Subgroups — C₂×C₁₃×#1866 #15707222

Order 3328.

1398 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1866	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#131	—	2	4	no	—
11	C₂×C₁₃×#131	—	2	4	no	—
12	C₂×C₁₃×#131	—	2	2	no	—
13	C₂×C₁₃×#131	C₂²	1	4	yes	—
14	C₂²×C₁₃×M₁₆	—	2	1	no	—
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	—	2	1	no	—
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#108	—	2	4	no	—
23	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
24	C₁₃×#424	—	2	2	no	—
25	C₁₃×#424	C₂²	1	4	yes	complemented
26	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
28	C₂×C₁₃×#104	—	2	4	no	—
29	C₂×C₁₃×#104	C₂²	1	4	yes	—
30	C₁₃×#416	C₄	1	4	yes	complemented
31	C₁₃×#416	C₂²	1	4	yes	—
32	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
36	C₁₃×#339	C₂²	1	4	yes	complemented
37	C₁₃×#336	C₂²	1	4	yes	complemented
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×#41	D₄	1	4	yes	—
44	C₂×C₁₃×#41	Q₈	1	4	yes	—
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#131	—	2	16	no	—
53	C₁₃×#131	—	2	8	no	—
54	C₁₃×#131	—	2	8	no	—
55	C₂×C₁₃×M₁₆	—	2	8	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	4	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃	—	2	8	no	—
66	C₂²×C₈×C₁₃	—	2	2	no	—
67	C₂²×C₈×C₁₃	—	2	2	no	—
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	4	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₁₃	D₄	1	2	yes	—
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
81	C₁₃×#117	—	2	1	no	—
82	C₁₃×#117	—	2	1	no	—
83	C₁₃×#117	C₂×C₄	1	2	yes	—
84	C₁₃×#117	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	2	no	—
90	C₂×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#108	—	2	8	no	—
94	C₁₃×C₄⋊C₈	—	2	4	no	—
95	C₁₃×C₄⋊C₈	—	2	4	no	—
96	C₁₃×#104	—	2	8	no	—
97	C₁₃×#103	C₂×C₄	1	4	yes	complemented
98	C₁₃×#103	C₂×C₄	1	4	yes	complemented
99	C₁₃×#102	C₂×C₄	1	4	yes	complemented
100	C₁₃×#102	C₂×C₄	1	4	yes	complemented
101	C₂×#1866	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	#41	1	1	yes	characteristic
104	C₁₃×#41	—	2	4	no	—
105	C₁₃×#41	—	2	4	no	—
106	C₁₃×#41	—	2	4	no	—
107	C₁₃×#41	—	2	4	no	—
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	C₄⋊C₄	1	8	yes	—
112	C₁₃×#41	C₂×D₄	1	4	yes	—
113	C₁₃×#41	C₂×Q₈	1	4	yes	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
117	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
125	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	#41	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×M₁₆	—	2	16	no	—
148	C₁₃×M₁₆	—	2	4	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	2	no	—
152	C₁₃×M₁₆	—	4	2	no	—
153	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
154	C₂×C₈×C₁₃	—	2	16	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	4	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	4	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	4	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	4	2	no	—
169	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	4	2	no	—
184	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic
185	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
188	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
189	#1866	C₂×C₁₃	1	8	yes	direct product factor
190	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₂³×C₁₃	#123	1	2	yes	—
202	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	2	no	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	2	4	no	—
208	D₄×C₁₃	—	2	8	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	4	no	—
211	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	#120	1	2	yes	—
232	C₂×C₄×C₁₃	#120	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
234	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
236	C₂×C₄×C₁₃	#123	1	2	yes	—
237	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	2	2	no	—
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	—	2	4	no	—
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	—	4	2	no	—
249	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#131	—	2	4	no	—
251	C₂×#131	—	2	4	no	—
252	C₂×#131	—	2	2	no	—
253	C₂×#131	C₂²×C₁₃	1	4	yes	—
254	C₂²×M₁₆	—	2	1	no	—
255	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
257	C₂³×C₈	—	2	1	no	—
258	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#108	—	2	4	no	—
263	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
264	#424	—	2	2	no	—
265	#424	C₂²×C₁₃	1	4	yes	complemented
266	C₂×C₄⋊C₈	—	2	1	no	—
267	C₂×C₄⋊C₈	—	2	1	no	—
268	C₂×#104	—	2	4	no	—
269	C₂×#104	C₂²×C₁₃	1	4	yes	—
270	#416	C₄×C₁₃	1	4	yes	complemented
271	#416	C₂²×C₁₃	1	4	yes	—
272	C₂×#103	C₄×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#103	C₄×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#102	C₄×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#102	C₄×C₁₃	1	1	yes	characteristic, complemented
276	#339	C₂²×C₁₃	1	4	yes	complemented
277	#336	C₂²×C₁₃	1	4	yes	complemented
278	C₂²×C₁₃	—	2	4	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	4	8	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	#385	1	2	yes	—
289	C₂²×C₁₃	#385	1	2	yes	—
290	C₂²×C₁₃	#443	1	2	yes	—
291	C₂²×C₁₃	#444	1	2	yes	—
292	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
294	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
295	C₄×C₁₃	—	2	4	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	2	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	#385	1	2	yes	—
300	C₄×C₁₃	#385	1	2	yes	—
301	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
302	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
304	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
310	C₂×#41	D₄×C₁₃	1	4	yes	—
311	C₂×#41	Q₈×C₁₃	1	4	yes	—
312	C₂×#41	C₂³×C₁₃	1	2	yes	—
313	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	#131	—	2	16	no	—
320	#131	—	2	8	no	—
321	#131	—	2	8	no	—
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	4	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	2	2	no	—
329	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
331	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	—	2	8	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
343	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₈	D₄×C₁₃	1	2	yes	—
346	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
347	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	C₂×C₄×C₁₃	1	2	yes	—
351	#117	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
360	#108	—	2	8	no	—
361	C₄⋊C₈	—	2	4	no	—
362	C₄⋊C₈	—	2	4	no	—
363	#104	—	2	8	no	—
364	#103	C₂×C₄×C₁₃	1	4	yes	complemented
365	#103	C₂×C₄×C₁₃	1	4	yes	complemented
366	#102	C₂×C₄×C₁₃	1	4	yes	complemented
367	#102	C₂×C₄×C₁₃	1	4	yes	complemented
368	C₂×C₁₃	—	2	1	no	—
369	C₂×C₁₃	—	2	1	no	—
370	C₂×C₁₃	—	2	2	no	—
371	C₂×C₁₃	—	4	4	no	—
372	C₂×C₁₃	#1866	1	4	yes	direct product factor
373	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
375	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
376	C₂⁴	—	2	1	no	—
377	C₂⁴	C₁₃×#41	1	1	yes	characteristic
378	#41	—	2	4	no	—
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₁₃×C₄⋊C₄	1	8	yes	—
386	#41	C₂×D₄×C₁₃	1	4	yes	—
387	#41	C₂×Q₈×C₁₃	1	4	yes	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
391	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
399	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
418	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
419	C₂²×C₄	C₁₃×#41	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
421	M₁₆	—	2	16	no	—
422	M₁₆	—	2	4	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	2	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
428	C₂×C₈	—	2	16	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	4	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	4	2	no	—
443	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
444	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
445	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
446	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	4	2	no	—
458	C₁₃	C₂×#1866	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
466	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
467	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
468	C₂³	C₁₃×#123	1	2	yes	—
469	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
473	D₄	—	2	8	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	2	no	—
478	D₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
493	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
494	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
497	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₁₃×#120	1	2	yes	—
499	C₂×C₄	C₁₃×#120	1	2	yes	—
500	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
501	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
502	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
503	C₂×C₄	C₁₃×#123	1	2	yes	—
504	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
509	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	4	no	—
514	C₈	—	2	2	no	—
515	C₈	—	4	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	8	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	C₁₃×#385	1	2	yes	—
527	C₂²	C₁₃×#385	1	2	yes	—
528	C₂²	C₁₃×#443	1	2	yes	—
529	C₂²	C₁₃×#444	1	2	yes	—
530	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
531	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
532	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₁₃×#385	1	2	yes	—
538	C₄	C₁₃×#385	1	2	yes	—
539	C₄	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
540	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
541	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
542	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂	—	2	1	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	C₁₃×#1866	1	4	yes	direct product factor
548	C₂	C₂×C₁₃×#385	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#443	1	1	yes	characteristic
550	C₂	C₂×C₁₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#108	C₂	semidirect
3. C₂×C₁₃×#424	C₂	semidirect
6. C₁₃×#1866	C₂	direct (N × H)
7. C₂×C₁₃×#339	C₂	semidirect
8. C₂×C₁₃×#336	C₂	semidirect
23. C₂×C₁₃×#108	C₂²	semidirect
25. C₁₃×#424	C₂²	semidirect
30. C₁₃×#416	C₄	semidirect
32. C₂×C₁₃×#103	C₄	semidirect
33. C₂×C₁₃×#103	C₄	semidirect
34. C₂×C₁₃×#102	C₄	semidirect
35. C₂×C₁₃×#102	C₄	semidirect
36. C₁₃×#339	C₂²	semidirect
37. C₁₃×#336	C₂²	semidirect
97. C₁₃×#103	C₂×C₄	semidirect
98. C₁₃×#103	C₂×C₄	semidirect
99. C₁₃×#102	C₂×C₄	semidirect
100. C₁₃×#102	C₂×C₄	semidirect
101. C₂×#1866	C₁₃	direct (N × H)
185. C₂²×#108	C₂×C₁₃	semidirect
186. C₂×#424	C₂×C₁₃	semidirect
189. #1866	C₂×C₁₃	direct (N × H)
190. C₂×#339	C₂×C₁₃	semidirect
191. C₂×#336	C₂×C₁₃	semidirect
263. C₂×#108	C₂²×C₁₃	semidirect
265. #424	C₂²×C₁₃	semidirect
270. #416	C₄×C₁₃	semidirect
272. C₂×#103	C₄×C₁₃	semidirect
273. C₂×#103	C₄×C₁₃	semidirect
274. C₂×#102	C₄×C₁₃	semidirect
275. C₂×#102	C₄×C₁₃	semidirect
276. #339	C₂²×C₁₃	semidirect
277. #336	C₂²×C₁₃	semidirect
364. #103	C₂×C₄×C₁₃	semidirect
365. #103	C₂×C₄×C₁₃	semidirect
366. #102	C₂×C₄×C₁₃	semidirect
367. #102	C₂×C₄×C₁₃	semidirect
372. C₂×C₁₃	#1866	direct (N × H)
458. C₁₃	C₂×#1866	direct (N × H)
547. C₂	C₁₃×#1866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#131	2
C₂²×C₁₃×#108	2
C₂×C₁₃×#424	2
C₂²×C₁₃×#104	2
C₂×C₁₃×#416	2
C₁₃×#1866	2
C₂×C₁₃×#339	2
C₂×C₁₃×#336	2
C₂×#1866	13

Subgroups — C2×C13×#1866 #15707222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1866 #15707222