Subgroups — C₁₃×#18032 #15704371

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1497	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1479	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#484	C₄	1	1	yes	characteristic
19	C₁₃×#484	C₄	1	1	yes	characteristic
20	C₁₃×#477	C₄	1	1	yes	characteristic
21	C₁₃×#477	C₄	1	1	yes	characteristic
22	C₁₃×#462	C₄	1	1	yes	characteristic
23	C₁₃×#462	C₄	1	1	yes	characteristic
24	C₁₃×#451	C₄	1	1	yes	characteristic
25	C₁₃×#451	C₄	1	1	yes	characteristic
26	C₁₃×#446	—	2	1	no	—
27	C₁₃×#446	—	2	1	no	—
28	C₁₃×#446	—	2	1	no	—
29	C₁₃×#446	C₂²	1	1	yes	characteristic
30	C₁₃×#446	C₂²	1	1	yes	characteristic
31	C₁₃×#446	C₂²	1	1	yes	characteristic
32	C₁₃×#446	C₂²	1	1	yes	characteristic
33	C₈×Q₈×C₁₃	—	2	1	no	—
34	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
42	C₁₃×#433	—	2	1	no	—
43	C₁₃×#433	—	2	1	no	—
44	C₁₃×#432	—	2	1	no	—
45	C₁₃×#432	C₂²	1	1	yes	characteristic
46	C₁₃×#431	—	2	1	no	—
47	C₁₃×#431	C₂²	1	1	yes	characteristic
48	C₁₃×#431	C₂²	1	1	yes	characteristic
49	C₁₃×#431	C₂²	1	1	yes	characteristic
50	C₁₃×#431	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×#322	C₂²	1	1	yes	characteristic
64	C₁₃×#322	C₂²	1	1	yes	characteristic
65	C₁₃×#322	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×Q₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
74	C₁₃×#125	—	2	1	no	—
75	C₁₃×C₂²⋊Q₈	—	2	1	no	—
76	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₃	—	2	1	no	—
79	C₄×Q₈×C₁₃	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#117	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	—	2	1	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#103	C₂×C₄	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×C₂²⋊C₈	—	2	1	no	—
122	C₁₃×C₂²⋊C₈	—	2	1	no	—
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
128	C₁₃×#97	—	2	1	no	—
129	C₁₃×#97	—	2	1	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	1	no	—
132	C₁₃×#97	—	2	1	no	—
133	C₄×C₈×C₁₃	—	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	#18032	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	4	1	no	—
149	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×Q₈×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	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
158	C₁₃×Q₁₆	—	2	2	no	—
159	C₁₃×Q₁₆	—	2	2	no	—
160	C₁₃×Q₁₆	—	4	1	no	—
161	C₁₃×Q₁₆	—	4	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	#41	1	1	yes	characteristic
203	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
204	#3104	C₂×C₁₃	1	1	yes	characteristic
205	#2986	C₂×C₁₃	1	1	yes	characteristic
206	#2984	C₂×C₁₃	1	1	yes	characteristic
207	#1593	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1591	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1587	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1572	C₂×C₁₃	1	1	yes	characteristic
216	#1497	C₂×C₁₃	1	1	yes	characteristic
217	#1479	C₂×C₁₃	1	1	yes	characteristic
218	#1454	C₂×C₁₃	1	1	yes	characteristic
219	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	1	no	—
221	Q₈×C₁₃	—	2	1	no	—
222	Q₈×C₁₃	—	2	1	no	—
223	Q₈×C₁₃	—	2	1	no	—
224	Q₈×C₁₃	—	2	1	no	—
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	4	2	no	—
228	Q₈×C₁₃	—	4	2	no	—
229	Q₈×C₁₃	#131	1	2	yes	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₈×C₁₃	—	2	1	no	—
252	C₈×C₁₃	—	2	1	no	—
253	C₈×C₁₃	—	2	1	no	—
254	C₈×C₁₃	—	2	1	no	—
255	C₈×C₁₃	—	2	1	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	—	2	1	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₈×C₁₃	—	4	1	no	—
261	C₈×C₁₃	—	4	1	no	—
262	C₈×C₁₃	—	4	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	#533	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	#484	C₄×C₁₃	1	1	yes	characteristic
268	#484	C₄×C₁₃	1	1	yes	characteristic
269	#477	C₄×C₁₃	1	1	yes	characteristic
270	#477	C₄×C₁₃	1	1	yes	characteristic
271	#462	C₄×C₁₃	1	1	yes	characteristic
272	#462	C₄×C₁₃	1	1	yes	characteristic
273	#451	C₄×C₁₃	1	1	yes	characteristic
274	#451	C₄×C₁₃	1	1	yes	characteristic
275	#446	—	2	1	no	—
276	#446	—	2	1	no	—
277	#446	—	2	1	no	—
278	#446	C₂²×C₁₃	1	1	yes	characteristic
279	#446	C₂²×C₁₃	1	1	yes	characteristic
280	#446	C₂²×C₁₃	1	1	yes	characteristic
281	#446	C₂²×C₁₃	1	1	yes	characteristic
282	C₈×Q₈	—	2	1	no	—
283	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
288	C₄×Q₁₆	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	#433	—	2	1	no	—
292	#433	—	2	1	no	—
293	#432	—	2	1	no	—
294	#432	C₂²×C₁₃	1	1	yes	characteristic
295	#431	—	2	1	no	—
296	#431	C₂²×C₁₃	1	1	yes	characteristic
297	#431	C₂²×C₁₃	1	1	yes	characteristic
298	#431	C₂²×C₁₃	1	1	yes	characteristic
299	#431	C₂²×C₁₃	1	1	yes	characteristic
300	#335	C₂²×C₁₃	1	1	yes	characteristic
301	#335	C₂²×C₁₃	1	1	yes	characteristic
302	#334	C₂²×C₁₃	1	1	yes	characteristic
303	#334	C₂²×C₁₃	1	1	yes	characteristic
304	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
306	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
307	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
308	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	Q₈⋊C₈	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	#322	C₂²×C₁₃	1	1	yes	characteristic
313	#322	C₂²×C₁₃	1	1	yes	characteristic
314	#322	C₂²×C₁₃	1	1	yes	characteristic
315	C₈²	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	4	1	no	—
326	C₄×C₁₃	—	4	1	no	—
327	C₄×C₁₃	—	4	1	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
333	C₄×C₁₃	#568	1	1	yes	characteristic
334	C₄×C₁₃	#578	1	1	yes	characteristic
335	C₄×C₁₃	#578	1	1	yes	characteristic
336	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
337	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
338	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
339	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
340	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
341	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
342	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
343	#125	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
346	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
351	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
352	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
356	#117	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
362	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
363	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
364	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₄⋊C₈	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
375	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
376	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
377	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
378	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
382	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
384	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
385	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
386	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
387	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
388	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
389	#103	C₂×C₄×C₁₃	1	1	yes	characteristic
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
395	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
396	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
397	#97	—	2	1	no	—
398	#97	—	2	1	no	—
399	#97	—	2	1	no	—
400	#97	—	2	1	no	—
401	#97	—	2	1	no	—
402	C₄×C₈	—	2	1	no	—
403	C₄×C₈	—	2	1	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₁₃	—	4	1	no	—
414	C₂×C₁₃	#2933	1	1	yes	characteristic
415	C₂×C₁₃	#2950	1	1	yes	characteristic
416	C₂×C₁₃	#2955	1	1	yes	characteristic
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
422	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
423	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
424	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
430	Q₁₆	—	2	2	no	—
431	Q₁₆	—	2	2	no	—
432	Q₁₆	—	4	1	no	—
433	Q₁₆	—	4	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
441	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
442	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
443	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
444	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
461	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
462	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
473	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₄²	C₁₃×#41	1	1	yes	characteristic
475	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
476	C₁₃	#18032	1	1	yes	characteristic, direct product factor, Sylow
477	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	Q₈	C₁₃×#131	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
527	C₄	—	2	1	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
540	C₄	C₁₃×#568	1	1	yes	characteristic
541	C₄	C₁₃×#578	1	1	yes	characteristic
542	C₄	C₁₃×#578	1	1	yes	characteristic
543	C₂	—	4	1	no	—
544	C₂	C₁₃×#2933	1	1	yes	characteristic
545	C₂	C₁₃×#2950	1	1	yes	characteristic
546	C₂	C₁₃×#2955	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	C₂³×C₁₃	C₄×D₄
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
4. C₁₃×#1593	C₂	semidirect
5. C₁₃×#1591	C₂	semidirect
6. C₁₃×#1587	C₂	semidirect
7. C₁₃×#1587	C₂	semidirect
8. C₁₃×#1584	C₂	semidirect
9. C₁₃×#1584	C₂	semidirect
10. C₁₃×#1579	C₂	semidirect
11. C₈×C₁₃×Q₁₆	C₂	semidirect
144. #18032	C₁₃	direct (N × H)
207. #1593	C₂×C₁₃	semidirect
208. #1591	C₂×C₁₃	semidirect
209. #1587	C₂×C₁₃	semidirect
210. #1587	C₂×C₁₃	semidirect
211. #1584	C₂×C₁₃	semidirect
212. #1584	C₂×C₁₃	semidirect
213. #1579	C₂×C₁₃	semidirect
214. C₈×Q₁₆	C₂×C₁₃	semidirect
476. C₁₃	#18032	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×#3104	2
C₁₃×#2986	2
C₁₃×#2984	2
C₁₃×#1593	2
C₁₃×#1591	2
C₁₃×#1587	2
C₁₃×#1584	2
C₁₃×#1579	2
C₈×C₁₃×Q₁₆	2
C₁₃×#1572	2
C₁₃×#1497	2
C₁₃×#1479	2
C₁₃×#1454	2
#18032	13

Subgroups — C13×#18032 #15704371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18032 #15704371