
285	#462	C₂²×C₁₃	1	1	yes	characteristic
286	#462	C₂²×C₁₃	1	1	yes	characteristic
287	#461	C₂²×C₁₃	1	1	yes	characteristic
288	#461	C₂²×C₁₃	1	1	yes	characteristic
289	#452	—	2	1	no	—
290	#452	—	2	1	no	—
291	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
293	#441	—	2	1	no	—
294	#440	—	2	1	no	—
295	C₄×Q₁₆	—	2	1	no	—
296	C₄×SD₁₆	—	2	1	no	—
297	C₈×D₄	—	2	1	no	—
298	C₈×D₄	—	2	1	no	—
299	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	#432	C₂²×C₁₃	1	1	yes	characteristic
302	#431	—	2	1	no	—
303	#431	C₂²×C₁₃	1	1	yes	characteristic
304	#431	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₈	—	2	1	no	—
306	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
307	#335	C₂²×C₁₃	1	1	yes	characteristic
308	#335	C₂²×C₁₃	1	1	yes	characteristic
309	#334	C₂²×C₁₃	1	1	yes	characteristic
310	#334	C₂²×C₁₃	1	1	yes	characteristic
311	#333	C₂²×C₁₃	1	1	yes	characteristic
312	#333	C₂²×C₁₃	1	1	yes	characteristic
313	#332	C₂²×C₁₃	1	1	yes	characteristic
314	#332	C₂²×C₁₃	1	1	yes	characteristic
315	#332	C₂²×C₁₃	1	1	yes	characteristic
316	#332	C₂²×C₁₃	1	1	yes	characteristic
317	#332	C₂²×C₁₃	1	1	yes	characteristic
318	#332	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	—	8	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
338	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
339	C₄×C₁₃	#577	1	1	yes	characteristic
340	C₄×C₁₃	#578	1	1	yes	characteristic
341	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×Q₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂²×C₈	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
353	#125	—	2	1	no	—
354	#125	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
364	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
368	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	#106	—	2	1	no	—
382	#106	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
387	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
411	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
412	#97	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₁₃	—	4	1	no	—
419	C₂×C₁₃	—	4	2	no	—
420	C₂×C₁₃	#3046	1	1	yes	characteristic
421	C₂×C₁₃	#3050	1	1	yes	characteristic
422	C₂×C₁₃	#3069	1	1	yes	characteristic
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
438	Q₁₆	—	4	2	no	—
439	Q₁₆	—	4	2	no	—
440	SD₁₆	—	4	2	no	—
441	SD₁₆	—	4	2	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	8	1	no	—
449	C₂×C₈	—	8	1	no	—
450	C₂×C₈	—	8	1	no	—
451	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄²	C₁₃×#41	1	1	yes	characteristic
484	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
485	C₁₃	#19418	1	1	yes	characteristic, direct product factor, Sylow
486	C₂³	—	2	1	no	—
487	C₂³	C₁₃×#121	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	C₁₃×#135	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	C₁₃×#135	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
517	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
518	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
551	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
552	C₄	C₁₃×#577	1	1	yes	characteristic
553	C₄	C₁₃×#578	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	4	2	no	—
556	C₂	C₁₃×#3046	1	1	yes	characteristic
557	C₂	C₁₃×#3050	1	1	yes	characteristic
558	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	D₄
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
1. C₁₃×#3231	C₂	semidirect
5. C₁₃×#1684	C₂	semidirect
6. C₁₃×#1683	C₂	semidirect
7. C₁₃×#1680	C₂	semidirect
8. C₁₃×#1679	C₂	semidirect
9. C₁₃×#1674	C₂	semidirect
10. C₁₃×#1673	C₂	semidirect
11. C₁₃×#1672	C₂	semidirect
12. C₁₃×#1671	C₂	semidirect
13. C₁₃×#1572	C₂	semidirect
14. C₁₃×#1552	C₂	semidirect
15. C₁₃×#1542	C₂	semidirect
144. #19418	C₁₃	direct (N × H)
207. #3231	C₂×C₁₃	semidirect
211. #1684	C₂×C₁₃	semidirect
212. #1683	C₂×C₁₃	semidirect
213. #1680	C₂×C₁₃	semidirect
214. #1679	C₂×C₁₃	semidirect
215. #1674	C₂×C₁₃	semidirect
216. #1673	C₂×C₁₃	semidirect
217. #1672	C₂×C₁₃	semidirect
218. #1671	C₂×C₁₃	semidirect
219. #1572	C₂×C₁₃	semidirect
220. #1552	C₂×C₁₃	semidirect
221. #1542	C₂×C₁₃	semidirect
485. C₁₃	#19418	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×#3231	2
C₁₃×#3116	2
C₁₃×#3107	2
C₁₃×#2988	2
C₁₃×#1684	2
C₁₃×#1683	2
C₁₃×#1680	2
C₁₃×#1679	2
C₁₃×#1674	2
C₁₃×#1673	2
C₁₃×#1672	2
C₁₃×#1671	2
C₁₃×#1572	2
C₁₃×#1552	2
C₁₃×#1542	2
#19418	13

Subgroups — C13×#19418 #15705757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19418 #15705757