Subgroups — C₁₃×#60621 #15746960

Order 3328.

2078 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	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×#3137	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3136	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#544	—	2	4	no	—
13	C₁₃×#544	C₂²	1	8	yes	complemented
14	C₁₃×#537	—	2	1	no	—
15	C₁₃×#537	—	2	1	no	—
16	C₁₃×#536	C₂²	1	4	yes	—
17	C₁₃×#535	C₂²	1	4	yes	—
18	C₁₃×#534	—	2	2	no	—
19	C₁₃×#532	C₂²	1	4	yes	—
20	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#125	—	2	1	no	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
24	C₁₃×#525	—	2	4	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#491	C₂²	1	8	yes	complemented
30	C₁₃×#490	C₂²	1	8	yes	complemented
31	C₁₃×#489	C₂²	1	16	yes	complemented
32	C₁₃×#488	C₂²	1	16	yes	complemented
33	C₁₃×#487	C₂²	1	8	yes	complemented
34	C₁₃×#486	C₂²	1	8	yes	complemented
35	C₁₃×#419	C₂²	1	4	yes	complemented
36	C₁₃×#418	C₂²	1	4	yes	complemented
37	C₁₃×#417	C₂²	1	8	yes	—
38	C₁₃×#417	C₂²	1	4	yes	complemented
39	C₁₃×#417	C₂²	1	8	yes	complemented
40	C₁₃×#417	C₂²	1	4	yes	complemented
41	C₁₃×#416	C₂²	1	8	yes	—
42	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
44	C₁₃×#405	C₂²	1	8	yes	complemented
45	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	8	no	—
49	C₂×C₁₃×#41	—	2	8	no	—
50	C₂×C₁₃×#41	C₂³	1	4	yes	—
51	C₂×C₁₃×#41	C₂³	1	4	yes	—
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×M₁₆	—	2	8	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₁₃×C₄⋊Q₈	—	2	8	no	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₁₃×#127	C₂³	1	4	yes	—
68	C₁₃×#125	—	2	8	no	—
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	C₂³	1	8	yes	—
71	C₁₃×#124	C₂³	1	8	yes	—
72	C₁₃×#123	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	—	2	16	no	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#120	—	2	8	no	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	—	2	4	no	—
83	C₁₃×#117	—	2	2	no	—
84	C₁₃×#117	D₄	1	4	yes	—
85	C₁₃×#117	C₂³	1	4	yes	—
86	C₁₃×#117	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
102	C₁₃×#103	C₂³	1	16	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	16	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₁₃×#102	C₂³	1	8	yes	—
108	C₁₃×#97	C₂³	1	8	yes	—
109	C₄×C₈×C₁₃	C₂³	1	8	yes	—
110	#60621	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×#41	—	2	8	no	—
114	C₁₃×#41	—	2	8	no	—
115	C₁₃×#41	—	2	8	no	—
116	C₁₃×#41	—	2	8	no	—
117	C₁₃×#41	—	4	8	no	—
118	C₁₃×#41	—	4	8	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	8	4	no	—
124	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	4	8	no	—
133	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	4	8	no	—
142	C₂²×C₄×C₁₃	—	8	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	#41	1	8	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₁₃×M₁₆	—	2	8	no	—
151	C₁₃×M₁₆	—	2	8	no	—
152	C₂×C₈×C₁₃	—	2	8	no	—
153	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
172	C₄²×C₁₃	—	2	4	no	—
173	C₄²×C₁₃	C₂×D₄	1	4	yes	—
174	C₄²×C₁₃	C₂⁴	1	4	yes	—
175	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3449	C₂×C₁₃	1	1	yes	characteristic
177	#3142	C₂×C₁₃	1	4	yes	complemented
178	#3141	C₂×C₁₃	1	4	yes	complemented
179	#3137	C₂×C₁₃	1	8	yes	complemented
180	#3136	C₂×C₁₃	1	8	yes	complemented
181	#2896	C₂×C₁₃	1	2	yes	complemented
182	C₂×#417	C₂×C₁₃	1	2	yes	complemented
183	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	—	8	2	no	—
189	C₂³×C₁₃	—	8	2	no	—
190	C₂³×C₁₃	#124	1	4	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
192	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₃	—	2	4	no	—
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	Q₈×C₁₃	—	8	8	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	4	8	no	—
200	D₄×C₁₃	—	4	8	no	—
201	D₄×C₁₃	—	4	4	no	—
202	D₄×C₁₃	—	8	4	no	—
203	D₄×C₁₃	—	8	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	8	no	—
215	C₂×C₄×C₁₃	—	4	8	no	—
216	C₂×C₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	#124	1	8	yes	—
218	C₂×C₄×C₁₃	#124	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
224	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
225	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₈×C₁₃	—	2	8	no	—
228	C₂²×#41	C₂²×C₁₃	1	2	yes	—
229	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
230	#544	—	2	4	no	—
231	#544	C₂²×C₁₃	1	8	yes	complemented
232	#537	—	2	1	no	—
233	#537	—	2	1	no	—
234	#536	C₂²×C₁₃	1	4	yes	—
235	#535	C₂²×C₁₃	1	4	yes	—
236	#534	—	2	2	no	—
237	#532	C₂²×C₁₃	1	4	yes	—
238	C₂×C₄⋊Q₈	—	2	1	no	—
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
240	C₂×#125	—	2	1	no	—
241	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
242	#525	—	2	4	no	—
243	C₂×C₂²⋊Q₈	—	2	2	no	—
244	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	#491	C₂²×C₁₃	1	8	yes	complemented
248	#490	C₂²×C₁₃	1	8	yes	complemented
249	#489	C₂²×C₁₃	1	16	yes	complemented
250	#488	C₂²×C₁₃	1	16	yes	complemented
251	#487	C₂²×C₁₃	1	8	yes	complemented
252	#486	C₂²×C₁₃	1	8	yes	complemented
253	#419	C₂²×C₁₃	1	4	yes	complemented
254	#418	C₂²×C₁₃	1	4	yes	complemented
255	#417	C₂²×C₁₃	1	8	yes	—
256	#417	C₂²×C₁₃	1	4	yes	complemented
257	#417	C₂²×C₁₃	1	8	yes	complemented
258	#417	C₂²×C₁₃	1	4	yes	complemented
259	#416	C₂²×C₁₃	1	8	yes	—
260	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
261	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
262	#405	C₂²×C₁₃	1	8	yes	complemented
263	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	2	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	4	4	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	8	8	no	—
273	C₂²×C₁₃	C₂×#124	1	4	yes	—
274	C₂²×C₁₃	C₂×#124	1	2	yes	—
275	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₁₃	—	2	4	no	—
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	C₂×#124	1	2	yes	—
283	C₄×C₁₃	C₂×#124	1	4	yes	—
284	C₄×C₁₃	C₂²×#41	1	2	yes	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	8	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	C₂³×C₁₃	1	4	yes	—
290	C₂×#41	C₂³×C₁₃	1	4	yes	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×M₁₆	—	2	8	no	—
299	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
300	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
301	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
302	C₄⋊Q₈	—	2	8	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
305	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
306	#127	C₂³×C₁₃	1	4	yes	—
307	#125	—	2	8	no	—
308	#125	—	2	4	no	—
309	#125	C₂³×C₁₃	1	8	yes	—
310	#124	C₂³×C₁₃	1	8	yes	—
311	#123	—	2	8	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	—	2	16	no	—
315	#121	—	2	4	no	—
316	#121	—	2	4	no	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	#120	—	2	8	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	#117	—	2	2	no	—
323	#117	D₄×C₁₃	1	4	yes	—
324	#117	C₂³×C₁₃	1	4	yes	—
325	#117	C₂³×C₁₃	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
341	#103	C₂³×C₁₃	1	16	yes	—
342	#103	C₂³×C₁₃	1	8	yes	—
343	#103	C₂³×C₁₃	1	8	yes	—
344	#102	C₂³×C₁₃	1	16	yes	—
345	#102	C₂³×C₁₃	1	8	yes	—
346	#102	C₂³×C₁₃	1	8	yes	—
347	#97	C₂³×C₁₃	1	8	yes	—
348	C₄×C₈	C₂³×C₁₃	1	8	yes	—
349	C₂×C₁₃	—	2	4	no	—
350	C₂×C₁₃	—	2	2	no	—
351	C₂×C₁₃	—	8	4	no	—
352	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
353	C₂×C₁₃	#3585	1	1	yes	characteristic
354	C₂×C₁₃	#3586	1	1	yes	characteristic
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
357	#41	—	2	8	no	—
358	#41	—	2	8	no	—
359	#41	—	2	8	no	—
360	#41	—	2	8	no	—
361	#41	—	4	8	no	—
362	#41	—	4	8	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	8	4	no	—
368	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²×C₄	C₁₃×#41	1	8	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
394	M₁₆	—	2	8	no	—
395	M₁₆	—	2	8	no	—
396	C₂×C₈	—	2	8	no	—
397	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
409	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
411	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
416	C₄²	—	2	4	no	—
417	C₄²	C₂×D₄×C₁₃	1	4	yes	—
418	C₄²	C₂⁴×C₁₃	1	4	yes	—
419	C₁₃	#60621	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	—	2	4	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	C₁₃×#124	1	4	yes	—
427	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
428	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	2	4	no	—
431	Q₈	—	4	4	no	—
432	Q₈	—	8	8	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	4	no	—
435	D₄	—	4	8	no	—
436	D₄	—	4	8	no	—
437	D₄	—	4	4	no	—
438	D₄	—	8	4	no	—
439	D₄	—	8	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	8	4	no	—
453	C₂×C₄	C₁₃×#124	1	8	yes	—
454	C₂×C₄	C₁₃×#124	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
456	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
457	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
460	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
461	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
462	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
463	C₈	—	2	8	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	8	no	—
473	C₂²	C₂×C₁₃×#124	1	4	yes	—
474	C₂²	C₂×C₁₃×#124	1	2	yes	—
475	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
476	C₄	—	2	4	no	—
477	C₄	—	2	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	4	no	—
482	C₄	C₂×C₁₃×#124	1	2	yes	—
483	C₄	C₂×C₁₃×#124	1	4	yes	—
484	C₄	C₂²×C₁₃×#41	1	2	yes	—
485	C₂	—	2	4	no	—
486	C₂	—	2	2	no	—
487	C₂	—	8	4	no	—
488	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
489	C₂	C₁₃×#3585	1	1	yes	characteristic
490	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#544	C₂	semidirect
3. C₁₃×#3142	C₂	semidirect
4. C₁₃×#3141	C₂	semidirect
5. C₁₃×#3137	C₂	semidirect
6. C₁₃×#3136	C₂	semidirect
7. C₁₃×#2896	C₂	semidirect
8. C₂×C₁₃×#417	C₂	semidirect
9. C₁₃×#2873	C₂	semidirect
13. C₁₃×#544	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
29. C₁₃×#491	C₂²	semidirect
30. C₁₃×#490	C₂²	semidirect
31. C₁₃×#489	C₂²	semidirect
32. C₁₃×#488	C₂²	semidirect
33. C₁₃×#487	C₂²	semidirect
34. C₁₃×#486	C₂²	semidirect
35. C₁₃×#419	C₂²	semidirect
36. C₁₃×#418	C₂²	semidirect
38. C₁₃×#417	C₂²	semidirect
39. C₁₃×#417	C₂²	semidirect
40. C₁₃×#417	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₁₃×#405	C₂²	semidirect
45. C₄×C₁₃×M₁₆	C₂²	semidirect
110. #60621	C₁₃	direct (N × H)
175. C₂×#544	C₂×C₁₃	semidirect
177. #3142	C₂×C₁₃	semidirect
178. #3141	C₂×C₁₃	semidirect
179. #3137	C₂×C₁₃	semidirect
180. #3136	C₂×C₁₃	semidirect
181. #2896	C₂×C₁₃	semidirect
182. C₂×#417	C₂×C₁₃	semidirect
183. #2873	C₂×C₁₃	semidirect
231. #544	C₂²×C₁₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
241. C₂×#125	C₂²×C₁₃	semidirect
247. #491	C₂²×C₁₃	semidirect
248. #490	C₂²×C₁₃	semidirect
249. #489	C₂²×C₁₃	semidirect
250. #488	C₂²×C₁₃	semidirect
251. #487	C₂²×C₁₃	semidirect
252. #486	C₂²×C₁₃	semidirect
253. #419	C₂²×C₁₃	semidirect
254. #418	C₂²×C₁₃	semidirect
256. #417	C₂²×C₁₃	semidirect
257. #417	C₂²×C₁₃	semidirect
258. #417	C₂²×C₁₃	semidirect
260. C₂×#103	C₂²×C₁₃	semidirect
261. C₂×#102	C₂²×C₁₃	semidirect
262. #405	C₂²×C₁₃	semidirect
263. C₄×M₁₆	C₂²×C₁₃	semidirect
419. C₁₃	#60621	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×#544	2
C₁₃×#3449	2
C₁₃×#3142	2
C₁₃×#3141	2
C₁₃×#3137	2
C₁₃×#3136	2
C₁₃×#2896	2
C₂×C₁₃×#417	2
C₁₃×#2873	2
#60621	13

Subgroups — C13×#60621 #15746960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60621 #15746960