Subgroups — C₂×C₁₃×#3399 #15747735

Order 3328.

2314 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
19	C₁₃×#559	—	2	4	no	—
20	C₁₃×#559	C₂²	1	8	yes	complemented
21	C₁₃×#550	—	2	4	no	—
22	C₁₃×#550	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	2	yes	—
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	—	2	1	no	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	—	2	2	no	—
29	C₂×C₁₃×#121	—	2	1	no	—
30	C₂×C₁₃×#121	—	2	2	no	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#496	C₂²	1	16	yes	complemented
38	C₁₃×#493	C₂²	1	8	yes	complemented
39	C₁₃×#463	C₂²	1	16	yes	complemented
40	C₁₃×#460	C₂²	1	8	yes	complemented
41	C₁₃×#459	C₂²	1	16	yes	complemented
42	C₁₃×#459	C₂²	1	8	yes	complemented
43	C₁₃×#446	C₂²	1	8	yes	complemented
44	C₁₃×#442	C₂²	1	16	yes	complemented
45	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#41	—	2	8	no	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	—	2	2	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	4	no	—
72	C₂×C₁₃×SD₁₆	—	4	4	no	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×D₈	—	2	8	no	—
76	C₂×C₁₃×D₈	—	4	4	no	—
77	C₂×C₁₃×D₈	—	4	4	no	—
78	C₂×C₁₃×D₈	C₂³	1	8	yes	—
79	C₂×C₁₃×D₈	C₂³	1	8	yes	—
80	C₂×C₁₃×D₈	C₂³	1	8	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#127	—	2	4	no	—
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	C₂³	1	4	yes	—
88	C₁₃×#127	C₂³	1	8	yes	—
89	C₁₃×#127	C₂³	1	4	yes	—
90	C₁₃×#124	—	2	8	no	—
91	C₁₃×#124	—	2	4	no	—
92	C₁₃×#124	C₂³	1	8	yes	—
93	C₁₃×#123	—	2	16	no	—
94	C₁₃×#121	—	2	8	no	—
95	C₁₃×#121	—	2	16	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	D₄	1	4	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	4	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	C₂³	1	8	yes	—
106	C₄×D₄×C₁₃	C₂³	1	8	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₄²×C₁₃	—	2	1	no	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₁₃×#106	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	4	yes	—
124	C₁₃×#102	C₂³	1	4	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×#102	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	8	yes	—
128	C₄×C₈×C₁₃	C₂³	1	4	yes	—
129	C₂×#3399	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₁₃×#41	—	4	32	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	4	no	—
157	C₂×D₄×C₁₃	—	4	4	no	—
158	C₂×D₄×C₁₃	—	8	4	no	—
159	C₂×D₄×C₁₃	—	8	2	no	—
160	C₂×D₄×C₁₃	—	8	2	no	—
161	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	4	8	no	—
171	C₂²×C₄×C₁₃	—	4	4	no	—
172	C₂²×C₄×C₁₃	—	8	4	no	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×SD₁₆	—	2	8	no	—
179	C₁₃×SD₁₆	—	4	8	no	—
180	C₁₃×D₈	—	2	16	no	—
181	C₁₃×D₈	—	4	8	no	—
182	C₁₃×D₈	—	4	8	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	4	no	—
185	C₂×C₈×C₁₃	#41	1	4	yes	complemented
186	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
187	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
188	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₄²×C₁₃	—	2	4	no	—
202	C₄²×C₁₃	C₂×D₄	1	4	yes	—
203	C₄²×C₁₃	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃	C₂⁴	1	2	yes	—
205	C₄²×C₁₃	C₂⁴	1	4	yes	—
206	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3399	C₂×C₁₃	1	16	yes	direct product factor
209	C₂×#496	C₂×C₁₃	1	2	yes	complemented
210	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#463	C₂×C₁₃	1	2	yes	complemented
213	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#459	C₂×C₁₃	1	2	yes	complemented
215	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#442	C₂×C₁₃	1	2	yes	complemented
217	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	4	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	4	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	—	4	4	no	—
230	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	8	no	—
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	4	16	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	8	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	—	8	8	no	—
248	D₄×C₁₃	—	8	4	no	—
249	D₄×C₁₃	—	8	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	4	16	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	8	no	—
261	C₂×C₄×C₁₃	—	8	8	no	—
262	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
269	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	2	4	no	—
273	C₈×C₁₃	C₂×#41	1	4	yes	complemented
274	C₂²×#41	—	2	1	no	—
275	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
277	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
278	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
279	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
280	#559	—	2	4	no	—
281	#559	C₂²×C₁₃	1	8	yes	complemented
282	#550	—	2	4	no	—
283	#550	C₂²×C₁₃	1	8	yes	complemented
284	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#127	C₂²×C₁₃	1	2	yes	—
287	C₂×#124	—	2	1	no	—
288	C₂×#124	C₂²×C₁₃	1	2	yes	—
289	C₂×#123	—	2	2	no	—
290	C₂×#121	—	2	1	no	—
291	C₂×#121	—	2	2	no	—
292	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×D₄	—	2	1	no	—
295	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
298	#496	C₂²×C₁₃	1	16	yes	complemented
299	#493	C₂²×C₁₃	1	8	yes	complemented
300	#463	C₂²×C₁₃	1	16	yes	complemented
301	#460	C₂²×C₁₃	1	8	yes	complemented
302	#459	C₂²×C₁₃	1	16	yes	complemented
303	#459	C₂²×C₁₃	1	8	yes	complemented
304	#446	C₂²×C₁₃	1	8	yes	complemented
305	#442	C₂²×C₁₃	1	16	yes	complemented
306	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
307	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
309	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₃	1	2	yes	—
313	C₂×#102	C₂²×C₁₃	1	2	yes	—
314	C₂×#97	C₂²×C₁₃	1	2	yes	—
315	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	4	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	8	8	no	—
326	C₂²×C₁₃	—	8	4	no	—
327	C₂²×C₁₃	—	8	8	no	—
328	C₂²×C₁₃	#550	1	2	yes	—
329	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
330	C₂²×C₁₃	#576	1	2	yes	—
331	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₁₃	—	2	4	no	—
333	C₄×C₁₃	—	2	4	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	#550	1	2	yes	—
339	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
340	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
341	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×#41	—	2	8	no	—
343	C₂×#41	—	4	8	no	—
344	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
345	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
353	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
354	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂³×C₄	—	2	2	no	—
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	—	2	2	no	—
358	C₂×SD₁₆	—	2	4	no	—
359	C₂×SD₁₆	—	4	4	no	—
360	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
361	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
362	C₂×D₈	—	2	8	no	—
363	C₂×D₈	—	4	4	no	—
364	C₂×D₈	—	4	4	no	—
365	C₂×D₈	C₂³×C₁₃	1	8	yes	—
366	C₂×D₈	C₂³×C₁₃	1	8	yes	—
367	C₂×D₈	C₂³×C₁₃	1	8	yes	—
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	#127	—	2	4	no	—
372	#127	—	2	2	no	—
373	#127	—	2	2	no	—
374	#127	C₂³×C₁₃	1	8	yes	—
375	#127	C₂³×C₁₃	1	4	yes	—
376	#127	C₂³×C₁₃	1	4	yes	—
377	#124	—	2	8	no	—
378	#124	—	2	4	no	—
379	#124	C₂³×C₁₃	1	8	yes	—
380	#123	—	2	16	no	—
381	#121	—	2	8	no	—
382	#121	—	2	16	no	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	D₄×C₁₃	1	4	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
386	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	C₂³×C₁₃	1	4	yes	—
392	C₄×D₄	C₂³×C₁₃	1	8	yes	—
393	C₄×D₄	C₂³×C₁₃	1	8	yes	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
407	#106	C₂³×C₁₃	1	4	yes	—
408	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
409	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
410	#103	C₂³×C₁₃	1	4	yes	—
411	#102	C₂³×C₁₃	1	4	yes	—
412	#102	C₂³×C₁₃	1	8	yes	—
413	#102	C₂³×C₁₃	1	8	yes	—
414	#97	C₂³×C₁₃	1	8	yes	—
415	C₄×C₈	C₂³×C₁₃	1	4	yes	—
416	C₂×C₁₃	—	8	4	no	—
417	C₂×C₁₃	—	8	2	no	—
418	C₂×C₁₃	—	8	4	no	—
419	C₂×C₁₃	#3399	1	4	yes	direct product factor
420	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
421	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	2	1	no	—
426	#41	—	4	32	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
432	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	4	8	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	—	8	4	no	—
452	C₂×D₄	—	8	2	no	—
453	C₂×D₄	—	8	2	no	—
454	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
455	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
456	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	8	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	4	8	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	8	4	no	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
471	SD₁₆	—	2	8	no	—
472	SD₁₆	—	4	8	no	—
473	D₈	—	2	16	no	—
474	D₈	—	4	8	no	—
475	D₈	—	4	8	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	C₁₃×#41	1	4	yes	complemented
479	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
480	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
481	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
486	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
487	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
488	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₄²	—	2	4	no	—
495	C₄²	C₂×D₄×C₁₃	1	4	yes	—
496	C₄²	C₂×D₄×C₁₃	1	2	yes	—
497	C₄²	C₂⁴×C₁₃	1	2	yes	—
498	C₄²	C₂⁴×C₁₃	1	4	yes	—
499	C₁₃	C₂×#3399	1	1	yes	characteristic, direct product factor, Sylow
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	4	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	4	no	—
512	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
513	Q₈	—	2	8	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	4	2	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	4	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	4	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	4	no	—
523	D₄	—	4	16	no	—
524	D₄	—	4	4	no	—
525	D₄	—	4	4	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	8	no	—
529	D₄	—	8	8	no	—
530	D₄	—	8	4	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	4	16	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	8	no	—
543	C₂×C₄	—	8	8	no	—
544	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
546	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
551	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
552	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	4	no	—
555	C₈	C₂×C₁₃×#41	1	4	yes	complemented
556	C₂²	—	4	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	8	no	—
566	C₂²	—	8	4	no	—
567	C₂²	—	8	8	no	—
568	C₂²	C₁₃×#550	1	2	yes	—
569	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
570	C₂²	C₁₃×#576	1	2	yes	—
571	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
572	C₄	—	2	4	no	—
573	C₄	—	2	4	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	C₁₃×#550	1	2	yes	—
579	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
580	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
581	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂	—	8	4	no	—
583	C₂	—	8	2	no	—
584	C₂	—	8	4	no	—
585	C₂	C₁₃×#3399	1	4	yes	direct product factor
586	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
587	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
588	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#559	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3399	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#493	C₂	semidirect
6. C₂×C₁₃×#460	C₂	semidirect
7. C₂×C₁₃×#463	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#459	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#442	C₂	semidirect
12. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#493	C₂²	semidirect
39. C₁₃×#463	C₂²	semidirect
40. C₁₃×#460	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₁₃×#442	C₂²	semidirect
45. C₄×C₁₃×SD₁₆	C₂²	semidirect
129. C₂×#3399	C₁₃	direct (N × H)
185. C₂×C₈×C₁₃	#41	semidirect
206. C₂×#559	C₂×C₁₃	semidirect
207. C₂×#550	C₂×C₁₃	semidirect
208. #3399	C₂×C₁₃	direct (N × H)
209. C₂×#496	C₂×C₁₃	semidirect
210. C₂×#493	C₂×C₁₃	semidirect
211. C₂×#460	C₂×C₁₃	semidirect
212. C₂×#463	C₂×C₁₃	semidirect
213. C₂×#459	C₂×C₁₃	semidirect
214. C₂×#459	C₂×C₁₃	semidirect
215. C₂×#446	C₂×C₁₃	semidirect
216. C₂×#442	C₂×C₁₃	semidirect
217. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
273. C₈×C₁₃	C₂×#41	semidirect
281. #559	C₂²×C₁₃	semidirect
283. #550	C₂²×C₁₃	semidirect
298. #496	C₂²×C₁₃	semidirect
299. #493	C₂²×C₁₃	semidirect
300. #463	C₂²×C₁₃	semidirect
301. #460	C₂²×C₁₃	semidirect
302. #459	C₂²×C₁₃	semidirect
303. #459	C₂²×C₁₃	semidirect
304. #446	C₂²×C₁₃	semidirect
305. #442	C₂²×C₁₃	semidirect
306. C₄×SD₁₆	C₂²×C₁₃	semidirect
419. C₂×C₁₃	#3399	direct (N × H)
478. C₂×C₈	C₁₃×#41	semidirect
499. C₁₃	C₂×#3399	direct (N × H)
555. C₈	C₂×C₁₃×#41	semidirect
585. C₂	C₁₃×#3399	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×#559	2
C₂×C₁₃×#550	2
C₁₃×#3399	2
C₂×C₁₃×#496	2
C₂×C₁₃×#493	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3399	13

Subgroups — C2×C13×#3399 #15747735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3399 #15747735