Subgroups — C₂×C₁₃×#3238 #15747188

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3238	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#483	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#480	C₂	1	2	yes	maximal
8	C₂×C₁₃×#477	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#476	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	—	2	1	no	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
18	C₁₃×#529	—	2	4	no	—
19	C₁₃×#529	C₂²	1	8	yes	—
20	C₂×C₁₃×#126	—	2	1	no	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	—	2	1	no	—
30	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#501	C₂²	1	16	yes	complemented
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#483	C₂²	1	16	yes	complemented
36	C₁₃×#480	C₂²	1	16	yes	—
37	C₁₃×#477	C₂²	1	16	yes	complemented
38	C₁₃×#476	C₂²	1	16	yes	complemented
39	C₁₃×#432	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#107	C₂²	1	4	yes	—
41	C₂×C₁₃×#106	C₂²	1	4	yes	—
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	4	yes	—
44	C₂×C₁₃×#102	C₂²	1	4	yes	—
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×C₁₃×#97	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	8	no	—
50	C₂²×Q₈×C₁₃	—	4	8	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	8	no	—
63	C₁₃×C₄⋊Q₈	—	2	8	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
65	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₁₃×#126	—	2	8	no	—
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	C₂³	1	4	yes	—
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×#124	C₂³	1	4	yes	—
71	C₁₃×#123	—	2	8	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	C₂³	1	4	yes	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
78	C₄×D₄×C₁₃	—	2	8	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	C₂³	1	4	yes	—
81	C₁₃×#117	—	2	8	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	D₄	1	4	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₁₃×#107	C₂³	1	16	yes	—
108	C₁₃×#106	C₂³	1	16	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
110	C₁₃×#103	C₂³	1	16	yes	—
111	C₁₃×#102	C₂³	1	16	yes	—
112	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
113	C₁₃×#97	C₂³	1	8	yes	—
114	C₂×#3238	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₃	—	2	1	no	—
116	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	2	8	no	—
120	C₂×Q₈×C₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	4	8	no	—
122	C₂×Q₈×C₁₃	—	4	8	no	—
123	C₂×Q₈×C₁₃	—	4	32	no	—
124	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	4	8	no	—
140	C₂²×C₄×C₁₃	—	4	4	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₈×C₁₃	—	2	8	no	—
152	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
166	C₁₃×C₂²⋊C₄	—	2	4	no	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂×D₄	1	4	yes	—
176	C₄²×C₁₃	C₂⁴	1	2	yes	—
177	C₄²×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
180	#3238	C₂×C₁₃	1	16	yes	direct product factor
181	C₂×#501	C₂×C₁₃	1	2	yes	complemented
182	C₂×#489	C₂×C₁₃	1	2	yes	complemented
183	C₂×#483	C₂×C₁₃	1	2	yes	complemented
184	C₂×#480	C₂×C₁₃	1	2	yes	—
185	C₂×#477	C₂×C₁₃	1	2	yes	complemented
186	C₂×#476	C₂×C₁₃	1	2	yes	complemented
187	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
195	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	4	no	—
198	Q₈×C₁₃	—	4	16	no	—
199	Q₈×C₁₃	—	4	16	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	D₄×C₁₃	—	2	4	no	—
202	D₄×C₁₃	—	4	8	no	—
203	D₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	16	no	—
218	C₂×C₄×C₁₃	—	4	8	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	#137	1	4	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	8	no	—
232	C₂³×Q₈	—	2	1	no	—
233	C₂×C₄⋊Q₈	—	2	1	no	—
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	—	2	4	no	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
239	#529	—	2	4	no	—
240	#529	C₂²×C₁₃	1	8	yes	—
241	C₂×#126	—	2	1	no	—
242	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#123	—	2	1	no	—
245	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×D₄	—	2	1	no	—
249	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#117	—	2	1	no	—
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
254	#501	C₂²×C₁₃	1	16	yes	complemented
255	#489	C₂²×C₁₃	1	16	yes	complemented
256	#483	C₂²×C₁₃	1	16	yes	complemented
257	#480	C₂²×C₁₃	1	16	yes	—
258	#477	C₂²×C₁₃	1	16	yes	complemented
259	#476	C₂²×C₁₃	1	16	yes	complemented
260	#432	C₂²×C₁₃	1	8	yes	complemented
261	C₂×#107	C₂²×C₁₃	1	4	yes	—
262	C₂×#106	C₂²×C₁₃	1	4	yes	—
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#103	C₂²×C₁₃	1	4	yes	—
265	C₂×#102	C₂²×C₁₃	1	4	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
267	C₂×#97	C₂²×C₁₃	1	2	yes	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	8	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	8	4	no	—
275	C₂²×C₁₃	#536	1	2	yes	—
276	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
277	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
278	C₂²×C₁₃	C₂×#137	1	2	yes	—
279	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	4	8	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	#536	1	2	yes	—
289	C₄×C₁₃	C₂×#137	1	4	yes	—
290	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	—	2	8	no	—
294	C₂²×Q₈	—	4	8	no	—
295	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
304	C₄⋊Q₈	—	2	4	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	8	no	—
307	C₄⋊Q₈	—	2	8	no	—
308	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
310	#126	—	2	8	no	—
311	#125	—	2	2	no	—
312	#125	C₂³×C₁₃	1	4	yes	—
313	#124	—	2	2	no	—
314	#124	C₂³×C₁₃	1	4	yes	—
315	#123	—	2	8	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
318	#121	—	2	2	no	—
319	#121	C₂³×C₁₃	1	4	yes	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
322	C₄×D₄	—	2	8	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	C₂³×C₁₃	1	4	yes	—
325	#117	—	2	8	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄²	D₄×C₁₃	1	4	yes	—
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
351	#107	C₂³×C₁₃	1	16	yes	—
352	#106	C₂³×C₁₃	1	16	yes	—
353	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
354	#103	C₂³×C₁₃	1	16	yes	—
355	#102	C₂³×C₁₃	1	16	yes	—
356	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
357	#97	C₂³×C₁₃	1	8	yes	—
358	C₂×C₁₃	—	2	4	no	—
359	C₂×C₁₃	—	8	2	no	—
360	C₂×C₁₃	#3238	1	4	yes	direct product factor
361	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
362	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
364	C₂⁴	—	2	1	no	—
365	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	4	8	no	—
371	C₂×Q₈	—	4	8	no	—
372	C₂×Q₈	—	4	32	no	—
373	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	8	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₂×C₈	—	2	8	no	—
401	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
413	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
414	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₄²	—	2	4	no	—
421	C₄²	C₂×D₄×C₁₃	1	4	yes	—
422	C₄²	C₂×D₄×C₁₃	1	2	yes	—
423	C₄²	C₂×D₄×C₁₃	1	2	yes	—
424	C₄²	C₂×D₄×C₁₃	1	4	yes	—
425	C₄²	C₂⁴×C₁₃	1	2	yes	—
426	C₄²	C₂⁴×C₁₃	1	2	yes	—
427	C₁₃	C₂×#3238	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
436	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
437	Q₈	—	2	4	no	—
438	Q₈	—	4	16	no	—
439	Q₈	—	4	16	no	—
440	Q₈	—	4	2	no	—
441	D₄	—	2	4	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	C₁₃×#137	1	4	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
470	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
471	C₈	—	2	8	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	8	4	no	—
479	C₂²	C₁₃×#536	1	2	yes	—
480	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
481	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
482	C₂²	C₂×C₁₃×#137	1	2	yes	—
483	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	8	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	C₁₃×#536	1	2	yes	—
493	C₄	C₂×C₁₃×#137	1	4	yes	—
494	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
495	C₂	—	2	4	no	—
496	C₂	—	8	2	no	—
497	C₂	C₁₃×#3238	1	4	yes	direct product factor
498	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
499	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
500	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#3238	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#483	C₂	semidirect
8. C₂×C₁₃×#477	C₂	semidirect
9. C₂×C₁₃×#476	C₂	semidirect
10. C₂×C₁₃×#432	C₂	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₁₃×#501	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#483	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#432	C₂²	semidirect
114. C₂×#3238	C₁₃	direct (N × H)
178. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
180. #3238	C₂×C₁₃	direct (N × H)
181. C₂×#501	C₂×C₁₃	semidirect
182. C₂×#489	C₂×C₁₃	semidirect
183. C₂×#483	C₂×C₁₃	semidirect
185. C₂×#477	C₂×C₁₃	semidirect
186. C₂×#476	C₂×C₁₃	semidirect
187. C₂×#432	C₂×C₁₃	semidirect
238. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
254. #501	C₂²×C₁₃	semidirect
255. #489	C₂²×C₁₃	semidirect
256. #483	C₂²×C₁₃	semidirect
258. #477	C₂²×C₁₃	semidirect
259. #476	C₂²×C₁₃	semidirect
260. #432	C₂²×C₁₃	semidirect
360. C₂×C₁₃	#3238	direct (N × H)
427. C₁₃	C₂×#3238	direct (N × H)
497. C₂	C₁₃×#3238	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#529	2
C₁₃×#3238	2
C₂×C₁₃×#501	2
C₂×C₁₃×#489	2
C₂×C₁₃×#483	2
C₂×C₁₃×#480	2
C₂×C₁₃×#477	2
C₂×C₁₃×#476	2
C₂×C₁₃×#432	2
C₂×#3238	13

Subgroups — C2×C13×#3238 #15747188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3238 #15747188