Subgroups — C₂×C₁₃×#3250 #15747238

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 466 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×#3250	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#529	—	2	8	no	—
17	C₁₃×#529	C₂²	1	16	yes	complemented
18	C₂×C₁₃×#126	—	2	2	no	—
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×#123	—	2	2	no	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	—	2	2	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	—	2	2	no	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#479	C₂²	1	16	yes	complemented
30	C₁₃×#478	C₂²	1	16	yes	complemented
31	C₁₃×#467	C₂²	1	8	yes	complemented
32	C₁₃×#466	C₂²	1	8	yes	—
33	C₁₃×#465	C₂²	1	16	yes	complemented
34	C₁₃×#464	C₂²	1	16	yes	complemented
35	C₁₃×#463	C₂²	1	16	yes	complemented
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#106	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	8	yes	complemented
42	C₂×C₁₃×#103	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#102	C₂²	1	2	yes	—
45	C₂×C₁₃×#102	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×Q₁₆	—	4	2	no	—
54	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
55	C₂×C₁₃×SD₁₆	—	4	4	no	—
56	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×D₈	—	4	2	no	—
58	C₂×C₁₃×D₈	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₃	—	4	2	no	—
60	C₂²×C₈×C₁₃	—	4	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
66	C₁₃×#126	—	2	16	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	C₂³	1	8	yes	—
69	C₁₃×#124	—	2	4	no	—
70	C₁₃×#124	C₂³	1	8	yes	—
71	C₁₃×#123	—	2	16	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
74	C₁₃×#121	—	2	4	no	—
75	C₁₃×#121	C₂³	1	8	yes	—
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
78	C₄×D₄×C₁₃	—	2	16	no	—
79	C₄×D₄×C₁₃	—	2	4	no	—
80	C₄×D₄×C₁₃	C₂³	1	8	yes	—
81	C₁₃×#117	—	2	16	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₁₃	—	2	2	no	—
94	C₂×C₄²×C₁₃	D₄	1	2	yes	—
95	C₂×C₄²×C₁₃	D₄	1	4	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₁₃×#107	C₂³	1	4	yes	—
99	C₁₃×#107	C₂³	1	4	yes	—
100	C₁₃×#106	C₂³	1	8	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₂×#3250	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	4	8	no	—
119	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	8	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	8	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×Q₁₆	—	4	4	no	—
138	C₁₃×SD₁₆	—	4	8	no	—
139	C₁₃×D₈	—	4	4	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	4	4	no	—
144	C₂×C₈×C₁₃	—	4	4	no	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₄²×C₁₃	—	2	8	no	—
162	C₄²×C₁₃	C₂×D₄	1	8	yes	—
163	C₄²×C₁₃	C₂×D₄	1	4	yes	—
164	C₄²×C₁₃	C₂⁴	1	4	yes	—
165	C₂×#529	C₂×C₁₃	1	2	yes	complemented
166	#3250	C₂×C₁₃	1	16	yes	direct product factor
167	C₂×#479	C₂×C₁₃	1	2	yes	complemented
168	C₂×#478	C₂×C₁₃	1	2	yes	complemented
169	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
171	C₂×#465	C₂×C₁₃	1	2	yes	complemented
172	C₂×#464	C₂×C₁₃	1	2	yes	complemented
173	C₂×#463	C₂×C₁₃	1	2	yes	complemented
174	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	4	4	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	#135	1	4	yes	—
182	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	2	4	no	—
186	Q₈×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	2	4	no	—
189	D₄×C₁₃	—	4	16	no	—
190	D₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	8	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
211	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
212	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	2	4	no	—
215	C₈×C₁₃	—	2	2	no	—
216	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
218	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	#529	—	2	8	no	—
222	#529	C₂²×C₁₃	1	16	yes	complemented
223	C₂×#126	—	2	2	no	—
224	C₂×#125	C₂²×C₁₃	1	2	yes	—
225	C₂×#124	C₂²×C₁₃	1	2	yes	—
226	C₂×#123	—	2	2	no	—
227	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#121	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×D₄	—	2	2	no	—
231	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
232	C₂×#117	—	2	2	no	—
233	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
234	#479	C₂²×C₁₃	1	16	yes	complemented
235	#478	C₂²×C₁₃	1	16	yes	complemented
236	#467	C₂²×C₁₃	1	8	yes	complemented
237	#466	C₂²×C₁₃	1	8	yes	—
238	#465	C₂²×C₁₃	1	16	yes	complemented
239	#464	C₂²×C₁₃	1	16	yes	complemented
240	#463	C₂²×C₁₃	1	16	yes	complemented
241	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#106	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₁₃	1	8	yes	complemented
247	C₂×#103	C₂²×C₁₃	1	2	yes	—
248	C₂×#103	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	8	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	8	8	no	—
258	C₂²×C₁₃	#537	1	2	yes	—
259	C₂²×C₁₃	C₂×#135	1	4	yes	—
260	C₂²×C₁₃	C₂×#135	1	2	yes	—
261	C₂²×C₁₃	#575	1	2	yes	—
262	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	2	4	no	—
266	C₄×C₁₃	—	4	4	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	4	no	—
269	C₄×C₁₃	#537	1	2	yes	—
270	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×Q₁₆	—	4	2	no	—
280	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
281	C₂×SD₁₆	—	4	4	no	—
282	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
283	C₂×D₈	—	4	2	no	—
284	C₂×D₈	C₂³×C₁₃	1	4	yes	—
285	C₂²×C₈	—	4	2	no	—
286	C₂²×C₈	—	4	2	no	—
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
292	#126	—	2	16	no	—
293	#125	—	2	4	no	—
294	#125	C₂³×C₁₃	1	8	yes	—
295	#124	—	2	4	no	—
296	#124	C₂³×C₁₃	1	8	yes	—
297	#123	—	2	16	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
300	#121	—	2	4	no	—
301	#121	C₂³×C₁₃	1	8	yes	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
304	C₄×D₄	—	2	16	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	C₂³×C₁₃	1	8	yes	—
307	#117	—	2	16	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	D₄×C₁₃	1	2	yes	—
321	C₂×C₄²	D₄×C₁₃	1	4	yes	—
322	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
324	#107	C₂³×C₁₃	1	4	yes	—
325	#107	C₂³×C₁₃	1	4	yes	—
326	#106	C₂³×C₁₃	1	8	yes	—
327	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
328	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
329	#103	C₂³×C₁₃	1	8	yes	—
330	#103	C₂³×C₁₃	1	8	yes	—
331	#102	C₂³×C₁₃	1	8	yes	—
332	#102	C₂³×C₁₃	1	8	yes	—
333	C₂×C₁₃	—	2	4	no	—
334	C₂×C₁₃	—	8	4	no	—
335	C₂×C₁₃	#3250	1	4	yes	direct product factor
336	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
337	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
338	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
339	C₂⁴	—	2	2	no	—
340	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	8	no	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	4	8	no	—
370	D₈	—	4	4	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	—	4	4	no	—
376	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
377	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
378	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
386	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	C₂×D₄×C₁₃	1	8	yes	—
394	C₄²	C₂×D₄×C₁₃	1	4	yes	—
395	C₄²	C₂⁴×C₁₃	1	4	yes	—
396	C₁₃	C₂×#3250	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	C₁₃×#135	1	4	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
433	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
434	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₈	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	8	no	—
445	C₂²	C₁₃×#537	1	2	yes	—
446	C₂²	C₂×C₁₃×#135	1	4	yes	—
447	C₂²	C₂×C₁₃×#135	1	2	yes	—
448	C₂²	C₁₃×#575	1	2	yes	—
449	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	C₁₃×#537	1	2	yes	—
457	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
458	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	8	4	no	—
461	C₂	C₁₃×#3250	1	4	yes	direct product factor
462	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
463	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
464	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×#466	C₂
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
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#3250	C₂	direct (N × H)
3. C₂×C₁₃×#479	C₂	semidirect
4. C₂×C₁₃×#478	C₂	semidirect
5. C₂×C₁₃×#467	C₂	semidirect
7. C₂×C₁₃×#465	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#463	C₂	semidirect
10. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
17. C₁₃×#529	C₂²	semidirect
29. C₁₃×#479	C₂²	semidirect
30. C₁₃×#478	C₂²	semidirect
31. C₁₃×#467	C₂²	semidirect
33. C₁₃×#465	C₂²	semidirect
34. C₁₃×#464	C₂²	semidirect
35. C₁₃×#463	C₂²	semidirect
41. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
107. C₂×#3250	C₁₃	direct (N × H)
165. C₂×#529	C₂×C₁₃	semidirect
166. #3250	C₂×C₁₃	direct (N × H)
167. C₂×#479	C₂×C₁₃	semidirect
168. C₂×#478	C₂×C₁₃	semidirect
169. C₂×#467	C₂×C₁₃	semidirect
171. C₂×#465	C₂×C₁₃	semidirect
172. C₂×#464	C₂×C₁₃	semidirect
173. C₂×#463	C₂×C₁₃	semidirect
174. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
222. #529	C₂²×C₁₃	semidirect
234. #479	C₂²×C₁₃	semidirect
235. #478	C₂²×C₁₃	semidirect
236. #467	C₂²×C₁₃	semidirect
238. #465	C₂²×C₁₃	semidirect
239. #464	C₂²×C₁₃	semidirect
240. #463	C₂²×C₁₃	semidirect
246. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
335. C₂×C₁₃	#3250	direct (N × H)
396. C₁₃	C₂×#3250	direct (N × H)
461. C₂	C₁₃×#3250	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×#3250	2
C₂×C₁₃×#479	2
C₂×C₁₃×#478	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#465	2
C₂×C₁₃×#464	2
C₂×C₁₃×#463	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×#3250	13

Subgroups — C2×C13×#3250 #15747238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3250 #15747238