Subgroups — C₁₃×#60618 #15746957

Order 3328.

2170 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3142	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3141	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3140	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3139	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3138	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3135	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3131	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2896	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₁₃×#533	—	2	2	no	—
15	C₁₃×#533	—	2	2	no	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₁₃×#533	C₂²	1	2	yes	—
18	C₁₃×#533	C₂²	1	2	yes	complemented
19	C₁₃×#533	C₂²	1	2	yes	complemented
20	C₁₃×#532	—	2	2	no	—
21	C₁₃×#532	—	2	2	no	—
22	C₁₃×#532	C₂²	1	2	yes	—
23	C₁₃×#532	C₂²	1	2	yes	—
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#124	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
34	C₂×C₄×D₄×C₁₃	—	2	2	no	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#491	C₂²	1	8	yes	complemented
38	C₁₃×#490	C₂²	1	8	yes	complemented
39	C₁₃×#489	C₂²	1	16	yes	complemented
40	C₁₃×#488	C₂²	1	16	yes	complemented
41	C₁₃×#487	C₂²	1	8	yes	complemented
42	C₁₃×#486	C₂²	1	8	yes	complemented
43	C₁₃×#419	C₂²	1	8	yes	—
44	C₁₃×#418	C₂²	1	8	yes	—
45	C₁₃×#417	C₂²	1	16	yes	complemented
46	C₁₃×#416	C₂²	1	16	yes	complemented
47	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
48	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
49	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
50	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
52	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	2	16	no	—
56	C₂×C₁₃×#41	C₂³	1	4	yes	—
57	C₂×C₁₃×#41	C₂³	1	4	yes	—
58	C₂²×Q₈×C₁₃	—	2	2	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	D₄	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×M₁₆	—	2	8	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×#127	—	2	2	no	—
78	C₁₃×#127	C₂³	1	2	yes	—
79	C₁₃×#127	C₂³	1	2	yes	—
80	C₁₃×#125	—	2	4	no	—
81	C₁₃×#125	C₂³	1	4	yes	—
82	C₁₃×#125	C₂³	1	4	yes	—
83	C₁₃×#124	—	2	4	no	—
84	C₁₃×#124	C₂³	1	4	yes	—
85	C₁₃×#124	C₂³	1	4	yes	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	4	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₁₃×#121	—	2	4	no	—
92	C₁₃×#121	—	2	4	no	—
93	C₁₃×#121	—	2	4	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	—	2	4	no	—
96	C₄×Q₈×C₁₃	—	2	4	no	—
97	C₄×Q₈×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	—	2	4	no	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	C₂³	1	4	yes	—
105	C₁₃×#117	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
112	C₂×C₄²×C₁₃	—	2	2	no	—
113	C₂×C₄²×C₁₃	D₄	1	2	yes	—
114	C₂×C₄²×C₁₃	D₄	1	2	yes	—
115	C₂×C₄²×C₁₃	D₄	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#103	C₂³	1	32	yes	—
123	C₁₃×#102	C₂³	1	32	yes	—
124	C₁₃×#97	C₂³	1	4	yes	—
125	C₁₃×#97	C₂³	1	4	yes	—
126	C₄×C₈×C₁₃	C₂³	1	4	yes	—
127	C₄×C₈×C₁₃	C₂³	1	4	yes	—
128	#60618	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	2	no	—
130	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₁₃×#41	—	2	16	no	—
132	C₁₃×#41	—	2	16	no	—
133	C₁₃×#41	—	4	8	no	—
134	C₁₃×#41	—	4	8	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	8	no	—
139	C₂×Q₈×C₁₃	—	4	8	no	—
140	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	4	8	no	—
148	C₂×D₄×C₁₃	—	4	8	no	—
149	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	8	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	#41	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₁₃×M₁₆	—	2	8	no	—
170	C₁₃×M₁₆	—	2	8	no	—
171	C₂×C₈×C₁₃	—	2	8	no	—
172	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₄²×C₁₃	—	2	4	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	C₂×D₄	1	2	yes	—
189	C₄²×C₁₃	C₂×D₄	1	2	yes	—
190	C₄²×C₁₃	C₂×D₄	1	2	yes	—
191	C₄²×C₁₃	C₂×D₄	1	2	yes	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
199	#3142	C₂×C₁₃	1	4	yes	complemented
200	#3141	C₂×C₁₃	1	4	yes	complemented
201	#3140	C₂×C₁₃	1	4	yes	complemented
202	#3139	C₂×C₁₃	1	2	yes	complemented
203	#3138	C₂×C₁₃	1	2	yes	complemented
204	#3135	C₂×C₁₃	1	4	yes	complemented
205	#3131	C₂×C₁₃	1	4	yes	complemented
206	#2896	C₂×C₁₃	1	4	yes	complemented
207	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	8	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	#124	1	4	yes	—
213	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₁₃	—	2	8	no	—
217	Q₈×C₁₃	—	4	8	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	2	8	no	—
221	D₄×C₁₃	—	4	8	no	—
222	D₄×C₁₃	—	4	8	no	—
223	D₄×C₁₃	—	4	8	no	—
224	D₄×C₁₃	—	4	4	no	—
225	D₄×C₁₃	—	4	8	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	4	8	no	—
238	C₂×C₄×C₁₃	#124	1	4	yes	—
239	C₂×C₄×C₁₃	#124	1	4	yes	—
240	C₂×C₄×C₁₃	#124	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₃	—	2	8	no	—
253	C₂²×#41	C₂²×C₁₃	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
255	#533	—	2	2	no	—
256	#533	—	2	2	no	—
257	#533	C₂²×C₁₃	1	2	yes	—
258	#533	C₂²×C₁₃	1	2	yes	—
259	#533	C₂²×C₁₃	1	2	yes	complemented
260	#533	C₂²×C₁₃	1	2	yes	complemented
261	#532	—	2	2	no	—
262	#532	—	2	2	no	—
263	#532	C₂²×C₁₃	1	2	yes	—
264	#532	C₂²×C₁₃	1	2	yes	—
265	#532	C₂²×C₁₃	1	2	yes	—
266	#532	C₂²×C₁₃	1	2	yes	—
267	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
269	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
271	C₂×#124	C₂²×C₁₃	1	2	yes	—
272	C₂×C₂²⋊Q₈	—	2	2	no	—
273	C₂×#121	—	2	2	no	—
274	C₂×C₄×Q₈	—	2	2	no	—
275	C₂×C₄×D₄	—	2	2	no	—
276	C₂×#117	C₂²×C₁₃	1	2	yes	—
277	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
278	#491	C₂²×C₁₃	1	8	yes	complemented
279	#490	C₂²×C₁₃	1	8	yes	complemented
280	#489	C₂²×C₁₃	1	16	yes	complemented
281	#488	C₂²×C₁₃	1	16	yes	complemented
282	#487	C₂²×C₁₃	1	8	yes	complemented
283	#486	C₂²×C₁₃	1	8	yes	complemented
284	#419	C₂²×C₁₃	1	8	yes	—
285	#418	C₂²×C₁₃	1	8	yes	—
286	#417	C₂²×C₁₃	1	16	yes	complemented
287	#416	C₂²×C₁₃	1	16	yes	complemented
288	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
289	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
290	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
291	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
292	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
293	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	4	4	no	—
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	—	4	8	no	—
300	C₂²×C₁₃	—	8	8	no	—
301	C₂²×C₁₃	C₂×#124	1	2	yes	—
302	C₂²×C₁₃	C₂×#124	1	2	yes	—
303	C₂²×C₁₃	C₂×#124	1	2	yes	—
304	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	8	no	—
310	C₄×C₁₃	C₂×#124	1	2	yes	—
311	C₄×C₁₃	C₂×#124	1	2	yes	—
312	C₄×C₁₃	C₂×#124	1	2	yes	—
313	C₄×C₁₃	#575	1	4	yes	—
314	C₄×C₁₃	C₂²×#41	1	2	yes	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	16	no	—
318	C₂×#41	C₂³×C₁₃	1	4	yes	—
319	C₂×#41	C₂³×C₁₃	1	4	yes	—
320	C₂²×Q₈	—	2	2	no	—
321	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
325	C₂³×C₄	—	2	2	no	—
326	C₂³×C₄	D₄×C₁₃	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×M₁₆	—	2	8	no	—
329	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
331	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
336	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
337	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
338	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
339	#127	—	2	2	no	—
340	#127	C₂³×C₁₃	1	2	yes	—
341	#127	C₂³×C₁₃	1	2	yes	—
342	#125	—	2	4	no	—
343	#125	C₂³×C₁₃	1	4	yes	—
344	#125	C₂³×C₁₃	1	4	yes	—
345	#124	—	2	4	no	—
346	#124	C₂³×C₁₃	1	4	yes	—
347	#124	C₂³×C₁₃	1	4	yes	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#121	—	2	4	no	—
355	#121	—	2	4	no	—
356	C₄×Q₈	—	2	4	no	—
357	C₄×Q₈	—	2	4	no	—
358	C₄×Q₈	—	2	4	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×D₄	—	2	4	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	#117	—	2	2	no	—
365	#117	—	2	2	no	—
366	#117	C₂³×C₁₃	1	4	yes	—
367	#117	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	D₄×C₁₃	1	2	yes	—
376	C₂×C₄²	D₄×C₁₃	1	2	yes	—
377	C₂×C₄²	D₄×C₁₃	1	2	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	#103	C₂³×C₁₃	1	32	yes	—
385	#102	C₂³×C₁₃	1	32	yes	—
386	#97	C₂³×C₁₃	1	4	yes	—
387	#97	C₂³×C₁₃	1	4	yes	—
388	C₄×C₈	C₂³×C₁₃	1	4	yes	—
389	C₄×C₈	C₂³×C₁₃	1	4	yes	—
390	C₂×C₁₃	—	2	2	no	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	2	2	no	—
393	C₂×C₁₃	—	8	4	no	—
394	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#575	1	2	yes	—
396	C₂⁴	—	2	2	no	—
397	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
398	#41	—	2	16	no	—
399	#41	—	2	16	no	—
400	#41	—	4	8	no	—
401	#41	—	4	8	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	8	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	8	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₁₃×#41	1	8	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	M₁₆	—	2	8	no	—
437	M₁₆	—	2	8	no	—
438	C₂×C₈	—	2	8	no	—
439	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	C₂×D₄×C₁₃	1	2	yes	—
455	C₄²	C₂×D₄×C₁₃	1	2	yes	—
456	C₄²	C₂×D₄×C₁₃	1	2	yes	—
457	C₄²	C₂×D₄×C₁₃	1	2	yes	—
458	C₄²	C₂×D₄×C₁₃	1	2	yes	—
459	C₄²	C₂×D₄×C₁₃	1	2	yes	—
460	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₁₃	#60618	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	4	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	4	no	—
469	C₂³	C₁₃×#124	1	4	yes	—
470	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	Q₈	—	2	8	no	—
474	Q₈	—	4	8	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	8	no	—
477	D₄	—	2	8	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	C₁₃×#124	1	4	yes	—
496	C₂×C₄	C₁₃×#124	1	4	yes	—
497	C₂×C₄	C₁₃×#124	1	4	yes	—
498	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
506	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
507	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
508	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
509	C₈	—	2	8	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	8	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	8	8	no	—
517	C₂²	C₂×C₁₃×#124	1	2	yes	—
518	C₂²	C₂×C₁₃×#124	1	2	yes	—
519	C₂²	C₂×C₁₃×#124	1	2	yes	—
520	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	8	no	—
525	C₄	—	4	4	no	—
526	C₄	C₂×C₁₃×#124	1	2	yes	—
527	C₄	C₂×C₁₃×#124	1	2	yes	—
528	C₄	C₂×C₁₃×#124	1	2	yes	—
529	C₄	C₁₃×#575	1	4	yes	—
530	C₄	C₂²×C₁₃×#41	1	2	yes	—
531	C₂	—	2	2	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	2	no	—
534	C₂	—	8	4	no	—
535	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
536	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3142	C₂	semidirect
4. C₁₃×#3141	C₂	semidirect
5. C₁₃×#3140	C₂	semidirect
6. C₁₃×#3139	C₂	semidirect
7. C₁₃×#3138	C₂	semidirect
8. C₁₃×#3135	C₂	semidirect
9. C₁₃×#3131	C₂	semidirect
10. C₁₃×#2896	C₂	semidirect
11. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
18. C₁₃×#533	C₂²	semidirect
19. C₁₃×#533	C₂²	semidirect
27. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#125	C₂²	semidirect
37. C₁₃×#491	C₂²	semidirect
38. C₁₃×#490	C₂²	semidirect
39. C₁₃×#489	C₂²	semidirect
40. C₁₃×#488	C₂²	semidirect
41. C₁₃×#487	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
45. C₁₃×#417	C₂²	semidirect
46. C₁₃×#416	C₂²	semidirect
49. C₄×C₁₃×M₁₆	C₂²	semidirect
50. C₄×C₁₃×M₁₆	C₂²	semidirect
51. C₂×C₁₃×#97	C₂²	semidirect
52. C₂×C₄×C₈×C₁₃	C₂²	semidirect
128. #60618	C₁₃	direct (N × H)
197. C₂×#533	C₂×C₁₃	semidirect
199. #3142	C₂×C₁₃	semidirect
200. #3141	C₂×C₁₃	semidirect
201. #3140	C₂×C₁₃	semidirect
202. #3139	C₂×C₁₃	semidirect
203. #3138	C₂×C₁₃	semidirect
204. #3135	C₂×C₁₃	semidirect
205. #3131	C₂×C₁₃	semidirect
206. #2896	C₂×C₁₃	semidirect
207. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
259. #533	C₂²×C₁₃	semidirect
260. #533	C₂²×C₁₃	semidirect
268. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
270. C₂×#125	C₂²×C₁₃	semidirect
278. #491	C₂²×C₁₃	semidirect
279. #490	C₂²×C₁₃	semidirect
280. #489	C₂²×C₁₃	semidirect
281. #488	C₂²×C₁₃	semidirect
282. #487	C₂²×C₁₃	semidirect
283. #486	C₂²×C₁₃	semidirect
286. #417	C₂²×C₁₃	semidirect
287. #416	C₂²×C₁₃	semidirect
290. C₄×M₁₆	C₂²×C₁₃	semidirect
291. C₄×M₁₆	C₂²×C₁₃	semidirect
292. C₂×#97	C₂²×C₁₃	semidirect
293. C₂×C₄×C₈	C₂²×C₁₃	semidirect
464. C₁₃	#60618	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₁₃×#3142	2
C₁₃×#3141	2
C₁₃×#3140	2
C₁₃×#3139	2
C₁₃×#3138	2
C₁₃×#3135	2
C₁₃×#3131	2
C₁₃×#2896	2
C₂×C₄×C₁₃×M₁₆	2
#60618	13

Subgroups — C13×#60618 #15746957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60618 #15746957