Subgroups — C₁₃×#60682 #15747021

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3177	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3176	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3175	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3174	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3173	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3135	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3054	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3050	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2943	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#135	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#542	C₂²	1	8	yes	—
20	C₁₃×#541	C₂²	1	4	yes	—
21	C₁₃×#540	C₂²	1	4	yes	—
22	C₁₃×#539	—	2	4	no	—
23	C₁₃×#538	—	2	4	no	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₁₃×#529	—	2	8	no	—
27	C₁₃×#525	C₂²	1	4	yes	—
28	C₄×C₁₃×#41	C₂²	1	4	yes	—
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₁₃×#500	C₂²	1	2	yes	complemented
31	C₁₃×#499	C₂²	1	2	yes	complemented
32	C₁₃×#499	C₂²	1	2	yes	complemented
33	C₁₃×#498	C₂²	1	2	yes	complemented
34	C₁₃×#495	C₂²	1	2	yes	complemented
35	C₁₃×#495	C₂²	1	2	yes	complemented
36	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#492	C₂²	1	2	yes	complemented
39	C₁₃×#491	C₂²	1	4	yes	complemented
40	C₁₃×#490	C₂²	1	4	yes	complemented
41	C₁₃×#489	C₂²	1	8	yes	complemented
42	C₁₃×#470	C₂²	1	4	yes	—
43	C₁₃×#469	C₂²	1	4	yes	—
44	C₁₃×#468	C₂²	1	8	yes	—
45	C₁₃×#467	C₂²	1	4	yes	—
46	C₁₃×#466	C₂²	1	4	yes	—
47	C₁₃×#465	C₂²	1	8	yes	—
48	C₁₃×#442	C₂²	1	4	yes	complemented
49	C₁₃×#441	C₂²	1	4	yes	complemented
50	C₁₃×#440	C₂²	1	8	yes	complemented
51	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
52	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
53	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
54	C₁₃×#427	C₂²	1	2	yes	—
55	C₁₃×#427	C₂²	1	2	yes	—
56	C₁₃×#416	C₂²	1	4	yes	—
57	C₁₃×#416	C₂²	1	4	yes	—
58	C₁₃×#405	C₂²	1	2	yes	—
59	C₁₃×#405	C₂²	1	2	yes	—
60	C₁₃×#405	C₂²	1	2	yes	—
61	C₁₃×#405	C₂²	1	2	yes	—
62	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#41	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#135	—	2	8	no	—
69	C₁₃×#135	—	2	8	no	—
70	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×D₈	C₂³	1	2	yes	—
75	C₂×C₁₃×D₈	C₂³	1	2	yes	—
76	C₂×C₁₃×M₁₆	—	2	4	no	—
77	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₃	—	2	4	no	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#126	—	2	8	no	—
90	C₁₃×#126	—	2	8	no	—
91	C₁₃×#125	—	2	8	no	—
92	C₁₃×#125	C₂³	1	4	yes	—
93	C₁₃×#124	—	2	8	no	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×#123	—	2	4	no	—
96	C₁₃×#123	—	2	8	no	—
97	C₁₃×#123	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₁₃×#120	—	2	4	no	—
105	C₄×Q₈×C₁₃	—	2	4	no	—
106	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₄×D₄×C₁₃	—	2	8	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	C₂³	1	8	yes	—
111	C₁₃×#117	—	2	4	no	—
112	C₁₃×#117	D₄	1	4	yes	—
113	C₁₃×#117	C₂³	1	4	yes	—
114	C₁₃×#117	C₂³	1	2	yes	—
115	C₁₃×#117	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	4	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	C₂³	1	4	yes	—
122	C₁₃×#107	C₂³	1	4	yes	—
123	C₁₃×#106	C₂³	1	4	yes	—
124	C₁₃×#106	C₂³	1	4	yes	—
125	C₁₃×#103	C₂³	1	8	yes	—
126	C₁₃×#103	C₂³	1	8	yes	—
127	C₁₃×#102	C₂³	1	8	yes	—
128	C₁₃×#102	C₂³	1	8	yes	—
129	C₁₃×#97	C₂³	1	2	yes	—
130	C₁₃×#97	C₂³	1	2	yes	—
131	C₁₃×#97	C₂³	1	2	yes	—
132	C₁₃×#97	C₂³	1	2	yes	—
133	C₄×C₈×C₁₃	C₂³	1	2	yes	—
134	C₄×C₈×C₁₃	C₂³	1	2	yes	—
135	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	#60682	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×#41	—	2	8	no	—
142	C₁₃×#41	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	4	no	—
160	C₁₃×Q₁₆	—	2	4	no	—
161	C₁₃×SD₁₆	—	2	8	no	—
162	C₁₃×SD₁₆	—	2	8	no	—
163	C₁₃×D₈	—	2	4	no	—
164	C₁₃×D₈	—	2	4	no	—
165	C₁₃×M₁₆	—	2	4	no	—
166	C₁₃×M₁₆	—	2	4	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₂×C₈×C₁₃	#41	1	4	yes	—
172	C₂×C₈×C₁₃	#41	1	4	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
193	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃	—	2	8	no	—
195	C₄²×C₁₃	—	2	4	no	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₄²×C₁₃	C₂×D₄	1	2	yes	—
198	C₄²×C₁₃	C₂⁴	1	2	yes	—
199	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
201	#3455	C₂×C₁₃	1	2	yes	complemented
202	#3177	C₂×C₁₃	1	2	yes	complemented
203	#3176	C₂×C₁₃	1	2	yes	complemented
204	#3175	C₂×C₁₃	1	4	yes	complemented
205	#3174	C₂×C₁₃	1	4	yes	complemented
206	#3173	C₂×C₁₃	1	4	yes	complemented
207	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3135	C₂×C₁₃	1	2	yes	complemented
210	#3054	C₂×C₁₃	1	2	yes	complemented
211	#3050	C₂×C₁₃	1	2	yes	complemented
212	#2943	C₂×C₁₃	1	2	yes	complemented
213	C₄×#135	C₂×C₁₃	1	2	yes	complemented
214	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	8	4	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	8	4	no	—
227	D₄×C₁₃	—	8	8	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	8	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	8	8	no	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	C₂×#41	1	2	yes	—
249	C₈×C₁₃	C₂×#41	1	2	yes	—
250	C₈×C₁₃	C₂×#41	1	2	yes	—
251	C₈×C₁₃	C₂×#41	1	2	yes	—
252	C₂×#135	C₂²×C₁₃	1	2	yes	—
253	C₂×#135	C₂²×C₁₃	1	2	yes	—
254	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
256	#542	C₂²×C₁₃	1	8	yes	—
257	#541	C₂²×C₁₃	1	4	yes	—
258	#540	C₂²×C₁₃	1	4	yes	—
259	#539	—	2	4	no	—
260	#538	—	2	4	no	—
261	#533	C₂²×C₁₃	1	2	yes	—
262	#532	C₂²×C₁₃	1	2	yes	—
263	#529	—	2	8	no	—
264	#525	C₂²×C₁₃	1	4	yes	—
265	C₄×#41	C₂²×C₁₃	1	4	yes	—
266	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
267	#500	C₂²×C₁₃	1	2	yes	complemented
268	#499	C₂²×C₁₃	1	2	yes	complemented
269	#499	C₂²×C₁₃	1	2	yes	complemented
270	#498	C₂²×C₁₃	1	2	yes	complemented
271	#495	C₂²×C₁₃	1	2	yes	complemented
272	#495	C₂²×C₁₃	1	2	yes	complemented
273	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
274	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	#492	C₂²×C₁₃	1	2	yes	complemented
276	#491	C₂²×C₁₃	1	4	yes	complemented
277	#490	C₂²×C₁₃	1	4	yes	complemented
278	#489	C₂²×C₁₃	1	8	yes	complemented
279	#470	C₂²×C₁₃	1	4	yes	—
280	#469	C₂²×C₁₃	1	4	yes	—
281	#468	C₂²×C₁₃	1	8	yes	—
282	#467	C₂²×C₁₃	1	4	yes	—
283	#466	C₂²×C₁₃	1	4	yes	—
284	#465	C₂²×C₁₃	1	8	yes	—
285	#442	C₂²×C₁₃	1	4	yes	complemented
286	#441	C₂²×C₁₃	1	4	yes	complemented
287	#440	C₂²×C₁₃	1	8	yes	complemented
288	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
289	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
290	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
291	#427	C₂²×C₁₃	1	2	yes	—
292	#427	C₂²×C₁₃	1	2	yes	—
293	#416	C₂²×C₁₃	1	4	yes	—
294	#416	C₂²×C₁₃	1	4	yes	—
295	#405	C₂²×C₁₃	1	2	yes	—
296	#405	C₂²×C₁₃	1	2	yes	—
297	#405	C₂²×C₁₃	1	2	yes	—
298	#405	C₂²×C₁₃	1	2	yes	—
299	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	8	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	#532	1	2	yes	—
310	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	4	8	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	#532	1	2	yes	—
318	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
319	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
320	C₂×#41	C₂³×C₁₃	1	4	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	#135	—	2	8	no	—
323	#135	—	2	8	no	—
324	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
325	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
327	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
328	C₂×D₈	C₂³×C₁₃	1	2	yes	—
329	C₂×D₈	C₂³×C₁₃	1	2	yes	—
330	C₂×M₁₆	—	2	4	no	—
331	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
332	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
333	C₂²×C₈	—	2	4	no	—
334	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
341	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
342	#127	C₂³×C₁₃	1	2	yes	—
343	#126	—	2	8	no	—
344	#126	—	2	8	no	—
345	#125	—	2	8	no	—
346	#125	C₂³×C₁₃	1	4	yes	—
347	#124	—	2	8	no	—
348	#124	C₂³×C₁₃	1	4	yes	—
349	#123	—	2	4	no	—
350	#123	—	2	8	no	—
351	#123	—	2	8	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	C₂²⋊Q₈	—	2	8	no	—
354	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
355	#121	—	2	4	no	—
356	#121	—	2	8	no	—
357	#121	C₂³×C₁₃	1	8	yes	—
358	#120	—	2	4	no	—
359	C₄×Q₈	—	2	4	no	—
360	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
361	C₄×D₄	—	2	8	no	—
362	C₄×D₄	—	2	8	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	C₂³×C₁₃	1	8	yes	—
365	#117	—	2	4	no	—
366	#117	D₄×C₁₃	1	4	yes	—
367	#117	C₂³×C₁₃	1	4	yes	—
368	#117	C₂³×C₁₃	1	2	yes	—
369	#117	C₂³×C₁₃	1	2	yes	—
370	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
371	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
372	C₂×C₄²	—	2	4	no	—
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#107	C₂³×C₁₃	1	4	yes	—
376	#107	C₂³×C₁₃	1	4	yes	—
377	#106	C₂³×C₁₃	1	4	yes	—
378	#106	C₂³×C₁₃	1	4	yes	—
379	#103	C₂³×C₁₃	1	8	yes	—
380	#103	C₂³×C₁₃	1	8	yes	—
381	#102	C₂³×C₁₃	1	8	yes	—
382	#102	C₂³×C₁₃	1	8	yes	—
383	#97	C₂³×C₁₃	1	2	yes	—
384	#97	C₂³×C₁₃	1	2	yes	—
385	#97	C₂³×C₁₃	1	2	yes	—
386	#97	C₂³×C₁₃	1	2	yes	—
387	C₄×C₈	C₂³×C₁₃	1	2	yes	—
388	C₄×C₈	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	2	2	no	—
394	C₂×C₁₃	—	4	2	no	—
395	C₂×C₁₃	—	8	4	no	—
396	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
397	C₂×C₁₃	#3584	1	2	yes	—
398	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
399	#41	—	2	8	no	—
400	#41	—	2	8	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	Q₁₆	—	2	4	no	—
418	Q₁₆	—	2	4	no	—
419	SD₁₆	—	2	8	no	—
420	SD₁₆	—	2	8	no	—
421	D₈	—	2	4	no	—
422	D₈	—	2	4	no	—
423	M₁₆	—	2	4	no	—
424	M₁₆	—	2	4	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	C₁₃×#41	1	4	yes	—
430	C₂×C₈	C₁₃×#41	1	4	yes	—
431	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
433	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
434	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
451	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	8	no	—
454	C₄²	C₂×D₄×C₁₃	1	2	yes	—
455	C₄²	C₂×D₄×C₁₃	1	2	yes	—
456	C₄²	C₂⁴×C₁₃	1	2	yes	—
457	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
458	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
459	C₁₃	#60682	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	8	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	8	4	no	—
472	D₄	—	8	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	8	8	no	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
489	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
490	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂×C₁₃×#41	1	2	yes	—
494	C₈	C₂×C₁₃×#41	1	2	yes	—
495	C₈	C₂×C₁₃×#41	1	2	yes	—
496	C₈	C₂×C₁₃×#41	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	4	no	—
503	C₂²	C₁₃×#532	1	2	yes	—
504	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	8	no	—
510	C₄	—	4	4	no	—
511	C₄	C₁₃×#532	1	2	yes	—
512	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
513	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	4	2	no	—
516	C₂	—	8	4	no	—
517	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
518	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₁₃×#3177	C₂	semidirect
3. C₁₃×#3176	C₂	semidirect
4. C₁₃×#3175	C₂	semidirect
5. C₁₃×#3174	C₂	semidirect
6. C₁₃×#3173	C₂	semidirect
7. C₁₃×#3160	C₂	semidirect
8. C₁₃×#3147	C₂	semidirect
9. C₁₃×#3135	C₂	semidirect
10. C₁₃×#3054	C₂	semidirect
11. C₁₃×#3050	C₂	semidirect
12. C₁₃×#2943	C₂	semidirect
13. C₄×C₁₃×#135	C₂	semidirect
14. C₂×C₁₃×#405	C₂	semidirect
30. C₁₃×#500	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#499	C₂²	semidirect
33. C₁₃×#498	C₂²	semidirect
34. C₁₃×#495	C₂²	semidirect
35. C₁₃×#495	C₂²	semidirect
36. C₁₃×#494	C₂²	semidirect
37. C₁₃×#493	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#491	C₂²	semidirect
40. C₁₃×#490	C₂²	semidirect
41. C₁₃×#489	C₂²	semidirect
48. C₁₃×#442	C₂²	semidirect
49. C₁₃×#441	C₂²	semidirect
50. C₁₃×#440	C₂²	semidirect
51. C₄×C₁₃×Q₁₆	C₂²	semidirect
52. C₄×C₁₃×SD₁₆	C₂²	semidirect
53. C₄×C₁₃×D₈	C₂²	semidirect
139. #60682	C₁₃	direct (N × H)
201. #3455	C₂×C₁₃	semidirect
202. #3177	C₂×C₁₃	semidirect
203. #3176	C₂×C₁₃	semidirect
204. #3175	C₂×C₁₃	semidirect
205. #3174	C₂×C₁₃	semidirect
206. #3173	C₂×C₁₃	semidirect
207. #3160	C₂×C₁₃	semidirect
208. #3147	C₂×C₁₃	semidirect
209. #3135	C₂×C₁₃	semidirect
210. #3054	C₂×C₁₃	semidirect
211. #3050	C₂×C₁₃	semidirect
212. #2943	C₂×C₁₃	semidirect
213. C₄×#135	C₂×C₁₃	semidirect
214. C₂×#405	C₂×C₁₃	semidirect
267. #500	C₂²×C₁₃	semidirect
268. #499	C₂²×C₁₃	semidirect
269. #499	C₂²×C₁₃	semidirect
270. #498	C₂²×C₁₃	semidirect
271. #495	C₂²×C₁₃	semidirect
272. #495	C₂²×C₁₃	semidirect
273. #494	C₂²×C₁₃	semidirect
274. #493	C₂²×C₁₃	semidirect
275. #492	C₂²×C₁₃	semidirect
276. #491	C₂²×C₁₃	semidirect
277. #490	C₂²×C₁₃	semidirect
278. #489	C₂²×C₁₃	semidirect
285. #442	C₂²×C₁₃	semidirect
286. #441	C₂²×C₁₃	semidirect
287. #440	C₂²×C₁₃	semidirect
288. C₄×Q₁₆	C₂²×C₁₃	semidirect
289. C₄×SD₁₆	C₂²×C₁₃	semidirect
290. C₄×D₈	C₂²×C₁₃	semidirect
459. C₁₃	#60682	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×#3455	2
C₁₃×#3177	2
C₁₃×#3176	2
C₁₃×#3175	2
C₁₃×#3174	2
C₁₃×#3173	2
C₁₃×#3160	2
C₁₃×#3147	2
C₁₃×#3135	2
C₁₃×#3054	2
C₁₃×#3050	2
C₁₃×#2943	2
C₄×C₁₃×#135	2
C₂×C₁₃×#405	2
#60682	13

Subgroups — C13×#60682 #15747021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60682 #15747021