Subgroups — C₁₃×#17600 #15703939

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1520	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1516	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1513	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1511	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1506	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1500	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#556	C₄	1	1	yes	characteristic, complemented
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#552	C₄	1	2	yes	complemented
15	C₁₃×#551	—	2	2	no	—
16	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#548	C₄	1	2	yes	complemented
18	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#546	—	2	1	no	—
21	C₁₃×#542	—	2	1	no	—
22	C₁₃×#539	—	2	2	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₁₃×#525	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#436	—	2	1	no	—
30	C₁₃×#435	—	2	2	no	—
31	C₈×D₄×C₁₃	—	2	1	no	—
32	C₁₃×#432	C₂²	1	1	yes	characteristic
33	C₁₃×#431	C₂²	1	1	yes	characteristic
34	C₁₃×#407	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₁₃×#390	—	2	1	no	—
37	C₁₃×#389	—	2	1	no	—
38	C₁₃×#388	—	2	2	no	—
39	C₁₃×#381	C₂²	1	2	yes	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#376	C₂²	1	1	yes	characteristic
43	C₁₃×#328	C₂²	1	1	yes	characteristic
44	C₁₃×#328	C₂²	1	1	yes	characteristic
45	C₁₃×#328	C₂²	1	2	yes	—
46	C₁₃×#328	C₂²	1	2	yes	—
47	C₁₃×#328	C₂²	1	2	yes	—
48	C₁₃×#328	C₂²	1	2	yes	—
49	C₁₃×#328	C₂²	1	2	yes	—
50	C₁₃×#327	C₂²	1	1	yes	characteristic
51	C₁₃×#327	C₂²	1	1	yes	characteristic
52	C₁₃×#327	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
55	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#126	—	2	2	no	—
64	C₁₃×#126	—	2	2	no	—
65	C₁₃×#126	—	2	1	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	1	no	—
68	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#123	—	2	2	no	—
73	C₁₃×#123	—	2	2	no	—
74	C₁₃×#123	—	2	1	no	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	C₂×C₄	1	2	yes	—
91	C₁₃×#121	C₂³	1	1	yes	characteristic
92	C₁₃×#120	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
106	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₃	D₄	1	2	yes	—
108	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₁₃×#117	—	2	1	no	—
110	C₁₃×#117	—	2	2	no	—
111	C₁₃×#117	—	2	1	no	—
112	C₁₃×#117	C₂×C₄	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
132	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
133	C₁₃×#97	—	2	1	no	—
134	C₄×C₈×C₁₃	—	2	1	no	—
135	C₁₃×#95	—	2	2	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	1	yes	characteristic
139	C₁₃×#95	C₂³	1	1	yes	characteristic
140	#17600	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	8	2	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	8	2	no	—
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
156	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	8	2	no	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×M₁₆	—	8	2	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	8	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	—	8	2	no	—
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	8	2	no	—
211	C₁₃×C₂²⋊C₄	—	8	2	no	—
212	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
213	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
214	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
215	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
216	C₄²×C₁₃	—	2	2	no	—
217	C₄²×C₁₃	—	2	2	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	4	2	no	—
220	C₄²×C₁₃	—	8	1	no	—
221	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
223	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
225	#3520	C₂×C₁₃	1	1	yes	characteristic
226	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2319	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1520	C₂×C₁₃	1	2	yes	complemented
229	#1516	C₂×C₁₃	1	2	yes	complemented
230	#1513	C₂×C₁₃	1	2	yes	complemented
231	#1511	C₂×C₁₃	1	2	yes	complemented
232	#1509	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1506	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1500	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	4	2	no	—
240	C₂³×C₁₃	—	4	2	no	—
241	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
242	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	2	no	—
246	Q₈×C₁₃	—	4	2	no	—
247	Q₈×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	4	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	8	2	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	8	2	no	—
282	C₂×C₄×C₁₃	—	8	2	no	—
283	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	—	4	2	no	—
293	C₈×C₁₃	—	4	1	no	—
294	#556	C₄×C₁₃	1	1	yes	characteristic, complemented
295	#554	—	2	1	no	—
296	#552	C₄×C₁₃	1	2	yes	complemented
297	#551	—	2	2	no	—
298	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
299	#548	C₄×C₁₃	1	2	yes	complemented
300	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
301	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
302	#546	—	2	1	no	—
303	#542	—	2	1	no	—
304	#539	—	2	2	no	—
305	#533	C₂²×C₁₃	1	1	yes	characteristic
306	#529	C₂²×C₁₃	1	1	yes	characteristic
307	#525	C₂²×C₁₃	1	2	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
309	#520	—	2	1	no	—
310	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	#436	—	2	1	no	—
312	#435	—	2	2	no	—
313	C₈×D₄	—	2	1	no	—
314	#432	C₂²×C₁₃	1	1	yes	characteristic
315	#431	C₂²×C₁₃	1	1	yes	characteristic
316	#407	C₂²×C₁₃	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
318	#390	—	2	1	no	—
319	#389	—	2	1	no	—
320	#388	—	2	2	no	—
321	#381	C₂²×C₁₃	1	2	yes	—
322	#380	C₂²×C₁₃	1	2	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
324	#376	C₂²×C₁₃	1	1	yes	characteristic
325	#328	C₂²×C₁₃	1	1	yes	characteristic
326	#328	C₂²×C₁₃	1	1	yes	characteristic
327	#328	C₂²×C₁₃	1	2	yes	—
328	#328	C₂²×C₁₃	1	2	yes	—
329	#328	C₂²×C₁₃	1	2	yes	—
330	#328	C₂²×C₁₃	1	2	yes	—
331	#328	C₂²×C₁₃	1	2	yes	—
332	#327	C₂²×C₁₃	1	1	yes	characteristic
333	#327	C₂²×C₁₃	1	1	yes	characteristic
334	#327	C₂²×C₁₃	1	2	yes	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	8	2	no	—
347	C₂²×C₁₃	—	8	2	no	—
348	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₁₃	#577	1	1	yes	characteristic
350	C₂²×C₁₃	#578	1	1	yes	characteristic
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	1	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	2	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	#421	1	2	yes	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
369	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
370	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
376	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
377	#126	—	2	2	no	—
378	#126	—	2	2	no	—
379	#126	—	2	1	no	—
380	#125	—	2	2	no	—
381	#125	—	2	1	no	—
382	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#124	—	2	1	no	—
384	#124	—	2	2	no	—
385	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	#123	—	2	1	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
398	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
399	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
400	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
402	#121	—	2	2	no	—
403	#121	—	2	1	no	—
404	#121	C₂×C₄×C₁₃	1	2	yes	—
405	#121	C₂³×C₁₃	1	1	yes	characteristic
406	#120	—	2	2	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
410	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
417	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
418	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
419	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
420	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
421	C₄×D₄	D₄×C₁₃	1	2	yes	—
422	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
423	#117	—	2	1	no	—
424	#117	—	2	2	no	—
425	#117	—	2	1	no	—
426	#117	C₂×C₄×C₁₃	1	2	yes	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	2	no	—
431	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
432	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	—	2	2	no	—
436	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
446	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
447	#97	—	2	1	no	—
448	C₄×C₈	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	2	no	—
451	#95	C₂³×C₁₃	1	1	yes	characteristic
452	#95	C₂³×C₁₃	1	1	yes	characteristic
453	#95	C₂³×C₁₃	1	2	yes	—
454	C₂×C₁₃	—	2	1	no	—
455	C₂×C₁₃	—	2	1	no	—
456	C₂×C₁₃	—	4	2	no	—
457	C₂×C₁₃	—	4	2	no	—
458	C₂×C₁₃	—	8	1	no	—
459	C₂×C₁₃	#2883	1	1	yes	characteristic
460	C₂×C₁₃	#2898	1	1	yes	characteristic
461	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
462	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
463	#41	—	4	4	no	—
464	#41	—	8	2	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	8	2	no	—
468	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
469	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
475	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
477	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	8	2	no	—
486	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
494	M₁₆	—	8	2	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	8	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	8	2	no	—
514	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
515	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
516	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	8	2	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
534	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
535	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
536	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	4	2	no	—
541	C₄²	—	8	1	no	—
542	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
543	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₁₃	#17600	1	1	yes	characteristic, direct product factor, Sylow
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
553	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
554	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	Q₈	—	4	1	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	8	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	4	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	8	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
595	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
596	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
597	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
598	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
599	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
600	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
602	C₈	—	4	1	no	—
603	C₈	—	4	2	no	—
604	C₈	—	4	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	2	no	—
618	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
619	C₂²	C₁₃×#577	1	1	yes	characteristic
620	C₂²	C₁₃×#578	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	2	no	—
635	C₄	—	8	1	no	—
636	C₄	C₁₃×#421	1	2	yes	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	2	no	—
641	C₂	—	8	1	no	—
642	C₂	C₁₃×#2883	1	1	yes	characteristic
643	C₂	C₁₃×#2898	1	1	yes	characteristic
644	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2974	C₂	semidirect
3. C₁₃×#2319	C₂	semidirect
4. C₁₃×#1520	C₂	semidirect
5. C₁₃×#1516	C₂	semidirect
6. C₁₃×#1513	C₂	semidirect
7. C₁₃×#1511	C₂	semidirect
8. C₁₃×#1509	C₂	semidirect
9. C₁₃×#1506	C₂	semidirect
10. C₁₃×#1503	C₂	semidirect
11. C₁₃×#1500	C₂	semidirect
12. C₁₃×#556	C₄	semidirect
14. C₁₃×#552	C₄	semidirect
16. D₄×Q₈×C₁₃	C₄	semidirect
17. C₁₃×#548	C₄	semidirect
18. C₁₃×#547	C₄	semidirect
19. C₁₃×#547	C₄	semidirect
140. #17600	C₁₃	direct (N × H)
226. #2974	C₂×C₁₃	semidirect
227. #2319	C₂×C₁₃	semidirect
228. #1520	C₂×C₁₃	semidirect
229. #1516	C₂×C₁₃	semidirect
230. #1513	C₂×C₁₃	semidirect
231. #1511	C₂×C₁₃	semidirect
232. #1509	C₂×C₁₃	semidirect
233. #1506	C₂×C₁₃	semidirect
234. #1503	C₂×C₁₃	semidirect
235. #1500	C₂×C₁₃	semidirect
294. #556	C₄×C₁₃	semidirect
296. #552	C₄×C₁₃	semidirect
298. D₄×Q₈	C₄×C₁₃	semidirect
299. #548	C₄×C₁₃	semidirect
300. #547	C₄×C₁₃	semidirect
301. #547	C₄×C₁₃	semidirect
546. C₁₃	#17600	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×#3520	2
C₁₃×#2974	2
C₁₃×#2319	2
C₁₃×#1520	2
C₁₃×#1516	2
C₁₃×#1513	2
C₁₃×#1511	2
C₁₃×#1509	2
C₁₃×#1506	2
C₁₃×#1503	2
C₁₃×#1500	2
#17600	13

Subgroups — C13×#17600 #15703939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17600 #15703939