Subgroups — C₂×C₁₃×#2423 #15721026

Order 3328.

2790 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2423	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#399	C₂	1	2	yes	maximal
5	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#388	C₂	1	2	yes	maximal
9	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
17	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#399	C₂²	1	16	yes	—
35	C₁₃×#398	C₂²	1	16	yes	complemented
36	C₁₃×#391	C₂²	1	8	yes	complemented
37	C₁₃×#389	C₂²	1	8	yes	complemented
38	C₁₃×#388	C₂²	1	16	yes	—
39	C₁₃×#387	C₂²	1	16	yes	complemented
40	C₁₃×#384	C₂²	1	8	yes	complemented
41	C₁₃×#380	C₂²	1	8	yes	—
42	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
43	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	4	no	—
52	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₃	—	2	4	no	—
55	C₂³×C₄×C₁₃	—	2	4	no	—
56	C₂³×C₄×C₁₃	—	2	4	no	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₂²⋊Q₈	—	2	32	no	—
69	C₄×Q₈×C₁₃	—	2	32	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₃	—	2	8	no	—
95	C₂×C₄²×C₁₃	—	2	4	no	—
96	C₂×C₄²×C₁₃	—	2	4	no	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₂×#2423	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
115	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×Q₈×C₁₃	—	2	32	no	—
117	C₂×Q₈×C₁₃	—	2	8	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	4	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	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	4	16	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
151	C₂²×C₄×C₁₃	#41	1	4	yes	—
152	C₂²×C₄×C₁₃	#41	1	4	yes	—
153	C₂²×C₄×C₁₃	#41	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	2	16	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	16	no	—
168	C₁₃×C₄⋊C₄	—	2	16	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	4	8	no	—
171	C₁₃×C₄⋊C₄	—	4	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	16	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	4	8	no	—
175	C₁₃×C₂²⋊C₄	C₂×Q₈	1	16	yes	complemented
176	C₄²×C₁₃	—	2	16	no	—
177	C₄²×C₁₃	—	2	8	no	—
178	C₄²×C₁₃	—	2	8	no	—
179	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
180	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#2423	C₂×C₁₃	1	16	yes	direct product factor
182	C₂×#399	C₂×C₁₃	1	2	yes	—
183	C₂×#398	C₂×C₁₃	1	2	yes	complemented
184	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×#388	C₂×C₁₃	1	2	yes	—
187	C₂×#387	C₂×C₁₃	1	2	yes	complemented
188	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
190	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	8	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	—	4	4	no	—
203	C₂³×C₁₃	—	4	4	no	—
204	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
206	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
207	C₂³×C₁₃	C₂×#41	1	2	yes	—
208	C₂³×C₁₃	C₂×#41	1	2	yes	—
209	C₂³×C₁₃	C₂×#41	1	2	yes	—
210	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
212	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	32	no	—
214	C₂×C₄×C₁₃	—	2	16	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	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	—	4	4	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	4	8	no	—
246	C₂×C₄×C₁₃	—	4	16	no	—
247	C₂×C₄×C₁₃	#123	1	16	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
251	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
252	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
253	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
255	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	—	2	8	no	—
258	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
259	C₂×C₄×Q₈	—	2	8	no	—
260	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
275	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
276	#399	C₂²×C₁₃	1	16	yes	—
277	#398	C₂²×C₁₃	1	16	yes	complemented
278	#391	C₂²×C₁₃	1	8	yes	complemented
279	#389	C₂²×C₁₃	1	8	yes	complemented
280	#388	C₂²×C₁₃	1	16	yes	—
281	#387	C₂²×C₁₃	1	16	yes	complemented
282	#384	C₂²×C₁₃	1	8	yes	complemented
283	#380	C₂²×C₁₃	1	8	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
285	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#95	C₂²×C₁₃	1	2	yes	—
287	C₂×#95	C₂²×C₁₃	1	2	yes	—
288	C₂×#95	C₂²×C₁₃	1	2	yes	—
289	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#95	C₂²×C₁₃	1	2	yes	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	2	4	no	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	16	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	C₂×#123	1	4	yes	—
300	C₂²×C₁₃	#533	1	4	yes	—
301	C₂²×C₁₃	#542	1	4	yes	—
302	C₂²×C₁₃	D₄×Q₈	1	4	yes	—
303	C₂²×C₁₃	#550	1	4	yes	—
304	C₂²×C₁₃	#552	1	4	yes	—
305	C₂²×C₁₃	#554	1	4	yes	—
306	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
307	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
308	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
309	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
310	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	C₄×C₁₃	—	2	8	no	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	2	4	no	—
316	C₄×C₁₃	—	2	4	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	4	2	no	—
320	C₄×C₁₃	—	4	4	no	—
321	C₄×C₁₃	—	4	4	no	—
322	C₄×C₁₃	C₂×#123	1	8	yes	—
323	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×Q₈	—	2	4	no	—
325	C₂²×Q₈	—	2	4	no	—
326	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
327	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
328	C₂³×C₄	—	2	4	no	—
329	C₂³×C₄	—	2	4	no	—
330	C₂³×C₄	—	2	4	no	—
331	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
337	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂²⋊Q₈	—	2	32	no	—
343	C₄×Q₈	—	2	32	no	—
344	C₂×C₄⋊C₄	—	2	8	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	8	no	—
348	C₂×C₄⋊C₄	—	2	8	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	4	4	no	—
351	C₂×C₄⋊C₄	—	4	4	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
360	C₂×C₂²⋊C₄	—	2	8	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	—	4	4	no	—
363	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
364	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
368	C₂×C₄²	—	2	8	no	—
369	C₂×C₄²	—	2	4	no	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
372	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
373	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
374	#95	C₂³×C₁₃	1	4	yes	—
375	#95	C₂³×C₁₃	1	4	yes	—
376	#95	C₂³×C₁₃	1	8	yes	—
377	#95	C₂³×C₁₃	1	8	yes	—
378	#95	C₂³×C₁₃	1	8	yes	—
379	#95	C₂³×C₁₃	1	8	yes	—
380	C₂×C₁₃	—	4	4	no	—
381	C₂×C₁₃	#2423	1	8	yes	direct product factor
382	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
385	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
386	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
387	C₂×C₁₃	C₂×#552	1	1	yes	characteristic
388	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
396	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
397	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₂×Q₈	—	2	32	no	—
399	C₂×Q₈	—	2	8	no	—
400	C₂×Q₈	—	2	8	no	—
401	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	4	16	no	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
431	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
433	C₂²×C₄	C₁₃×#41	1	4	yes	—
434	C₂²×C₄	C₁₃×#41	1	4	yes	—
435	C₂²×C₄	C₁₃×#41	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₄⋊C₄	—	2	16	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	16	no	—
450	C₄⋊C₄	—	2	16	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	4	8	no	—
453	C₄⋊C₄	—	4	8	no	—
454	C₂²⋊C₄	—	2	16	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	4	8	no	—
457	C₂²⋊C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
458	C₄²	—	2	16	no	—
459	C₄²	—	2	8	no	—
460	C₄²	—	2	8	no	—
461	C₁₃	C₂×#2423	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	—	2	8	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	8	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
476	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
477	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
478	C₂³	C₂×C₁₃×#41	1	2	yes	—
479	C₂³	C₂×C₁₃×#41	1	2	yes	—
480	C₂³	C₂×C₁₃×#41	1	2	yes	—
481	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
482	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
483	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
484	Q₈	—	2	32	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	16	no	—
518	C₂×C₄	C₁₃×#123	1	16	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
521	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
522	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
524	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
525	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	16	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	C₂×C₁₃×#123	1	4	yes	—
535	C₂²	C₁₃×#533	1	4	yes	—
536	C₂²	C₁₃×#542	1	4	yes	—
537	C₂²	D₄×Q₈×C₁₃	1	4	yes	—
538	C₂²	C₁₃×#550	1	4	yes	—
539	C₂²	C₁₃×#552	1	4	yes	—
540	C₂²	C₁₃×#554	1	4	yes	—
541	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
542	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
543	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
544	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
545	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
546	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
548	C₄	—	2	8	no	—
549	C₄	—	2	4	no	—
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	4	no	—
557	C₄	C₂×C₁₃×#123	1	8	yes	—
558	C₂	—	4	4	no	—
559	C₂	C₁₃×#2423	1	8	yes	direct product factor
560	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
561	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
562	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
563	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
564	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#552	1	1	yes	characteristic
566	C₂	C₂×C₁₃×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2423	C₂	direct (N × H)
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#391	C₂	semidirect
7. C₂×C₁₃×#389	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₁₃×#384	C₂	semidirect
18. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
35. C₁₃×#398	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
39. C₁₃×#387	C₂²	semidirect
40. C₁₃×#384	C₂²	semidirect
89. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
106. C₂×#2423	C₁₃	direct (N × H)
175. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
180. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
181. #2423	C₂×C₁₃	direct (N × H)
183. C₂×#398	C₂×C₁₃	semidirect
184. C₂×#391	C₂×C₁₃	semidirect
185. C₂×#389	C₂×C₁₃	semidirect
187. C₂×#387	C₂×C₁₃	semidirect
188. C₂×#384	C₂×C₁₃	semidirect
260. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
277. #398	C₂²×C₁₃	semidirect
278. #391	C₂²×C₁₃	semidirect
279. #389	C₂²×C₁₃	semidirect
281. #387	C₂²×C₁₃	semidirect
282. #384	C₂²×C₁₃	semidirect
363. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
381. C₂×C₁₃	#2423	direct (N × H)
457. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
461. C₁₃	C₂×#2423	direct (N × H)
559. C₂	C₁₃×#2423	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×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2423	2
C₂×C₁₃×#399	2
C₂×C₁₃×#398	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#384	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2423	13

Subgroups — C2×C13×#2423 #15721026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2423 #15721026