Subgroups — C₁₃×#18017 #15704356

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#483	C₄	1	1	yes	characteristic
19	C₁₃×#480	C₄	1	1	yes	characteristic
20	C₁₃×#479	C₄	1	1	yes	characteristic
21	C₁₃×#479	C₄	1	1	yes	characteristic
22	C₁₃×#464	C₄	1	1	yes	characteristic
23	C₁₃×#464	C₄	1	1	yes	characteristic
24	C₁₃×#451	C₄	1	1	yes	characteristic
25	C₁₃×#448	C₄	1	1	yes	characteristic
26	C₁₃×#446	—	2	1	no	—
27	C₁₃×#446	—	2	1	no	—
28	C₁₃×#446	C₂²	1	1	yes	characteristic
29	C₁₃×#446	C₂²	1	1	yes	characteristic
30	C₁₃×#446	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×#436	C₂²	1	1	yes	characteristic
39	C₁₃×#435	—	2	1	no	—
40	C₈×D₄×C₁₃	—	2	1	no	—
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#432	—	2	1	no	—
44	C₁₃×#432	C₂²	1	1	yes	characteristic
45	C₁₃×#431	—	2	1	no	—
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₁₃×#431	C₂²	1	1	yes	characteristic
48	C₁₃×#424	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×#335	C₂²	1	1	yes	characteristic
53	C₁₃×#334	C₂²	1	1	yes	characteristic
54	C₁₃×#334	C₂²	1	1	yes	characteristic
55	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×#322	C₂²	1	1	yes	characteristic
64	C₁₃×#322	C₂²	1	1	yes	characteristic
65	C₈²×C₁₃	C₂²	1	1	yes	characteristic
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₁₃×#126	—	2	1	no	—
77	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
78	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#123	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₃	—	2	1	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#117	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
100	C₁₃×C₄⋊C₈	—	2	1	no	—
101	C₁₃×C₄⋊C₈	—	2	1	no	—
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
121	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
122	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	1	no	—
125	C₁₃×C₂²⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	1	no	—
132	C₁₃×#97	—	2	1	no	—
133	C₁₃×#97	—	2	1	no	—
134	C₄×C₈×C₁₃	—	2	1	no	—
135	C₄×C₈×C₁₃	—	2	1	no	—
136	C₄×C₈×C₁₃	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#18017	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	4	1	no	—
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	2	no	—
160	C₁₃×Q₁₆	—	4	1	no	—
161	C₁₃×SD₁₆	—	2	2	no	—
162	C₁₃×SD₁₆	—	4	1	no	—
163	C₁₃×M₁₆	—	8	1	no	—
164	C₂×C₈×C₁₃	—	2	4	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	8	1	no	—
172	C₂×C₈×C₁₃	—	8	1	no	—
173	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	#41	1	1	yes	characteristic
207	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
208	#3108	C₂×C₁₃	1	1	yes	characteristic
209	#2994	C₂×C₁₃	1	1	yes	characteristic
210	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1591	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1590	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1588	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1585	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1573	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1494	C₂×C₁₃	1	1	yes	characteristic
221	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1450	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	#131	1	2	yes	—
232	D₄×C₁₃	—	2	1	no	—
233	D₄×C₁₃	—	2	1	no	—
234	D₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	2	2	no	—
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	1	no	—
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	#529	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	#483	C₄×C₁₃	1	1	yes	characteristic
274	#480	C₄×C₁₃	1	1	yes	characteristic
275	#479	C₄×C₁₃	1	1	yes	characteristic
276	#479	C₄×C₁₃	1	1	yes	characteristic
277	#464	C₄×C₁₃	1	1	yes	characteristic
278	#464	C₄×C₁₃	1	1	yes	characteristic
279	#451	C₄×C₁₃	1	1	yes	characteristic
280	#448	C₄×C₁₃	1	1	yes	characteristic
281	#446	—	2	1	no	—
282	#446	—	2	1	no	—
283	#446	C₂²×C₁₃	1	1	yes	characteristic
284	#446	C₂²×C₁₃	1	1	yes	characteristic
285	#446	C₂²×C₁₃	1	1	yes	characteristic
286	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
292	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
293	#436	C₂²×C₁₃	1	1	yes	characteristic
294	#435	—	2	1	no	—
295	C₈×D₄	—	2	1	no	—
296	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
297	#433	—	2	1	no	—
298	#432	—	2	1	no	—
299	#432	C₂²×C₁₃	1	1	yes	characteristic
300	#431	—	2	1	no	—
301	#431	C₂²×C₁₃	1	1	yes	characteristic
302	#431	C₂²×C₁₃	1	1	yes	characteristic
303	#424	—	2	1	no	—
304	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
306	#335	C₂²×C₁₃	1	1	yes	characteristic
307	#335	C₂²×C₁₃	1	1	yes	characteristic
308	#334	C₂²×C₁₃	1	1	yes	characteristic
309	#334	C₂²×C₁₃	1	1	yes	characteristic
310	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
311	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
312	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
313	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
314	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	#322	C₂²×C₁₃	1	1	yes	characteristic
319	#322	C₂²×C₁₃	1	1	yes	characteristic
320	C₈²	C₂²×C₁₃	1	1	yes	characteristic
321	C₈²	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	1	no	—
327	C₂²×C₁₃	#443	1	2	yes	—
328	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
341	C₄×C₁₃	#568	1	1	yes	characteristic
342	C₄×C₁₃	#577	1	1	yes	characteristic
343	C₄×C₁₃	#578	1	1	yes	characteristic
344	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
345	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
346	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
347	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
348	C₂×SD₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
349	C₂×M₁₆	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	#126	—	2	1	no	—
354	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
355	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
356	#123	—	2	1	no	—
357	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
358	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
362	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
368	#117	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
374	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
375	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
376	#106	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
385	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
386	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
387	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
392	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
393	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
394	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
395	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
397	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
398	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
399	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
405	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
406	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
407	#97	—	2	1	no	—
408	#97	—	2	1	no	—
409	#97	—	2	1	no	—
410	#97	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₁₃	—	2	2	no	—
422	C₂×C₁₃	—	8	1	no	—
423	C₂×C₁₃	#2933	1	1	yes	characteristic
424	C₂×C₁₃	#2947	1	1	yes	characteristic
425	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
430	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
431	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
440	Q₁₆	—	2	2	no	—
441	Q₁₆	—	4	1	no	—
442	SD₁₆	—	2	2	no	—
443	SD₁₆	—	4	1	no	—
444	M₁₆	—	8	1	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	8	1	no	—
453	C₂×C₈	—	8	1	no	—
454	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
456	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄²	C₁₃×#41	1	1	yes	characteristic
488	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₁₃	#18017	1	1	yes	characteristic, direct product factor, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	4	2	no	—
498	Q₈	C₁₃×#131	1	2	yes	—
499	D₄	—	2	1	no	—
500	D₄	—	2	1	no	—
501	D₄	—	4	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	C₁₃×#443	1	2	yes	—
544	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
557	C₄	C₁₃×#568	1	1	yes	characteristic
558	C₄	C₁₃×#577	1	1	yes	characteristic
559	C₄	C₁₃×#578	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	8	1	no	—
562	C₂	C₁₃×#2933	1	1	yes	characteristic
563	C₂	C₁₃×#2947	1	1	yes	characteristic
564	C₂	C₂×C₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#121	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2984	C₂	semidirect
4. C₁₃×#1591	C₂	semidirect
5. C₁₃×#1590	C₂	semidirect
6. C₁₃×#1588	C₂	semidirect
7. C₁₃×#1587	C₂	semidirect
8. C₁₃×#1587	C₂	semidirect
9. C₁₃×#1585	C₂	semidirect
10. C₈×C₁₃×Q₁₆	C₂	semidirect
11. C₈×C₁₃×SD₁₆	C₂	semidirect
12. C₁₃×#1573	C₂	semidirect
14. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
15. C₁₃×#1450	C₂	semidirect
144. #18017	C₁₃	direct (N × H)
210. #2984	C₂×C₁₃	semidirect
211. #1591	C₂×C₁₃	semidirect
212. #1590	C₂×C₁₃	semidirect
213. #1588	C₂×C₁₃	semidirect
214. #1587	C₂×C₁₃	semidirect
215. #1587	C₂×C₁₃	semidirect
216. #1585	C₂×C₁₃	semidirect
217. C₈×Q₁₆	C₂×C₁₃	semidirect
218. C₈×SD₁₆	C₂×C₁₃	semidirect
219. #1573	C₂×C₁₃	semidirect
221. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
222. #1450	C₂×C₁₃	semidirect
489. C₁₃	#18017	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3108	2
C₁₃×#2994	2
C₁₃×#2984	2
C₁₃×#1591	2
C₁₃×#1590	2
C₁₃×#1588	2
C₁₃×#1587	2
C₁₃×#1585	2
C₈×C₁₃×Q₁₆	2
C₈×C₁₃×SD₁₆	2
C₁₃×#1573	2
C₁₃×#1494	2
C₂×C₁₃×Q₈⋊C₈	2
C₁₃×#1450	2
#18017	13

Subgroups — C13×#18017 #15704356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18017 #15704356