Subgroups — C₁₃×#60964 #15747303

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3256	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3232	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3192	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#3183	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3117	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3114	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	—	2	2	no	—
13	C₁₃×#529	—	2	2	no	—
14	C₁₃×#529	—	2	2	no	—
15	C₁₃×#529	—	2	2	no	—
16	C₁₃×#529	C₂²	1	4	yes	—
17	C₁₃×#529	C₂²	1	4	yes	—
18	C₁₃×#529	C₂²	1	4	yes	complemented
19	C₁₃×#529	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#126	—	2	2	no	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₄×D₄×C₁₃	—	2	2	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#117	—	2	2	no	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	4	yes	complemented
32	C₁₃×#495	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#484	C₂²	1	4	yes	complemented
35	C₁₃×#483	C₂²	1	4	yes	complemented
36	C₁₃×#481	C₂²	1	4	yes	—
37	C₁₃×#480	C₂²	1	4	yes	—
38	C₁₃×#479	C₂²	1	8	yes	complemented
39	C₁₃×#478	C₂²	1	8	yes	complemented
40	C₁₃×#470	C₂²	1	4	yes	complemented
41	C₁₃×#469	C₂²	1	4	yes	—
42	C₁₃×#468	C₂²	1	8	yes	complemented
43	C₁₃×#464	C₂²	1	8	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#451	C₂²	1	4	yes	complemented
46	C₁₃×#450	C₂²	1	4	yes	complemented
47	C₁₃×#448	C₂²	1	4	yes	—
48	C₁₃×#447	C₂²	1	4	yes	—
49	C₁₃×#442	C₂²	1	4	yes	complemented
50	C₁₃×#441	C₂²	1	4	yes	complemented
51	C₁₃×#440	C₂²	1	8	yes	complemented
52	C₁₃×#432	C₂²	1	4	yes	complemented
53	C₁₃×#431	C₂²	1	4	yes	complemented
54	C₁₃×#423	C₂²	1	2	yes	complemented
55	C₁₃×#407	C₂²	1	1	yes	characteristic
56	C₁₃×#407	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	—	2	2	no	—
62	C₂³×C₄×C₁₃	D₄	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×D₈	C₂³	1	4	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₁₃×#126	—	2	4	no	—
70	C₁₃×#126	—	2	4	no	—
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	C₂³	1	4	yes	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	C₂³	1	4	yes	—
80	C₁₃×#124	C₂³	1	4	yes	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×#123	—	2	4	no	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×#123	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	C₂³	1	4	yes	—
92	C₁₃×#121	C₂³	1	4	yes	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
97	C₄×D₄×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	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	C₂³	1	4	yes	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₁₃×#117	—	2	4	no	—
106	C₁₃×#117	—	2	4	no	—
107	C₁₃×#117	—	2	4	no	—
108	C₁₃×#117	—	2	4	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₄²×C₁₃	—	2	2	no	—
121	C₂×C₄²×C₁₃	D₄	1	2	yes	—
122	C₂×C₄²×C₁₃	D₄	1	2	yes	—
123	C₂×C₄²×C₁₃	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₁₃×#107	C₂³	1	8	yes	—
129	C₁₃×#106	C₂³	1	4	yes	—
130	C₁₃×#106	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
132	C₁₃×#103	C₂³	1	8	yes	—
133	C₁₃×#103	C₂³	1	8	yes	—
134	C₁₃×#102	C₂³	1	8	yes	—
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
138	C₁₃×#97	C₂³	1	4	yes	—
139	C₄×C₈×C₁₃	C₂³	1	4	yes	—
140	#60964	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	2	no	—
142	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	4	4	no	—
145	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	—	4	8	no	—
151	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	—	4	8	no	—
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	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×Q₁₆	—	4	4	no	—
171	C₁₃×SD₁₆	—	4	8	no	—
172	C₁₃×D₈	—	4	4	no	—
173	C₁₃×M₁₆	—	4	2	no	—
174	C₁₃×M₁₆	—	4	2	no	—
175	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
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	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	4	no	—
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	2	yes	—
203	C₄²×C₁₃	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃	C₂×D₄	1	2	yes	—
205	C₄²×C₁₃	C₂×D₄	1	2	yes	—
206	C₄²×C₁₃	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	2	yes	—
211	C₂×#529	C₂×C₁₃	1	2	yes	complemented
212	#3256	C₂×C₁₃	1	4	yes	complemented
213	#3232	C₂×C₁₃	1	4	yes	complemented
214	#3211	C₂×C₁₃	1	4	yes	complemented
215	#3195	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3193	C₂×C₁₃	1	2	yes	complemented
217	#3192	C₂×C₁₃	1	1	yes	characteristic
218	#3183	C₂×C₁₃	1	4	yes	complemented
219	#3117	C₂×C₁₃	1	4	yes	complemented
220	#3114	C₂×C₁₃	1	4	yes	complemented
221	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	—	4	4	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
230	Q₈×C₁₃	—	2	8	no	—
231	Q₈×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	2	8	no	—
233	D₄×C₁₃	—	4	4	no	—
234	D₄×C₁₃	—	4	8	no	—
235	D₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	—	4	8	no	—
251	C₂×C₄×C₁₃	—	4	4	no	—
252	C₂×C₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	4	4	no	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
261	C₈×C₁₃	—	2	4	no	—
262	C₈×C₁₃	—	2	4	no	—
263	#529	—	2	2	no	—
264	#529	—	2	2	no	—
265	#529	—	2	2	no	—
266	#529	—	2	2	no	—
267	#529	C₂²×C₁₃	1	4	yes	—
268	#529	C₂²×C₁₃	1	4	yes	—
269	#529	C₂²×C₁₃	1	4	yes	complemented
270	#529	C₂²×C₁₃	1	4	yes	complemented
271	C₂×#126	—	2	2	no	—
272	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
273	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
274	C₂×#123	—	2	2	no	—
275	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
276	C₂×#121	C₂²×C₁₃	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
278	C₂×C₄×D₄	—	2	2	no	—
279	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
280	C₂×#117	—	2	2	no	—
281	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
282	#499	C₂²×C₁₃	1	4	yes	complemented
283	#495	C₂²×C₁₃	1	4	yes	complemented
284	#488	C₂²×C₁₃	1	8	yes	complemented
285	#484	C₂²×C₁₃	1	4	yes	complemented
286	#483	C₂²×C₁₃	1	4	yes	complemented
287	#481	C₂²×C₁₃	1	4	yes	—
288	#480	C₂²×C₁₃	1	4	yes	—
289	#479	C₂²×C₁₃	1	8	yes	complemented
290	#478	C₂²×C₁₃	1	8	yes	complemented
291	#470	C₂²×C₁₃	1	4	yes	complemented
292	#469	C₂²×C₁₃	1	4	yes	—
293	#468	C₂²×C₁₃	1	8	yes	complemented
294	#464	C₂²×C₁₃	1	8	yes	complemented
295	#463	C₂²×C₁₃	1	8	yes	complemented
296	#451	C₂²×C₁₃	1	4	yes	complemented
297	#450	C₂²×C₁₃	1	4	yes	complemented
298	#448	C₂²×C₁₃	1	4	yes	—
299	#447	C₂²×C₁₃	1	4	yes	—
300	#442	C₂²×C₁₃	1	4	yes	complemented
301	#441	C₂²×C₁₃	1	4	yes	complemented
302	#440	C₂²×C₁₃	1	8	yes	complemented
303	#432	C₂²×C₁₃	1	4	yes	complemented
304	#431	C₂²×C₁₃	1	4	yes	complemented
305	#423	C₂²×C₁₃	1	2	yes	complemented
306	#407	C₂²×C₁₃	1	1	yes	characteristic
307	#407	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	8	8	no	—
318	C₂²×C₁₃	#575	1	4	yes	—
319	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	—	4	4	no	—
328	C₄×C₁₃	—	4	4	no	—
329	C₄×C₁₃	#585	1	2	yes	—
330	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	D₄×C₁₃	1	2	yes	—
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
337	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
338	C₂×D₈	C₂³×C₁₃	1	4	yes	—
339	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
340	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
341	#126	—	2	4	no	—
342	#126	—	2	4	no	—
343	#126	—	2	4	no	—
344	#126	—	2	4	no	—
345	#125	—	2	2	no	—
346	#125	—	2	2	no	—
347	#125	C₂³×C₁₃	1	4	yes	—
348	#125	C₂³×C₁₃	1	4	yes	—
349	#124	—	2	2	no	—
350	#124	—	2	2	no	—
351	#124	C₂³×C₁₃	1	4	yes	—
352	#124	C₂³×C₁₃	1	4	yes	—
353	#123	—	2	4	no	—
354	#123	—	2	4	no	—
355	#123	—	2	4	no	—
356	#123	—	2	4	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
360	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	C₂³×C₁₃	1	4	yes	—
364	#121	C₂³×C₁₃	1	4	yes	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
368	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	C₂³×C₁₃	1	4	yes	—
376	C₄×D₄	C₂³×C₁₃	1	4	yes	—
377	#117	—	2	4	no	—
378	#117	—	2	4	no	—
379	#117	—	2	4	no	—
380	#117	—	2	4	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₄²	—	2	2	no	—
393	C₂×C₄²	D₄×C₁₃	1	2	yes	—
394	C₂×C₄²	D₄×C₁₃	1	2	yes	—
395	C₂×C₄²	D₄×C₁₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#107	C₂³×C₁₃	1	8	yes	—
401	#106	C₂³×C₁₃	1	4	yes	—
402	#106	C₂³×C₁₃	1	4	yes	—
403	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
404	#103	C₂³×C₁₃	1	8	yes	—
405	#103	C₂³×C₁₃	1	8	yes	—
406	#102	C₂³×C₁₃	1	8	yes	—
407	#102	C₂³×C₁₃	1	8	yes	—
408	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
409	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
410	#97	C₂³×C₁₃	1	4	yes	—
411	C₄×C₈	C₂³×C₁₃	1	4	yes	—
412	C₂×C₁₃	—	2	4	no	—
413	C₂×C₁₃	—	4	1	no	—
414	C₂×C₁₃	—	8	4	no	—
415	C₂×C₁₃	#3449	1	1	yes	characteristic
416	C₂×C₁₃	C₂×#575	1	2	yes	—
417	C₂⁴	—	2	2	no	—
418	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	8	no	—
427	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	Q₁₆	—	4	4	no	—
447	SD₁₆	—	4	8	no	—
448	D₈	—	4	4	no	—
449	M₁₆	—	4	2	no	—
450	M₁₆	—	4	2	no	—
451	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
452	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	4	no	—
477	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₁₃	1	2	yes	—
479	C₄²	C₂×D₄×C₁₃	1	2	yes	—
480	C₄²	C₂×D₄×C₁₃	1	2	yes	—
481	C₄²	C₂×D₄×C₁₃	1	2	yes	—
482	C₄²	C₂×D₄×C₁₃	1	2	yes	—
483	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
485	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₄²	C₂⁴×C₁₃	1	2	yes	—
487	C₁₃	#60964	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	4	no	—
494	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
495	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
496	Q₈	—	2	8	no	—
497	Q₈	—	4	4	no	—
498	D₄	—	2	8	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	8	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
524	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
526	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
527	C₈	—	2	4	no	—
528	C₈	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	8	8	no	—
538	C₂²	C₁₃×#575	1	4	yes	—
539	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	4	no	—
549	C₄	C₁₃×#585	1	2	yes	—
550	C₂	—	2	4	no	—
551	C₂	—	4	1	no	—
552	C₂	—	8	4	no	—
553	C₂	C₁₃×#3449	1	1	yes	characteristic
554	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3192	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#3256	C₂	semidirect
3. C₁₃×#3232	C₂	semidirect
4. C₁₃×#3211	C₂	semidirect
5. C₁₃×#3195	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
8. C₁₃×#3183	C₂	semidirect
9. C₁₃×#3117	C₂	semidirect
10. C₁₃×#3114	C₂	semidirect
11. C₁₃×#2920	C₂	semidirect
18. C₁₃×#529	C₂²	semidirect
19. C₁₃×#529	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#484	C₂²	semidirect
35. C₁₃×#483	C₂²	semidirect
38. C₁₃×#479	C₂²	semidirect
39. C₁₃×#478	C₂²	semidirect
40. C₁₃×#470	C₂²	semidirect
42. C₁₃×#468	C₂²	semidirect
43. C₁₃×#464	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#451	C₂²	semidirect
46. C₁₃×#450	C₂²	semidirect
49. C₁₃×#442	C₂²	semidirect
50. C₁₃×#441	C₂²	semidirect
51. C₁₃×#440	C₂²	semidirect
52. C₁₃×#432	C₂²	semidirect
53. C₁₃×#431	C₂²	semidirect
54. C₁₃×#423	C₂²	semidirect
57. C₄×C₁₃×M₁₆	C₂²	semidirect
140. #60964	C₁₃	direct (N × H)
211. C₂×#529	C₂×C₁₃	semidirect
212. #3256	C₂×C₁₃	semidirect
213. #3232	C₂×C₁₃	semidirect
214. #3211	C₂×C₁₃	semidirect
215. #3195	C₂×C₁₃	semidirect
216. #3193	C₂×C₁₃	semidirect
218. #3183	C₂×C₁₃	semidirect
219. #3117	C₂×C₁₃	semidirect
220. #3114	C₂×C₁₃	semidirect
221. #2920	C₂×C₁₃	semidirect
269. #529	C₂²×C₁₃	semidirect
270. #529	C₂²×C₁₃	semidirect
272. C₂×#125	C₂²×C₁₃	semidirect
273. C₂×#124	C₂²×C₁₃	semidirect
277. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
279. C₂×C₄×D₄	C₂²×C₁₃	semidirect
282. #499	C₂²×C₁₃	semidirect
283. #495	C₂²×C₁₃	semidirect
284. #488	C₂²×C₁₃	semidirect
285. #484	C₂²×C₁₃	semidirect
286. #483	C₂²×C₁₃	semidirect
289. #479	C₂²×C₁₃	semidirect
290. #478	C₂²×C₁₃	semidirect
291. #470	C₂²×C₁₃	semidirect
293. #468	C₂²×C₁₃	semidirect
294. #464	C₂²×C₁₃	semidirect
295. #463	C₂²×C₁₃	semidirect
296. #451	C₂²×C₁₃	semidirect
297. #450	C₂²×C₁₃	semidirect
300. #442	C₂²×C₁₃	semidirect
301. #441	C₂²×C₁₃	semidirect
302. #440	C₂²×C₁₃	semidirect
303. #432	C₂²×C₁₃	semidirect
304. #431	C₂²×C₁₃	semidirect
305. #423	C₂²×C₁₃	semidirect
308. C₄×M₁₆	C₂²×C₁₃	semidirect
487. C₁₃	#60964	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×#529	2
C₁₃×#3256	2
C₁₃×#3232	2
C₁₃×#3211	2
C₁₃×#3195	2
C₁₃×#3193	2
C₁₃×#3192	2
C₁₃×#3183	2
C₁₃×#3117	2
C₁₃×#3114	2
C₁₃×#2920	2
#60964	13

Subgroups — C13×#60964 #15747303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60964 #15747303