Subgroups — C₂×C₁₃×#3232 #15747179

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 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	1	yes	maximal, characteristic
2	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3232	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#529	—	2	4	no	—
14	C₁₃×#529	C₂²	1	8	yes	—
15	C₂×C₁₃×#126	—	2	1	no	—
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×#125	—	2	4	no	—
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	—	2	1	no	—
31	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
32	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#499	C₂²	1	16	yes	complemented
37	C₁₃×#488	C₂²	1	16	yes	complemented
38	C₁₃×#484	C₂²	1	8	yes	complemented
39	C₁₃×#483	C₂²	1	8	yes	complemented
40	C₁₃×#481	C₂²	1	8	yes	—
41	C₁₃×#480	C₂²	1	8	yes	—
42	C₁₃×#479	C₂²	1	16	yes	complemented
43	C₁₃×#478	C₂²	1	16	yes	complemented
44	C₁₃×#431	C₂²	1	8	yes	complemented
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#107	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	2	yes	—
48	C₂×C₁₃×#106	C₂²	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#102	C₂²	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₁₃×#126	—	2	8	no	—
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	—	2	4	no	—
71	C₁₃×#125	—	2	8	no	—
72	C₁₃×#125	—	2	8	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	C₂³	1	8	yes	—
75	C₁₃×#125	C₂³	1	8	yes	—
76	C₁₃×#125	C₂³	1	4	yes	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	C₂³	1	4	yes	—
79	C₁₃×#123	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	C₂³	1	4	yes	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	C₂³	1	4	yes	—
89	C₁₃×#117	—	2	8	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	D₄	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#107	C₂³	1	8	yes	—
123	C₁₃×#107	C₂³	1	8	yes	—
124	C₁₃×#106	C₂³	1	8	yes	—
125	C₁₃×#106	C₂³	1	8	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
127	C₁₃×#103	C₂³	1	8	yes	—
128	C₁₃×#103	C₂³	1	8	yes	—
129	C₁₃×#102	C₂³	1	8	yes	—
130	C₁₃×#102	C₂³	1	8	yes	—
131	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
133	C₄×C₈×C₁₃	C₂³	1	8	yes	—
134	C₂×#3232	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	4	4	no	—
144	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
172	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	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	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	C₂×D₄	1	4	yes	—
198	C₄²×C₁₃	C₂×D₄	1	2	yes	—
199	C₄²×C₁₃	C₂×D₄	1	2	yes	—
200	C₄²×C₁₃	C₂×D₄	1	4	yes	—
201	C₄²×C₁₃	C₂⁴	1	2	yes	—
202	C₄²×C₁₃	C₂⁴	1	2	yes	—
203	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
204	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3232	C₂×C₁₃	1	16	yes	direct product factor
206	C₂×#499	C₂×C₁₃	1	2	yes	complemented
207	C₂×#488	C₂×C₁₃	1	2	yes	complemented
208	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#481	C₂×C₁₃	1	1	yes	characteristic
210	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#480	C₂×C₁₃	1	1	yes	characteristic
212	C₂×#479	C₂×C₁₃	1	2	yes	complemented
213	C₂×#478	C₂×C₁₃	1	2	yes	complemented
214	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	#135	1	4	yes	—
222	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	4	no	—
225	Q₈×C₁₃	—	4	2	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	8	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	2₋¹⁺⁴	1	4	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
259	C₈×C₁₃	—	2	4	no	—
260	C₈×C₁₃	—	2	4	no	—
261	#529	—	2	4	no	—
262	#529	C₂²×C₁₃	1	8	yes	—
263	C₂×#126	—	2	1	no	—
264	C₂×#125	—	2	1	no	—
265	C₂×#125	—	2	1	no	—
266	C₂×#125	—	2	4	no	—
267	C₂×#125	C₂²×C₁₃	1	2	yes	—
268	C₂×#125	C₂²×C₁₃	1	2	yes	—
269	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
271	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#123	—	2	1	no	—
273	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#117	—	2	1	no	—
279	C₂²×C₄⋊C₄	—	2	1	no	—
280	C₂²×C₄⋊C₄	—	2	1	no	—
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
284	#499	C₂²×C₁₃	1	16	yes	complemented
285	#488	C₂²×C₁₃	1	16	yes	complemented
286	#484	C₂²×C₁₃	1	8	yes	complemented
287	#483	C₂²×C₁₃	1	8	yes	complemented
288	#481	C₂²×C₁₃	1	8	yes	—
289	#480	C₂²×C₁₃	1	8	yes	—
290	#479	C₂²×C₁₃	1	16	yes	complemented
291	#478	C₂²×C₁₃	1	16	yes	complemented
292	#431	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#107	C₂²×C₁₃	1	2	yes	—
294	C₂×#107	C₂²×C₁₃	1	2	yes	—
295	C₂×#106	C₂²×C₁₃	1	2	yes	—
296	C₂×#106	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
298	C₂×#103	C₂²×C₁₃	1	2	yes	—
299	C₂×#103	C₂²×C₁₃	1	2	yes	—
300	C₂×#102	C₂²×C₁₃	1	2	yes	—
301	C₂×#102	C₂²×C₁₃	1	2	yes	—
302	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	8	4	no	—
312	C₂²×C₁₃	#536	1	2	yes	—
313	C₂²×C₁₃	C₂×#135	1	4	yes	—
314	C₂²×C₁₃	C₂×#135	1	2	yes	—
315	C₂²×C₁₃	#575	1	2	yes	—
316	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	2	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	#536	1	2	yes	—
328	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
329	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
339	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
340	#126	—	2	8	no	—
341	#125	—	2	4	no	—
342	#125	—	2	4	no	—
343	#125	—	2	8	no	—
344	#125	—	2	8	no	—
345	#125	—	2	2	no	—
346	#125	C₂³×C₁₃	1	8	yes	—
347	#125	C₂³×C₁₃	1	8	yes	—
348	#125	C₂³×C₁₃	1	4	yes	—
349	#124	—	2	2	no	—
350	#124	C₂³×C₁₃	1	4	yes	—
351	#123	—	2	8	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
354	#121	—	2	2	no	—
355	#121	C₂³×C₁₃	1	4	yes	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
358	C₄×D₄	—	2	8	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	C₂³×C₁₃	1	4	yes	—
361	#117	—	2	8	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	8	no	—
367	C₂×C₄⋊C₄	—	2	8	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
389	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	D₄×C₁₃	1	4	yes	—
391	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
394	#107	C₂³×C₁₃	1	8	yes	—
395	#107	C₂³×C₁₃	1	8	yes	—
396	#106	C₂³×C₁₃	1	8	yes	—
397	#106	C₂³×C₁₃	1	8	yes	—
398	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
399	#103	C₂³×C₁₃	1	8	yes	—
400	#103	C₂³×C₁₃	1	8	yes	—
401	#102	C₂³×C₁₃	1	8	yes	—
402	#102	C₂³×C₁₃	1	8	yes	—
403	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
404	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
405	C₄×C₈	C₂³×C₁₃	1	8	yes	—
406	C₂×C₁₃	—	2	4	no	—
407	C₂×C₁₃	—	8	2	no	—
408	C₂×C₁₃	#3232	1	4	yes	direct product factor
409	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
410	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
411	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
412	C₂⁴	—	2	1	no	—
413	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
449	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
467	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	C₄²	—	2	4	no	—
474	C₄²	C₂×D₄×C₁₃	1	4	yes	—
475	C₄²	C₂×D₄×C₁₃	1	2	yes	—
476	C₄²	C₂×D₄×C₁₃	1	2	yes	—
477	C₄²	C₂×D₄×C₁₃	1	4	yes	—
478	C₄²	C₂⁴×C₁₃	1	2	yes	—
479	C₄²	C₂⁴×C₁₃	1	2	yes	—
480	C₁₃	C₂×#3232	1	1	yes	characteristic, direct product factor, Sylow
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	C₁₃×#135	1	4	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
489	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	Q₈	—	2	4	no	—
491	Q₈	—	4	2	no	—
492	D₄	—	2	4	no	—
493	D₄	—	4	8	no	—
494	D₄	—	4	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	C₁₃×2₋¹⁺⁴	1	4	yes	—
524	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	4	no	—
534	C₂²	C₁₃×#536	1	2	yes	—
535	C₂²	C₂×C₁₃×#135	1	4	yes	—
536	C₂²	C₂×C₁₃×#135	1	2	yes	—
537	C₂²	C₁₃×#575	1	2	yes	—
538	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	C₁₃×#536	1	2	yes	—
550	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
551	C₂	—	2	4	no	—
552	C₂	—	8	2	no	—
553	C₂	C₁₃×#3232	1	4	yes	direct product factor
554	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
555	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
556	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#125	C₂	semidirect
3. C₁₃×#3232	C₂	direct (N × H)
4. C₂×C₁₃×#499	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#484	C₂	semidirect
8. C₂×C₁₃×#483	C₂	semidirect
10. C₂×C₁₃×#479	C₂	semidirect
11. C₂×C₁₃×#478	C₂	semidirect
12. C₂×C₁₃×#431	C₂	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
36. C₁₃×#499	C₂²	semidirect
37. C₁₃×#488	C₂²	semidirect
38. C₁₃×#484	C₂²	semidirect
39. C₁₃×#483	C₂²	semidirect
42. C₁₃×#479	C₂²	semidirect
43. C₁₃×#478	C₂²	semidirect
44. C₁₃×#431	C₂²	semidirect
134. C₂×#3232	C₁₃	direct (N × H)
204. C₂²×#125	C₂×C₁₃	semidirect
205. #3232	C₂×C₁₃	direct (N × H)
206. C₂×#499	C₂×C₁₃	semidirect
207. C₂×#488	C₂×C₁₃	semidirect
208. C₂×#484	C₂×C₁₃	semidirect
210. C₂×#483	C₂×C₁₃	semidirect
212. C₂×#479	C₂×C₁₃	semidirect
213. C₂×#478	C₂×C₁₃	semidirect
214. C₂×#431	C₂×C₁₃	semidirect
270. C₂×#125	C₂²×C₁₃	semidirect
284. #499	C₂²×C₁₃	semidirect
285. #488	C₂²×C₁₃	semidirect
286. #484	C₂²×C₁₃	semidirect
287. #483	C₂²×C₁₃	semidirect
290. #479	C₂²×C₁₃	semidirect
291. #478	C₂²×C₁₃	semidirect
292. #431	C₂²×C₁₃	semidirect
408. C₂×C₁₃	#3232	direct (N × H)
480. C₁₃	C₂×#3232	direct (N × H)
553. C₂	C₁₃×#3232	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
C₂²×C₁₃×#125	2
C₁₃×#3232	2
C₂×C₁₃×#499	2
C₂×C₁₃×#488	2
C₂×C₁₃×#484	2
C₂×C₁₃×#481	2
C₂×C₁₃×#483	2
C₂×C₁₃×#480	2
C₂×C₁₃×#479	2
C₂×C₁₃×#478	2
C₂×C₁₃×#431	2
C₂×#3232	13

Subgroups — C2×C13×#3232 #15747179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3232 #15747179