Subgroups — C₁₃×#17684 #15704023

Order 3328.

932 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1536	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1530	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1530	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#557	C₄	1	1	yes	characteristic
13	C₁₃×#553	—	2	1	no	—
14	C₁₃×#553	—	2	2	no	—
15	C₁₃×#550	—	2	1	no	—
16	C₁₃×#550	C₄	1	1	yes	characteristic
17	C₁₃×#550	C₄	1	2	yes	—
18	C₁₃×#550	C₄	1	1	yes	characteristic
19	C₁₃×#547	C₄	1	1	yes	characteristic
20	C₁₃×#547	C₄	1	2	yes	—
21	C₁₃×#540	—	2	1	no	—
22	C₁₃×#540	—	2	2	no	—
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#529	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	2	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#446	—	2	1	no	—
30	C₁₃×#435	—	2	2	no	—
31	C₈×D₄×C₁₃	—	2	1	no	—
32	C₁₃×#433	—	2	2	no	—
33	C₁₃×#432	C₂²	1	1	yes	characteristic
34	C₁₃×#432	C₂²	1	2	yes	—
35	C₁₃×#432	C₂²	1	2	yes	—
36	C₁₃×#432	C₂²	1	2	yes	—
37	C₁₃×#424	—	2	1	no	—
38	C₁₃×#408	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#97	C₂²	1	2	yes	—
43	C₁₃×#330	C₂²	1	1	yes	characteristic
44	C₁₃×#330	C₂²	1	1	yes	characteristic
45	C₁₃×#330	C₂²	1	2	yes	—
46	C₁₃×#329	C₂²	1	1	yes	characteristic
47	C₁₃×#329	C₂²	1	1	yes	characteristic
48	C₁₃×#329	C₂²	1	2	yes	—
49	C₁₃×#329	C₂²	1	2	yes	—
50	C₁₃×#329	C₂²	1	2	yes	—
51	C₁₃×#329	C₂²	1	2	yes	—
52	C₁₃×#329	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₁₃×#127	—	2	1	no	—
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#127	C₂×C₄	1	2	yes	—
68	C₁₃×#126	—	2	1	no	—
69	C₁₃×#126	—	2	2	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	—	2	1	no	—
72	C₁₃×#125	C₂³	1	1	yes	characteristic
73	C₁₃×#124	C₂³	1	1	yes	characteristic
74	C₁₃×#124	C₂³	1	2	yes	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	1	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
81	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#121	C₂×C₄	1	2	yes	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	1	no	—
107	C₄×D₄×C₁₃	—	2	2	no	—
108	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
111	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
112	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
113	C₄×D₄×C₁₃	D₄	1	2	yes	—
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	—	2	2	no	—
116	C₁₃×#117	D₄	1	1	yes	characteristic
117	C₁₃×#117	D₄	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	2	no	—
132	C₁₃×#97	C₂³	1	1	yes	characteristic
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	1	yes	characteristic
135	C₁₃×#97	C₂³	1	2	yes	—
136	C₁₃×#97	C₂³	1	1	yes	characteristic
137	C₁₃×#97	C₂³	1	2	yes	—
138	C₄×C₈×C₁₃	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	#17684	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	4	2	no	—
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	8	2	no	—
144	C₁₃×#41	—	8	2	no	—
145	C₁₃×#41	—	8	2	no	—
146	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
160	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₁₃×M₁₆	—	4	2	no	—
174	C₁₃×M₁₆	—	4	2	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	4	4	no	—
182	C₂×C₈×C₁₃	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
215	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
221	#3517	C₂×C₁₃	1	1	yes	characteristic
222	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1536	C₂×C₁₃	1	2	yes	complemented
225	#1535	C₂×C₁₃	1	2	yes	complemented
226	#1532	C₂×C₁₃	1	2	yes	complemented
227	#1530	C₂×C₁₃	1	2	yes	complemented
228	#1530	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	4	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	8	1	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	1	no	—
249	D₄×C₁₃	—	8	2	no	—
250	D₄×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	8	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	8	2	no	—
266	C₂×C₄×C₁₃	—	8	2	no	—
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₈×C₁₃	—	2	2	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	2	no	—
280	C₈×C₁₃	—	4	2	no	—
281	C₈×C₁₃	—	4	1	no	—
282	#557	C₄×C₁₃	1	1	yes	characteristic
283	#553	—	2	1	no	—
284	#553	—	2	2	no	—
285	#550	—	2	1	no	—
286	#550	C₄×C₁₃	1	1	yes	characteristic
287	#550	C₄×C₁₃	1	2	yes	—
288	#550	C₄×C₁₃	1	1	yes	characteristic
289	#547	C₄×C₁₃	1	1	yes	characteristic
290	#547	C₄×C₁₃	1	2	yes	—
291	#540	—	2	1	no	—
292	#540	—	2	2	no	—
293	#532	C₂²×C₁₃	1	2	yes	—
294	#532	C₂²×C₁₃	1	1	yes	characteristic
295	#529	C₂²×C₁₃	1	1	yes	characteristic
296	#529	C₂²×C₁₃	1	2	yes	—
297	#520	—	2	1	no	—
298	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
299	#446	—	2	1	no	—
300	#435	—	2	2	no	—
301	C₈×D₄	—	2	1	no	—
302	#433	—	2	2	no	—
303	#432	C₂²×C₁₃	1	2	yes	—
304	#432	C₂²×C₁₃	1	2	yes	—
305	#432	C₂²×C₁₃	1	2	yes	—
306	#432	C₂²×C₁₃	1	1	yes	characteristic
307	#424	—	2	1	no	—
308	#408	—	2	1	no	—
309	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
310	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#97	C₂²×C₁₃	1	2	yes	—
313	#330	C₂²×C₁₃	1	1	yes	characteristic
314	#330	C₂²×C₁₃	1	1	yes	characteristic
315	#330	C₂²×C₁₃	1	2	yes	—
316	#329	C₂²×C₁₃	1	1	yes	characteristic
317	#329	C₂²×C₁₃	1	2	yes	—
318	#329	C₂²×C₁₃	1	2	yes	—
319	#329	C₂²×C₁₃	1	2	yes	—
320	#329	C₂²×C₁₃	1	1	yes	characteristic
321	#329	C₂²×C₁₃	1	2	yes	—
322	#329	C₂²×C₁₃	1	2	yes	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	4	2	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	#421	1	2	yes	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
351	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
352	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
353	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	2	no	—
358	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
359	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
360	#127	—	2	1	no	—
361	#127	—	2	2	no	—
362	#127	C₂×C₄×C₁₃	1	2	yes	—
363	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
364	#126	—	2	1	no	—
365	#126	—	2	2	no	—
366	#125	—	2	2	no	—
367	#125	—	2	1	no	—
368	#125	C₂³×C₁₃	1	1	yes	characteristic
369	#124	C₂³×C₁₃	1	1	yes	characteristic
370	#124	C₂³×C₁₃	1	2	yes	—
371	#123	—	2	2	no	—
372	#123	—	2	1	no	—
373	#123	—	2	2	no	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
378	#121	—	2	1	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	2	no	—
384	#121	—	2	2	no	—
385	#121	—	2	1	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
390	#121	C₂×C₄×C₁₃	1	2	yes	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
393	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
394	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
395	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
405	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
406	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
407	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
408	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
409	C₄×D₄	D₄×C₁₃	1	2	yes	—
410	#117	—	2	1	no	—
411	#117	—	2	2	no	—
412	#117	D₄×C₁₃	1	1	yes	characteristic
413	#117	D₄×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
418	C₄⋊C₈	—	2	2	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	—	2	2	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	#97	—	2	1	no	—
427	#97	—	2	2	no	—
428	#97	C₂³×C₁₃	1	1	yes	characteristic
429	#97	C₂³×C₁₃	1	1	yes	characteristic
430	#97	C₂³×C₁₃	1	2	yes	—
431	#97	C₂³×C₁₃	1	1	yes	characteristic
432	#97	C₂³×C₁₃	1	1	yes	characteristic
433	#97	C₂³×C₁₃	1	2	yes	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₂×C₁₃	—	4	1	no	—
437	C₂×C₁₃	—	4	2	no	—
438	C₂×C₁₃	—	8	2	no	—
439	C₂×C₁₃	—	8	1	no	—
440	C₂×C₁₃	#2888	1	1	yes	characteristic
441	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
442	C₂×C₁₃	#2901	1	1	yes	characteristic
443	#41	—	4	2	no	—
444	#41	—	4	4	no	—
445	#41	—	8	2	no	—
446	#41	—	8	2	no	—
447	#41	—	8	2	no	—
448	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
450	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
463	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	M₁₆	—	4	2	no	—
476	M₁₆	—	4	2	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	4	4	no	—
484	C₂×C₈	—	4	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
496	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
497	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
498	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
512	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
513	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	1	no	—
516	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
517	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
518	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₁₃	1	2	yes	—
521	C₄²	C₂×D₄×C₁₃	1	2	yes	—
522	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₁₃	#17684	1	1	yes	characteristic, direct product factor, Sylow
524	C₂³	—	2	2	no	—
525	C₂³	—	2	1	no	—
526	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
527	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
528	Q₈	—	2	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
560	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
562	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
564	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	C₁₃×#421	1	2	yes	—
600	C₂	—	4	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	8	1	no	—
604	C₂	C₁₃×#2888	1	1	yes	characteristic
605	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
606	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3517	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#2923	C₂	semidirect
4. C₁₃×#1536	C₂	semidirect
5. C₁₃×#1535	C₂	semidirect
6. C₁₃×#1532	C₂	semidirect
7. C₁₃×#1530	C₂	semidirect
8. C₁₃×#1530	C₂	semidirect
9. C₁₃×#1529	C₂	semidirect
10. C₁₃×#1525	C₂	semidirect
11. C₁₃×#1524	C₂	semidirect
140. #17684	C₁₃	direct (N × H)
222. #2970	C₂×C₁₃	semidirect
223. #2923	C₂×C₁₃	semidirect
224. #1536	C₂×C₁₃	semidirect
225. #1535	C₂×C₁₃	semidirect
226. #1532	C₂×C₁₃	semidirect
227. #1530	C₂×C₁₃	semidirect
228. #1530	C₂×C₁₃	semidirect
229. #1529	C₂×C₁₃	semidirect
230. #1525	C₂×C₁₃	semidirect
231. #1524	C₂×C₁₃	semidirect
523. C₁₃	#17684	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×#3517	2
C₁₃×#2970	2
C₁₃×#2923	2
C₁₃×#1536	2
C₁₃×#1535	2
C₁₃×#1532	2
C₁₃×#1530	2
C₁₃×#1529	2
C₁₃×#1525	2
C₁₃×#1524	2
#17684	13

Subgroups — C13×#17684 #15704023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17684 #15704023