Subgroups — C₂×C₁₃×#3330 #15747489

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3330	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
18	C₁₃×#547	—	2	4	no	—
19	C₁₃×#547	—	2	4	no	—
20	C₁₃×#547	C₂²	1	8	yes	complemented
21	C₁₃×#547	C₂²	1	8	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₁₃×#123	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	—	2	1	no	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#487	C₂²	1	8	yes	complemented
36	C₁₃×#484	C₂²	1	16	yes	complemented
37	C₁₃×#474	C₂²	1	8	yes	complemented
38	C₁₃×#468	C₂²	1	16	yes	complemented
39	C₁₃×#461	C₂²	1	8	yes	complemented
40	C₁₃×#449	C₂²	1	16	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#417	C₂²	1	16	yes	complemented
47	C₂×C₁₃×#103	C₂²	1	2	yes	—
48	C₂×C₁₃×#103	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	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	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	8	no	—
58	C₂×C₁₃×#41	—	4	4	no	—
59	C₂×C₁₃×#41	—	4	8	no	—
60	C₂×C₁₃×#41	C₂³	1	8	yes	—
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂×C₁₃×SD₁₆	—	4	4	no	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×D₈	—	2	4	no	—
76	C₂×C₁₃×D₈	C₂³	1	4	yes	—
77	C₂×C₁₃×M₁₆	—	4	4	no	—
78	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×#123	—	2	16	no	—
87	C₁₃×#123	—	2	16	no	—
88	C₁₃×C₂²⋊Q₈	—	2	4	no	—
89	C₁₃×C₂²⋊Q₈	—	2	8	no	—
90	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
91	C₁₃×#121	—	2	8	no	—
92	C₁₃×#121	—	2	4	no	—
93	C₁₃×#121	C₂³	1	8	yes	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	D₄	1	4	yes	—
97	C₄×D₄×C₁₃	C₂³	1	4	yes	—
98	C₄×D₄×C₁₃	C₂³	1	4	yes	—
99	C₄×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	C₂³	1	4	yes	—
119	C₁₃×#107	C₂³	1	8	yes	—
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₃×#103	C₂³	1	8	yes	—
122	C₁₃×#103	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	4	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×#102	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₈×C₁₃	C₂³	1	4	yes	—
129	C₂×#3330	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	C₂×D₄	1	2	yes	—
133	C₁₃×#41	—	2	16	no	—
134	C₁₃×#41	—	4	8	no	—
135	C₁₃×#41	—	4	16	no	—
136	C₁₃×#41	—	4	32	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	4	4	no	—
142	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	4	8	no	—
152	C₂×D₄×C₁₃	—	4	8	no	—
153	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂×D₄×C₁₃	#41	1	4	yes	complemented
155	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
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	2	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	4	8	no	—
168	C₂²×C₄×C₁₃	—	4	8	no	—
169	C₂²×C₄×C₁₃	—	4	4	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×SD₁₆	—	4	8	no	—
178	C₁₃×D₈	—	2	8	no	—
179	C₁₃×M₁₆	—	4	8	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	4	no	—
183	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
203	C₄²×C₁₃	C₂×D₄	1	2	yes	—
204	C₄²×C₁₃	C₂⁴	1	2	yes	—
205	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3330	C₂×C₁₃	1	16	yes	direct product factor
208	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#484	C₂×C₁₃	1	2	yes	complemented
210	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#468	C₂×C₁₃	1	2	yes	complemented
212	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#449	C₂×C₁₃	1	2	yes	complemented
214	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#417	C₂×C₁₃	1	2	yes	complemented
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	2	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
229	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	Q₈×C₁₃	—	2	4	no	—
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	4	4	no	—
233	Q₈×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	8	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	4	16	no	—
240	D₄×C₁₃	—	4	16	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	C₂×#41	1	4	yes	complemented
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	8	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	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	4	16	no	—
253	C₂×C₄×C₁₃	—	4	16	no	—
254	C₂×C₄×C₁₃	—	4	4	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	—	4	8	no	—
260	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	4	no	—
271	C₂²×#41	—	2	1	no	—
272	C₂²×#41	C₂²×C₁₃	1	2	yes	—
273	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
274	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
276	#547	—	2	4	no	—
277	#547	—	2	4	no	—
278	#547	C₂²×C₁₃	1	8	yes	complemented
279	#547	C₂²×C₁₃	1	8	yes	complemented
280	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#123	—	2	2	no	—
283	C₂×#123	—	2	2	no	—
284	C₂×C₂²⋊Q₈	—	2	1	no	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
286	C₂×#121	—	2	1	no	—
287	C₂×#121	C₂²×C₁₃	1	2	yes	—
288	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	—	2	1	no	—
292	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
293	#487	C₂²×C₁₃	1	8	yes	complemented
294	#484	C₂²×C₁₃	1	16	yes	complemented
295	#474	C₂²×C₁₃	1	8	yes	complemented
296	#468	C₂²×C₁₃	1	16	yes	complemented
297	#461	C₂²×C₁₃	1	8	yes	complemented
298	#449	C₂²×C₁₃	1	16	yes	complemented
299	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
300	#436	C₂²×C₁₃	1	8	yes	complemented
301	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#107	C₂²×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	#417	C₂²×C₁₃	1	16	yes	complemented
305	C₂×#103	C₂²×C₁₃	1	2	yes	—
306	C₂×#103	C₂²×C₁₃	1	2	yes	—
307	C₂×#103	C₂²×C₁₃	1	2	yes	—
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	2	yes	—
310	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
312	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×C₁₃	—	2	4	no	—
314	C₂²×C₁₃	—	2	4	no	—
315	C₂²×C₁₃	—	2	4	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	4	8	no	—
318	C₂²×C₁₃	—	4	8	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	4	2	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	8	4	no	—
325	C₂²×C₁₃	#546	1	2	yes	—
326	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
327	C₂²×C₁₃	#578	1	2	yes	—
328	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
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	—	4	4	no	—
335	C₄×C₁₃	#546	1	2	yes	—
336	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
337	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
338	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×#41	—	2	8	no	—
340	C₂×#41	—	2	4	no	—
341	C₂×#41	—	2	8	no	—
342	C₂×#41	—	4	4	no	—
343	C₂×#41	—	4	8	no	—
344	C₂×#41	C₂³×C₁₃	1	8	yes	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	2	no	—
349	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	—	2	2	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	2	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×SD₁₆	—	4	4	no	—
358	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
359	C₂×D₈	—	2	4	no	—
360	C₂×D₈	C₂³×C₁₃	1	4	yes	—
361	C₂×M₁₆	—	4	4	no	—
362	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
365	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
369	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
370	#123	—	2	16	no	—
371	#123	—	2	16	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	—	2	8	no	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
375	#121	—	2	8	no	—
376	#121	—	2	4	no	—
377	#121	C₂³×C₁₃	1	8	yes	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	D₄×C₁₃	1	4	yes	—
381	C₄×D₄	C₂³×C₁₃	1	4	yes	—
382	C₄×D₄	C₂³×C₁₃	1	4	yes	—
383	C₄×D₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	8	no	—
391	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
402	#107	C₂³×C₁₃	1	4	yes	—
403	#107	C₂³×C₁₃	1	8	yes	—
404	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
405	#103	C₂³×C₁₃	1	8	yes	—
406	#103	C₂³×C₁₃	1	8	yes	—
407	#103	C₂³×C₁₃	1	8	yes	—
408	#102	C₂³×C₁₃	1	4	yes	—
409	#102	C₂³×C₁₃	1	8	yes	—
410	#102	C₂³×C₁₃	1	4	yes	—
411	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
412	C₄×C₈	C₂³×C₁₃	1	4	yes	—
413	C₂×C₁₃	—	4	4	no	—
414	C₂×C₁₃	—	4	4	no	—
415	C₂×C₁₃	—	8	2	no	—
416	C₂×C₁₃	#3330	1	4	yes	direct product factor
417	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
418	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
423	#41	—	2	16	no	—
424	#41	—	4	8	no	—
425	#41	—	4	16	no	—
426	#41	—	4	32	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₂×D₄	C₁₃×#41	1	4	yes	complemented
445	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	4	8	no	—
458	C₂²×C₄	—	4	8	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
467	SD₁₆	—	4	8	no	—
468	D₈	—	2	8	no	—
469	M₁₆	—	4	8	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
474	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
475	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
485	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
486	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
487	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
493	C₄²	C₂×D₄×C₁₃	1	2	yes	—
494	C₄²	C₂⁴×C₁₃	1	2	yes	—
495	C₁₃	C₂×#3330	1	1	yes	characteristic, direct product factor, Sylow
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
508	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	4	no	—
511	Q₈	—	4	4	no	—
512	Q₈	—	4	8	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	16	no	—
519	D₄	—	4	16	no	—
520	D₄	—	4	2	no	—
521	D₄	C₂×C₁₃×#41	1	4	yes	complemented
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	4	16	no	—
532	C₂×C₄	—	4	16	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
544	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
545	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
546	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₁₃×#546	1	2	yes	—
563	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
564	C₂²	C₁₃×#578	1	2	yes	—
565	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	4	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	4	no	—
572	C₄	C₁₃×#546	1	2	yes	—
573	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
574	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
575	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂	—	4	4	no	—
577	C₂	—	4	4	no	—
578	C₂	—	8	2	no	—
579	C₂	C₁₃×#3330	1	4	yes	direct product factor
580	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
581	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₂	C₂×C₁₃×#578	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#547	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3330	C₂	direct (N × H)
4. C₂×C₁₃×#487	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#474	C₂	semidirect
7. C₂×C₁₃×#468	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#449	C₂	semidirect
10. C₂×C₄×C₁₃×D₈	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#417	C₂	semidirect
20. C₁₃×#547	C₂²	semidirect
21. C₁₃×#547	C₂²	semidirect
35. C₁₃×#487	C₂²	semidirect
36. C₁₃×#484	C₂²	semidirect
37. C₁₃×#474	C₂²	semidirect
38. C₁₃×#468	C₂²	semidirect
39. C₁₃×#461	C₂²	semidirect
40. C₁₃×#449	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
46. C₁₃×#417	C₂²	semidirect
129. C₂×#3330	C₁₃	direct (N × H)
154. C₂×D₄×C₁₃	#41	semidirect
205. C₂×#547	C₂×C₁₃	semidirect
206. C₂×#547	C₂×C₁₃	semidirect
207. #3330	C₂×C₁₃	direct (N × H)
208. C₂×#487	C₂×C₁₃	semidirect
209. C₂×#484	C₂×C₁₃	semidirect
210. C₂×#474	C₂×C₁₃	semidirect
211. C₂×#468	C₂×C₁₃	semidirect
212. C₂×#461	C₂×C₁₃	semidirect
213. C₂×#449	C₂×C₁₃	semidirect
214. C₂×C₄×D₈	C₂×C₁₃	semidirect
215. C₂×#436	C₂×C₁₃	semidirect
216. C₂×#417	C₂×C₁₃	semidirect
242. D₄×C₁₃	C₂×#41	semidirect
278. #547	C₂²×C₁₃	semidirect
279. #547	C₂²×C₁₃	semidirect
293. #487	C₂²×C₁₃	semidirect
294. #484	C₂²×C₁₃	semidirect
295. #474	C₂²×C₁₃	semidirect
296. #468	C₂²×C₁₃	semidirect
297. #461	C₂²×C₁₃	semidirect
298. #449	C₂²×C₁₃	semidirect
299. C₄×D₈	C₂²×C₁₃	semidirect
300. #436	C₂²×C₁₃	semidirect
304. #417	C₂²×C₁₃	semidirect
416. C₂×C₁₃	#3330	direct (N × H)
444. C₂×D₄	C₁₃×#41	semidirect
495. C₁₃	C₂×#3330	direct (N × H)
521. D₄	C₂×C₁₃×#41	semidirect
579. C₂	C₁₃×#3330	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×#547	2
C₁₃×#3330	2
C₂×C₁₃×#487	2
C₂×C₁₃×#484	2
C₂×C₁₃×#474	2
C₂×C₁₃×#468	2
C₂×C₁₃×#461	2
C₂×C₁₃×#449	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×C₁₃×#417	2
C₂×#3330	13

Subgroups — C2×C13×#3330 #15747489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3330 #15747489