Subgroups — C₂×C₁₃×#3397 #15747733

Order 3328.

2250 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, 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×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
19	C₁₃×#556	—	2	4	no	—
20	C₁₃×#556	C₂²	1	8	yes	complemented
21	C₁₃×#550	—	2	4	no	—
22	C₁₃×#550	C₂²	1	8	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#127	C₂²	1	2	yes	—
26	C₂×C₁₃×#126	—	2	2	no	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₁₃×#121	—	2	1	no	—
30	C₂×C₁₃×#121	—	2	2	no	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₁₃×#496	C₂²	1	16	yes	complemented
38	C₁₃×#492	C₂²	1	8	yes	complemented
39	C₁₃×#463	C₂²	1	16	yes	complemented
40	C₁₃×#461	C₂²	1	8	yes	complemented
41	C₁₃×#460	C₂²	1	16	yes	complemented
42	C₁₃×#459	C₂²	1	8	yes	complemented
43	C₁₃×#446	C₂²	1	8	yes	complemented
44	C₁₃×#440	C₂²	1	16	yes	complemented
45	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
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	2	yes	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	—	2	8	no	—
70	C₂×C₁₃×SD₁₆	—	4	4	no	—
71	C₂×C₁₃×SD₁₆	—	4	4	no	—
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×D₈	—	2	4	no	—
76	C₂×C₁₃×D₈	—	4	4	no	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	8	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	—	2	4	no	—
86	C₁₃×#127	C₂³	1	4	yes	—
87	C₁₃×#127	C₂³	1	8	yes	—
88	C₁₃×#126	—	2	16	no	—
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#124	C₂³	1	8	yes	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₁₃×#121	—	2	8	no	—
93	C₁₃×#121	—	2	16	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	D₄	1	4	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
97	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	C₂³	1	4	yes	—
102	C₄×D₄×C₁₃	C₂³	1	4	yes	—
103	C₄×D₄×C₁₃	C₂³	1	8	yes	—
104	C₁₃×#117	—	2	8	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₄²×C₁₃	—	2	2	no	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₁₃×#107	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	8	yes	—
124	C₁₃×#102	C₂³	1	4	yes	—
125	C₁₃×#102	C₂³	1	4	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×#3397	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	1	no	—
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₁₃×#41	—	4	32	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	8	4	no	—
156	C₂×D₄×C₁₃	—	8	2	no	—
157	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	4	8	no	—
167	C₂²×C₄×C₁₃	—	4	4	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₁₃×SD₁₆	—	2	16	no	—
175	C₁₃×SD₁₆	—	4	8	no	—
176	C₁₃×SD₁₆	—	4	8	no	—
177	C₁₃×D₈	—	2	8	no	—
178	C₁₃×D₈	—	4	8	no	—
179	C₂×C₈×C₁₃	—	2	4	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	#41	1	4	yes	complemented
182	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
183	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
184	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	8	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₄²×C₁₃	—	2	8	no	—
200	C₄²×C₁₃	C₂×D₄	1	2	yes	—
201	C₄²×C₁₃	C₂×D₄	1	4	yes	—
202	C₄²×C₁₃	C₂⁴	1	2	yes	—
203	C₄²×C₁₃	C₂⁴	1	4	yes	—
204	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3397	C₂×C₁₃	1	16	yes	direct product factor
207	C₂×#496	C₂×C₁₃	1	2	yes	complemented
208	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#460	C₂×C₁₃	1	2	yes	complemented
210	C₂×#463	C₂×C₁₃	1	2	yes	complemented
211	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#440	C₂×C₁₃	1	2	yes	complemented
215	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	4	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	8	no	—
230	Q₈×C₁₃	—	2	4	no	—
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	2	2	no	—
234	D₄×C₁₃	—	2	2	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	4	16	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	8	no	—
244	D₄×C₁₃	—	8	8	no	—
245	D₄×C₁₃	—	8	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	16	no	—
253	C₂×C₄×C₁₃	—	4	4	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
267	C₈×C₁₃	—	2	4	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	C₂×#41	1	4	yes	complemented
270	C₂²×#41	—	2	1	no	—
271	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
272	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
273	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
274	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
276	#556	—	2	4	no	—
277	#556	C₂²×C₁₃	1	8	yes	complemented
278	#550	—	2	4	no	—
279	#550	C₂²×C₁₃	1	8	yes	complemented
280	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#127	C₂²×C₁₃	1	2	yes	—
283	C₂×#126	—	2	2	no	—
284	C₂×#124	C₂²×C₁₃	1	2	yes	—
285	C₂×C₂²⋊Q₈	—	2	1	no	—
286	C₂×#121	—	2	1	no	—
287	C₂×#121	—	2	2	no	—
288	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
293	C₂×#117	—	2	1	no	—
294	#496	C₂²×C₁₃	1	16	yes	complemented
295	#492	C₂²×C₁₃	1	8	yes	complemented
296	#463	C₂²×C₁₃	1	16	yes	complemented
297	#461	C₂²×C₁₃	1	8	yes	complemented
298	#460	C₂²×C₁₃	1	16	yes	complemented
299	#459	C₂²×C₁₃	1	8	yes	complemented
300	#446	C₂²×C₁₃	1	8	yes	complemented
301	#440	C₂²×C₁₃	1	16	yes	complemented
302	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
303	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
306	C₂×#103	C₂²×C₁₃	1	2	yes	—
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	2	yes	—
310	C₂×#97	C₂²×C₁₃	1	2	yes	—
311	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	8	4	no	—
322	C₂²×C₁₃	—	8	8	no	—
323	C₂²×C₁₃	—	8	4	no	—
324	C₂²×C₁₃	#550	1	2	yes	—
325	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
326	C₂²×C₁₃	#577	1	2	yes	—
327	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₁₃	—	2	4	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	2	no	—
334	C₄×C₁₃	#550	1	2	yes	—
335	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
336	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
337	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×#41	—	2	8	no	—
339	C₂×#41	—	4	8	no	—
340	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
341	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂×SD₁₆	—	2	8	no	—
353	C₂×SD₁₆	—	4	4	no	—
354	C₂×SD₁₆	—	4	4	no	—
355	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
356	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
357	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
358	C₂×D₈	—	2	4	no	—
359	C₂×D₈	—	4	4	no	—
360	C₂×D₈	C₂³×C₁₃	1	4	yes	—
361	C₂×D₈	C₂³×C₁₃	1	8	yes	—
362	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
367	#127	—	2	2	no	—
368	#127	—	2	4	no	—
369	#127	C₂³×C₁₃	1	4	yes	—
370	#127	C₂³×C₁₃	1	8	yes	—
371	#126	—	2	16	no	—
372	#124	—	2	4	no	—
373	#124	C₂³×C₁₃	1	8	yes	—
374	C₂²⋊Q₈	—	2	8	no	—
375	#121	—	2	8	no	—
376	#121	—	2	16	no	—
377	C₄×Q₈	—	2	4	no	—
378	C₄×Q₈	D₄×C₁₃	1	4	yes	—
379	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
380	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	C₂³×C₁₃	1	4	yes	—
385	C₄×D₄	C₂³×C₁₃	1	8	yes	—
386	C₄×D₄	C₂³×C₁₃	1	4	yes	—
387	#117	—	2	8	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	2	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₄²	—	2	2	no	—
401	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
403	#107	C₂³×C₁₃	1	4	yes	—
404	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
405	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
406	#103	C₂³×C₁₃	1	8	yes	—
407	#102	C₂³×C₁₃	1	4	yes	—
408	#102	C₂³×C₁₃	1	4	yes	—
409	#102	C₂³×C₁₃	1	8	yes	—
410	#97	C₂³×C₁₃	1	8	yes	—
411	C₄×C₈	C₂³×C₁₃	1	4	yes	—
412	C₂×C₁₃	—	8	2	no	—
413	C₂×C₁₃	—	8	4	no	—
414	C₂×C₁₃	—	8	2	no	—
415	C₂×C₁₃	#3397	1	4	yes	direct product factor
416	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
417	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
419	C₂⁴	—	2	1	no	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	2	2	no	—
422	#41	—	4	32	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
428	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	—	8	4	no	—
445	C₂×D₄	—	8	2	no	—
446	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
447	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
448	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	8	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	SD₁₆	—	2	16	no	—
464	SD₁₆	—	4	8	no	—
465	SD₁₆	—	4	8	no	—
466	D₈	—	2	8	no	—
467	D₈	—	4	8	no	—
468	C₂×C₈	—	2	4	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	C₁₃×#41	1	4	yes	complemented
471	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
472	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
480	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
481	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
482	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₄²	—	2	8	no	—
489	C₄²	C₂×D₄×C₁₃	1	2	yes	—
490	C₄²	C₂×D₄×C₁₃	1	4	yes	—
491	C₄²	C₂⁴×C₁₃	1	2	yes	—
492	C₄²	C₂⁴×C₁₃	1	4	yes	—
493	C₁₃	C₂×#3397	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	Q₈	—	2	8	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	2	4	no	—
510	Q₈	—	4	4	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	16	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	8	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	16	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
543	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
544	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
545	C₈	—	2	4	no	—
546	C₈	—	2	2	no	—
547	C₈	C₂×C₁₃×#41	1	4	yes	complemented
548	C₂²	—	4	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	8	no	—
559	C₂²	—	8	4	no	—
560	C₂²	C₁₃×#550	1	2	yes	—
561	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
562	C₂²	C₁₃×#577	1	2	yes	—
563	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	C₁₃×#550	1	2	yes	—
571	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
572	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
573	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂	—	8	4	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	2	no	—
577	C₂	C₁₃×#3397	1	4	yes	direct product factor
578	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
579	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
580	C₂	C₂×C₁₃×#577	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×#556	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3397	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#460	C₂	semidirect
7. C₂×C₁₃×#463	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#459	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#440	C₂	semidirect
12. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#556	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#463	C₂²	semidirect
40. C₁₃×#461	C₂²	semidirect
41. C₁₃×#460	C₂²	semidirect
42. C₁₃×#459	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₁₃×#440	C₂²	semidirect
45. C₄×C₁₃×D₈	C₂²	semidirect
129. C₂×#3397	C₁₃	direct (N × H)
181. C₂×C₈×C₁₃	#41	semidirect
204. C₂×#556	C₂×C₁₃	semidirect
205. C₂×#550	C₂×C₁₃	semidirect
206. #3397	C₂×C₁₃	direct (N × H)
207. C₂×#496	C₂×C₁₃	semidirect
208. C₂×#492	C₂×C₁₃	semidirect
209. C₂×#460	C₂×C₁₃	semidirect
210. C₂×#463	C₂×C₁₃	semidirect
211. C₂×#461	C₂×C₁₃	semidirect
212. C₂×#459	C₂×C₁₃	semidirect
213. C₂×#446	C₂×C₁₃	semidirect
214. C₂×#440	C₂×C₁₃	semidirect
215. C₂×C₄×D₈	C₂×C₁₃	semidirect
269. C₈×C₁₃	C₂×#41	semidirect
277. #556	C₂²×C₁₃	semidirect
279. #550	C₂²×C₁₃	semidirect
294. #496	C₂²×C₁₃	semidirect
295. #492	C₂²×C₁₃	semidirect
296. #463	C₂²×C₁₃	semidirect
297. #461	C₂²×C₁₃	semidirect
298. #460	C₂²×C₁₃	semidirect
299. #459	C₂²×C₁₃	semidirect
300. #446	C₂²×C₁₃	semidirect
301. #440	C₂²×C₁₃	semidirect
302. C₄×D₈	C₂²×C₁₃	semidirect
415. C₂×C₁₃	#3397	direct (N × H)
470. C₂×C₈	C₁₃×#41	semidirect
493. C₁₃	C₂×#3397	direct (N × H)
547. C₈	C₂×C₁₃×#41	semidirect
577. C₂	C₁₃×#3397	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×#556	2
C₂×C₁₃×#550	2
C₁₃×#3397	2
C₂×C₁₃×#496	2
C₂×C₁₃×#492	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#459	2
C₂×C₁₃×#446	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×D₈	2
C₂×#3397	13

Subgroups — C2×C13×#3397 #15747733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3397 #15747733