Subgroups — C₂×C₁₃×#3353 #15747585

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 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×#547	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3353	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₁₃×#556	—	2	4	no	—
17	C₁₃×#556	C₂²	1	8	yes	complemented
18	C₁₃×#547	—	2	4	no	—
19	C₁₃×#547	C₂²	1	8	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#126	—	2	2	no	—
23	C₂×C₁₃×#124	—	2	1	no	—
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#500	C₂²	1	8	yes	complemented
35	C₁₃×#484	C₂²	1	16	yes	complemented
36	C₁₃×#482	C₂²	1	16	yes	complemented
37	C₁₃×#475	C₂²	1	8	yes	complemented
38	C₁₃×#474	C₂²	1	8	yes	complemented
39	C₁₃×#468	C₂²	1	16	yes	complemented
40	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
41	C₁₃×#436	C₂²	1	8	yes	complemented
42	C₁₃×#428	C₂²	1	16	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#107	C₂²	1	2	yes	—
45	C₂×C₁₃×#107	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	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	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂×C₁₃×SD₁₆	—	2	4	no	—
67	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
68	C₂×C₁₃×M₁₆	—	2	8	no	—
69	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	—	2	2	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×#126	—	2	16	no	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#123	—	2	16	no	—
80	C₁₃×C₂²⋊Q₈	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₁₃×#121	—	2	4	no	—
84	C₁₃×#121	C₂³	1	8	yes	—
85	C₄×Q₈×C₁₃	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	D₄	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₁₃×#117	—	2	4	no	—
93	C₁₃×#117	C₂³	1	8	yes	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
111	C₂×C₄²×C₁₃	—	2	2	no	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#107	C₂³	1	8	yes	—
115	C₁₃×#107	C₂³	1	8	yes	—
116	C₁₃×#107	C₂³	1	8	yes	—
117	C₁₃×#106	C₂³	1	4	yes	—
118	C₁₃×#106	C₂³	1	8	yes	—
119	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
120	C₁₃×#103	C₂³	1	4	yes	—
121	C₁₃×#103	C₂³	1	8	yes	—
122	C₁₃×#102	C₂³	1	4	yes	—
123	C₁₃×#102	C₂³	1	8	yes	—
124	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
125	C₄×C₈×C₁₃	C₂³	1	4	yes	—
126	C₂×#3353	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
129	C₁₃×#41	—	4	32	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	4	4	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	4	8	no	—
144	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	4	8	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×SD₁₆	—	2	8	no	—
164	C₁₃×M₁₆	—	2	16	no	—
165	C₂×C₈×C₁₃	—	2	4	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	#41	1	4	yes	complemented
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
181	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂⁴	1	2	yes	—
194	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
196	#3353	C₂×C₁₃	1	16	yes	direct product factor
197	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#484	C₂×C₁₃	1	2	yes	complemented
199	C₂×#482	C₂×C₁₃	1	2	yes	complemented
200	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#468	C₂×C₁₃	1	2	yes	complemented
203	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#428	C₂×C₁₃	1	2	yes	complemented
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₁₃	—	2	2	no	—
216	Q₈×C₁₃	—	2	2	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	4	8	no	—
219	Q₈×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	2	8	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	2	2	no	—
223	D₄×C₁₃	—	4	16	no	—
224	D₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	4	16	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	4	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
248	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
250	C₈×C₁₃	—	2	4	no	—
251	C₈×C₁₃	—	2	2	no	—
252	C₈×C₁₃	C₂×#41	1	4	yes	complemented
253	C₂²×#41	—	2	1	no	—
254	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
256	#556	—	2	4	no	—
257	#556	C₂²×C₁₃	1	8	yes	complemented
258	#547	—	2	4	no	—
259	#547	C₂²×C₁₃	1	8	yes	—
260	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#126	—	2	2	no	—
263	C₂×#124	—	2	1	no	—
264	C₂×#123	—	2	2	no	—
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂×#121	C₂²×C₁₃	1	2	yes	—
268	C₂×C₄×Q₈	—	2	1	no	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#117	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
274	#500	C₂²×C₁₃	1	8	yes	complemented
275	#484	C₂²×C₁₃	1	16	yes	complemented
276	#482	C₂²×C₁₃	1	16	yes	complemented
277	#475	C₂²×C₁₃	1	8	yes	complemented
278	#474	C₂²×C₁₃	1	8	yes	complemented
279	#468	C₂²×C₁₃	1	16	yes	complemented
280	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
281	#436	C₂²×C₁₃	1	8	yes	complemented
282	#428	C₂²×C₁₃	1	16	yes	complemented
283	C₂×#107	C₂²×C₁₃	1	2	yes	—
284	C₂×#107	C₂²×C₁₃	1	2	yes	—
285	C₂×#107	C₂²×C₁₃	1	2	yes	—
286	C₂×#106	C₂²×C₁₃	1	2	yes	—
287	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃	1	2	yes	—
290	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#102	C₂²×C₁₃	1	2	yes	—
293	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
294	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	4	8	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	8	4	no	—
303	C₂²×C₁₃	#547	1	2	yes	—
304	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
305	C₂²×C₁₃	#578	1	2	yes	—
306	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	#547	1	2	yes	—
315	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
316	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂×#41	—	2	8	no	—
319	C₂×#41	—	4	8	no	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×SD₁₆	—	2	4	no	—
330	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
331	C₂×M₁₆	—	2	8	no	—
332	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
333	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
339	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
340	#126	—	2	16	no	—
341	#124	—	2	8	no	—
342	#123	—	2	16	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
346	#121	—	2	4	no	—
347	#121	C₂³×C₁₃	1	8	yes	—
348	C₄×Q₈	—	2	8	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	D₄×C₁₃	1	4	yes	—
353	C₄×D₄	C₂³×C₁₃	1	4	yes	—
354	C₄×D₄	C₂³×C₁₃	1	4	yes	—
355	#117	—	2	4	no	—
356	#117	C₂³×C₁₃	1	8	yes	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	#107	C₂³×C₁₃	1	8	yes	—
378	#107	C₂³×C₁₃	1	8	yes	—
379	#107	C₂³×C₁₃	1	8	yes	—
380	#106	C₂³×C₁₃	1	4	yes	—
381	#106	C₂³×C₁₃	1	8	yes	—
382	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
383	#103	C₂³×C₁₃	1	4	yes	—
384	#103	C₂³×C₁₃	1	8	yes	—
385	#102	C₂³×C₁₃	1	4	yes	—
386	#102	C₂³×C₁₃	1	8	yes	—
387	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
388	C₄×C₈	C₂³×C₁₃	1	4	yes	—
389	C₂×C₁₃	—	4	4	no	—
390	C₂×C₁₃	—	8	2	no	—
391	C₂×C₁₃	#3353	1	4	yes	direct product factor
392	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
393	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
395	C₂⁴	—	2	1	no	—
396	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
397	#41	—	4	32	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	8	no	—
412	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	8	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	SD₁₆	—	2	8	no	—
432	M₁₆	—	2	16	no	—
433	C₂×C₈	—	2	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	C₁₃×#41	1	4	yes	complemented
436	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
437	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
438	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
449	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
452	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
458	C₄²	—	2	8	no	—
459	C₄²	—	2	4	no	—
460	C₄²	C₂×D₄×C₁₃	1	2	yes	—
461	C₄²	C₂⁴×C₁₃	1	2	yes	—
462	C₁₃	C₂×#3353	1	1	yes	characteristic, direct product factor, Sylow
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
471	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	8	no	—
476	Q₈	—	4	8	no	—
477	D₄	—	2	8	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	16	no	—
481	D₄	—	4	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	4	16	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
505	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
506	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
507	C₈	—	2	4	no	—
508	C₈	—	2	2	no	—
509	C₈	C₂×C₁₃×#41	1	4	yes	complemented
510	C₂²	—	2	4	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	4	no	—
518	C₂²	C₁₃×#547	1	2	yes	—
519	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
520	C₂²	C₁₃×#578	1	2	yes	—
521	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₁₃×#547	1	2	yes	—
530	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
531	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
532	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂	—	4	4	no	—
534	C₂	—	8	2	no	—
535	C₂	C₁₃×#3353	1	4	yes	direct product factor
536	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
537	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3353	C₂	direct (N × H)
4. C₂×C₁₃×#500	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#482	C₂	semidirect
7. C₂×C₁₃×#475	C₂	semidirect
8. C₂×C₁₃×#474	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#428	C₂	semidirect
17. C₁₃×#556	C₂²	semidirect
34. C₁₃×#500	C₂²	semidirect
35. C₁₃×#484	C₂²	semidirect
36. C₁₃×#482	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#468	C₂²	semidirect
40. C₄×C₁₃×SD₁₆	C₂²	semidirect
41. C₁₃×#436	C₂²	semidirect
42. C₁₃×#428	C₂²	semidirect
126. C₂×#3353	C₁₃	direct (N × H)
167. C₂×C₈×C₁₃	#41	semidirect
194. C₂×#556	C₂×C₁₃	semidirect
196. #3353	C₂×C₁₃	direct (N × H)
197. C₂×#500	C₂×C₁₃	semidirect
198. C₂×#484	C₂×C₁₃	semidirect
199. C₂×#482	C₂×C₁₃	semidirect
200. C₂×#475	C₂×C₁₃	semidirect
201. C₂×#474	C₂×C₁₃	semidirect
202. C₂×#468	C₂×C₁₃	semidirect
203. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
204. C₂×#436	C₂×C₁₃	semidirect
205. C₂×#428	C₂×C₁₃	semidirect
252. C₈×C₁₃	C₂×#41	semidirect
257. #556	C₂²×C₁₃	semidirect
274. #500	C₂²×C₁₃	semidirect
275. #484	C₂²×C₁₃	semidirect
276. #482	C₂²×C₁₃	semidirect
277. #475	C₂²×C₁₃	semidirect
278. #474	C₂²×C₁₃	semidirect
279. #468	C₂²×C₁₃	semidirect
280. C₄×SD₁₆	C₂²×C₁₃	semidirect
281. #436	C₂²×C₁₃	semidirect
282. #428	C₂²×C₁₃	semidirect
391. C₂×C₁₃	#3353	direct (N × H)
435. C₂×C₈	C₁₃×#41	semidirect
462. C₁₃	C₂×#3353	direct (N × H)
509. C₈	C₂×C₁₃×#41	semidirect
535. C₂	C₁₃×#3353	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×#547	2
C₁₃×#3353	2
C₂×C₁₃×#500	2
C₂×C₁₃×#484	2
C₂×C₁₃×#482	2
C₂×C₁₃×#475	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#436	2
C₂×C₁₃×#428	2
C₂×#3353	13

Subgroups — C2×C13×#3353 #15747585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3353 #15747585