Subgroups — C₂×C₁₃×#3153 #15746977

Order 3328.

3390 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3153	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#495	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	—	2	16	no	—
14	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
15	C₂×C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
22	C₁₃×#532	—	2	4	no	—
23	C₁₃×#532	C₂²	1	8	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#124	—	2	2	no	—
27	C₂×C₁₃×#124	—	2	4	no	—
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×#124	C₂²	1	2	yes	—
30	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₄×D₄×C₁₃	—	2	2	no	—
34	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	16	yes	complemented
37	C₁₃×#496	C₂²	1	16	yes	complemented
38	C₁₃×#495	C₂²	1	32	yes	complemented
39	C₄×C₁₃×M₁₆	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₃	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	2	8	no	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	C₂³	1	8	yes	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	—	2	8	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	8	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	2	no	—
57	C₂²×D₄×C₁₃	—	2	1	no	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂³×C₄×C₁₃	D₄	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#137	—	2	64	no	—
66	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
67	C₂×C₁₃×Q₁₆	—	2	16	no	—
68	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	complemented
69	C₂×C₁₃×SD₁₆	—	2	16	no	—
70	C₂×C₁₃×SD₁₆	—	2	16	no	—
71	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	complemented
73	C₂×C₁₃×D₈	—	2	16	no	—
74	C₂×C₁₃×D₈	C₂³	1	16	yes	—
75	C₂×C₁₃×M₁₆	D₄	1	16	yes	complemented
76	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
80	C₁₃×#127	—	2	2	no	—
81	C₁₃×#127	C₂³	1	4	yes	complemented
82	C₁₃×#124	—	2	4	no	—
83	C₁₃×#124	—	2	4	no	—
84	C₁₃×#124	—	2	16	no	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	C₂³	1	8	yes	—
87	C₁₃×#124	C₂³	1	8	yes	—
88	C₁₃×#124	C₂³	1	8	yes	complemented
89	C₁₃×#121	—	2	16	no	—
90	C₄×D₄×C₁₃	—	2	16	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₄²×C₁₃	D₄	1	2	yes	—
97	C₂×C₄²×C₁₃	D₄	1	4	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₁₃×#97	C₂³	1	8	yes	complemented
102	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
103	C₂×#3153	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂⁴×C₁₃	—	4	8	no	—
108	C₂⁴×C₁₃	—	4	4	no	—
109	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₁₃×#41	—	2	16	no	—
111	C₁₃×#41	—	2	16	no	—
112	C₁₃×#41	—	4	16	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	2	8	no	—
118	C₂×Q₈×C₁₃	—	2	4	no	—
119	C₂×Q₈×C₁₃	—	2	16	no	—
120	C₂×Q₈×C₁₃	—	4	4	no	—
121	C₂×Q₈×C₁₃	—	4	8	no	—
122	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
123	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	16	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	—	4	8	no	—
135	C₂×D₄×C₁₃	—	4	4	no	—
136	C₂×D₄×C₁₃	—	4	8	no	—
137	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	8	no	—
143	C₂²×C₄×C₁₃	—	4	4	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	4	8	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₁₃×Q₁₆	—	2	32	no	—
155	C₁₃×SD₁₆	—	2	32	no	—
156	C₁₃×SD₁₆	—	2	32	no	—
157	C₁₃×D₈	—	2	32	no	—
158	C₁₃×M₁₆	C₂×D₄	1	32	yes	complemented
159	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	—
160	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	16	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	2	16	no	—
165	C₄²×C₁₃	C₂×D₄	1	8	yes	—
166	C₄²×C₁₃	C₂×D₄	1	2	yes	—
167	C₄²×C₁₃	C₂×D₄	1	2	yes	—
168	C₄²×C₁₃	C₂⁴	1	2	yes	—
169	C₄²×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
171	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
172	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#3153	C₂×C₁₃	1	16	yes	direct product factor
175	C₂×#497	C₂×C₁₃	1	2	yes	complemented
176	C₂×#496	C₂×C₁₃	1	2	yes	complemented
177	C₂×#495	C₂×C₁₃	1	4	yes	complemented
178	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	4	16	no	—
183	C₂³×C₁₃	—	4	4	no	—
184	C₂³×C₁₃	—	4	8	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	4	8	no	—
188	C₂³×C₁₃	—	8	16	no	—
189	C₂³×C₁₃	#127	1	4	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	2	8	no	—
194	Q₈×C₁₃	—	2	4	no	—
195	Q₈×C₁₃	—	4	8	no	—
196	Q₈×C₁₃	—	4	4	no	—
197	Q₈×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	2	8	no	—
200	D₄×C₁₃	—	2	4	no	—
201	D₄×C₁₃	—	4	16	no	—
202	D₄×C₁₃	—	4	16	no	—
203	D₄×C₁₃	—	4	8	no	—
204	D₄×C₁₃	—	4	4	no	—
205	D₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	4	8	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	16	no	—
215	C₂×C₄×C₁₃	#127	1	4	yes	—
216	C₂×C₄×C₁₃	#127	1	8	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₈×C₁₃	C₂²×D₄	1	16	yes	—
225	C₂²×#41	C₂²×C₁₃	1	2	yes	—
226	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#137	—	2	16	no	—
229	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
230	C₂×AGL(1,ℤ/8)	—	2	16	no	—
231	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	16	yes	complemented
232	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
233	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
234	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
235	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
236	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
237	#532	—	2	4	no	—
238	#532	C₂²×C₁₃	1	8	yes	complemented
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#124	—	2	2	no	—
242	C₂×#124	—	2	4	no	—
243	C₂×#124	C₂²×C₁₃	1	2	yes	—
244	C₂×#124	C₂²×C₁₃	1	2	yes	—
245	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
246	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
247	C₂×#121	—	2	2	no	—
248	C₂×C₄×D₄	—	2	2	no	—
249	C₂²×C₂²⋊C₄	—	2	2	no	—
250	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
251	#497	C₂²×C₁₃	1	16	yes	complemented
252	#496	C₂²×C₁₃	1	16	yes	complemented
253	#495	C₂²×C₁₃	1	32	yes	complemented
254	C₄×M₁₆	C₂²×C₁₃	1	8	yes	complemented
255	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
256	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
257	C₂²×C₁₃	—	2	8	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	4	8	no	—
262	C₂²×C₁₃	—	4	8	no	—
263	C₂²×C₁₃	—	8	16	no	—
264	C₂²×C₁₃	—	8	8	no	—
265	C₂²×C₁₃	—	8	8	no	—
266	C₂²×C₁₃	C₂×#127	1	4	yes	—
267	C₂²×C₁₃	C₂×#127	1	2	yes	—
268	C₂²×C₁₃	#575	1	4	yes	—
269	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
270	C₄×C₁₃	—	2	4	no	—
271	C₄×C₁₃	—	2	4	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	C₂×#127	1	4	yes	—
275	C₄×C₁₃	C₂×#127	1	2	yes	—
276	C₄×C₁₃	C₂³×D₄	1	2	yes	—
277	C₂⁵	—	2	1	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	8	no	—
280	C₂×#41	—	2	8	no	—
281	C₂×#41	C₂³×C₁₃	1	8	yes	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	—	2	8	no	—
285	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
286	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
287	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
294	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
295	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	D₄×C₁₃	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
300	#137	—	2	64	no	—
301	AGL(1,ℤ/8)	—	2	64	no	—
302	C₂×Q₁₆	—	2	16	no	—
303	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	complemented
304	C₂×SD₁₆	—	2	16	no	—
305	C₂×SD₁₆	—	2	16	no	—
306	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
307	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	complemented
308	C₂×D₈	—	2	16	no	—
309	C₂×D₈	C₂³×C₁₃	1	16	yes	—
310	C₂×M₁₆	D₄×C₁₃	1	16	yes	complemented
311	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
312	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
315	#127	—	2	2	no	—
316	#127	C₂³×C₁₃	1	4	yes	complemented
317	#124	—	2	4	no	—
318	#124	—	2	4	no	—
319	#124	—	2	16	no	—
320	#124	—	2	4	no	—
321	#124	C₂³×C₁₃	1	8	yes	—
322	#124	C₂³×C₁₃	1	8	yes	—
323	#124	C₂³×C₁₃	1	8	yes	complemented
324	#121	—	2	16	no	—
325	C₄×D₄	—	2	16	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	—	2	4	no	—
329	C₂×C₂²⋊C₄	—	2	16	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₄²	D₄×C₁₃	1	2	yes	—
332	C₂×C₄²	D₄×C₁₃	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
336	#97	C₂³×C₁₃	1	8	yes	complemented
337	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
338	C₂×C₁₃	—	2	4	no	—
339	C₂×C₁₃	—	8	4	no	—
340	C₂×C₁₃	—	8	4	no	—
341	C₂×C₁₃	#3153	1	4	yes	direct product factor
342	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#575	1	2	yes	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	4	8	no	—
348	C₂⁴	—	4	4	no	—
349	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
350	#41	—	2	16	no	—
351	#41	—	2	16	no	—
352	#41	—	4	16	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	16	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	—	4	8	no	—
362	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
363	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	16	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
378	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
394	Q₁₆	—	2	32	no	—
395	SD₁₆	—	2	32	no	—
396	SD₁₆	—	2	32	no	—
397	D₈	—	2	32	no	—
398	M₁₆	C₂×D₄×C₁₃	1	32	yes	complemented
399	C₂×C₈	C₂×D₄×C₁₃	1	16	yes	—
400	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
401	C₄⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	16	no	—
403	C₂²⋊C₄	—	2	16	no	—
404	C₂²⋊C₄	—	2	16	no	—
405	C₄²	C₂×D₄×C₁₃	1	8	yes	—
406	C₄²	C₂×D₄×C₁₃	1	2	yes	—
407	C₄²	C₂×D₄×C₁₃	1	2	yes	—
408	C₄²	C₂⁴×C₁₃	1	2	yes	—
409	C₄²	C₂⁴×C₁₃	1	2	yes	—
410	C₁₃	C₂×#3153	1	1	yes	characteristic, direct product factor, Sylow
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	4	16	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	8	no	—
420	C₂³	—	8	16	no	—
421	C₂³	C₁₃×#127	1	4	yes	—
422	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
423	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	Q₈	—	2	4	no	—
425	Q₈	—	2	8	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	8	no	—
428	Q₈	—	4	4	no	—
429	Q₈	—	4	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	2	4	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	16	no	—
435	D₄	—	4	8	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	16	no	—
447	C₂×C₄	C₁₃×#127	1	4	yes	—
448	C₂×C₄	C₁₃×#127	1	8	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
455	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
456	C₈	C₂²×D₄×C₁₃	1	16	yes	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	4	8	no	—
460	C₂²	—	4	8	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	16	no	—
464	C₂²	—	8	8	no	—
465	C₂²	—	8	8	no	—
466	C₂²	C₂×C₁₃×#127	1	4	yes	—
467	C₂²	C₂×C₁₃×#127	1	2	yes	—
468	C₂²	C₁₃×#575	1	4	yes	—
469	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	4	no	—
474	C₄	C₂×C₁₃×#127	1	4	yes	—
475	C₄	C₂×C₁₃×#127	1	2	yes	—
476	C₄	C₂³×D₄×C₁₃	1	2	yes	—
477	C₂	—	2	4	no	—
478	C₂	—	8	4	no	—
479	C₂	—	8	4	no	—
480	C₂	C₁₃×#3153	1	4	yes	direct product factor
481	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
482	C₂	C₂×C₁₃×#575	1	2	yes	—

	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₁₃×#532	C₂	semidirect
4. C₂²×C₁₃×#124	C₂	semidirect
5. C₁₃×#3153	C₂	direct (N × H)
6. C₂×C₁₃×#497	C₂	semidirect
7. C₂×C₁₃×#496	C₂	semidirect
8. C₂×C₁₃×#495	C₂	semidirect
9. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂²×C₁₃×Q₁₆	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₄×C₁₃×M₁₆	C₂²	semidirect
40. C₂×C₁₃×#97	C₂²	semidirect
41. C₂×C₄×C₈×C₁₃	C₂²	semidirect
68. C₂×C₁₃×Q₁₆	C₂³	semidirect
72. C₂×C₁₃×SD₁₆	C₂³	semidirect
75. C₂×C₁₃×M₁₆	D₄	semidirect
79. C₁₃×C₄⋊Q₈	C₂³	semidirect
81. C₁₃×#127	C₂³	semidirect
88. C₁₃×#124	C₂³	semidirect
101. C₁₃×#97	C₂³	semidirect
102. C₄×C₈×C₁₃	C₂³	semidirect
103. C₂×#3153	C₁₃	direct (N × H)
158. C₁₃×M₁₆	C₂×D₄	semidirect
170. C₂²×#137	C₂×C₁₃	semidirect
171. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
172. C₂×#532	C₂×C₁₃	semidirect
173. C₂²×#124	C₂×C₁₃	semidirect
174. #3153	C₂×C₁₃	direct (N × H)
175. C₂×#497	C₂×C₁₃	semidirect
176. C₂×#496	C₂×C₁₃	semidirect
177. C₂×#495	C₂×C₁₃	semidirect
178. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
229. C₂×#137	C₂²×C₁₃	semidirect
231. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
232. C₂²×Q₁₆	C₂²×C₁₃	semidirect
234. C₂²×SD₁₆	C₂²×C₁₃	semidirect
238. #532	C₂²×C₁₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
240. C₂×#127	C₂²×C₁₃	semidirect
245. C₂×#124	C₂²×C₁₃	semidirect
246. C₂×#124	C₂²×C₁₃	semidirect
251. #497	C₂²×C₁₃	semidirect
252. #496	C₂²×C₁₃	semidirect
253. #495	C₂²×C₁₃	semidirect
254. C₄×M₁₆	C₂²×C₁₃	semidirect
255. C₂×#97	C₂²×C₁₃	semidirect
256. C₂×C₄×C₈	C₂²×C₁₃	semidirect
303. C₂×Q₁₆	C₂³×C₁₃	semidirect
307. C₂×SD₁₆	C₂³×C₁₃	semidirect
310. C₂×M₁₆	D₄×C₁₃	semidirect
314. C₄⋊Q₈	C₂³×C₁₃	semidirect
316. #127	C₂³×C₁₃	semidirect
323. #124	C₂³×C₁₃	semidirect
336. #97	C₂³×C₁₃	semidirect
337. C₄×C₈	C₂³×C₁₃	semidirect
341. C₂×C₁₃	#3153	direct (N × H)
398. M₁₆	C₂×D₄×C₁₃	semidirect
410. C₁₃	C₂×#3153	direct (N × H)
480. C₂	C₁₃×#3153	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×#137	2
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#532	2
C₂²×C₁₃×#124	2
C₁₃×#3153	2
C₂×C₁₃×#497	2
C₂×C₁₃×#496	2
C₂×C₁₃×#495	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3153	13

Subgroups — C2×C13×#3153 #15746977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3153 #15746977