Subgroups — #15869977

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718672	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718658	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115451	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115129	C₂	1	1	yes	maximal, characteristic
8	#13115016	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114907	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114614	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2395	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×#6099	C₂²	1	1	yes	characteristic
19	C₂³×#1055	C₂²	1	1	yes	characteristic
20	C₂³×#1055	C₂²	1	1	yes	characteristic
21	C₁₃×#400	C₄	1	1	yes	characteristic
22	C₁₃×#399	C₄	1	1	yes	characteristic
23	C₁₃×#398	C₄	1	1	yes	characteristic
24	C₁₃×#397	C₄	1	1	yes	characteristic
25	C₁₃×#397	C₄	1	1	yes	characteristic
26	C₁₃×#397	C₄	1	1	yes	characteristic
27	C₁₃×#394	C₄	1	1	yes	characteristic
28	C₁₃×#394	C₄	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
39	#11718672	—	2	4	no	—
40	#11718658	—	2	4	no	—
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
44	C₂×#88043	C₂²	1	1	yes	characteristic
45	C₂×#88043	C₂²	1	1	yes	characteristic
46	C₂×#88043	C₂²	1	1	yes	characteristic
47	C₂×#88043	C₂²	1	1	yes	characteristic
48	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
49	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
50	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
51	#11718116	C₂²	1	1	yes	characteristic
52	#11718116	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	#11718116	C₂²	1	1	yes	characteristic
60	#11718116	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₁₃×#117	—	2	2	no	—
67	C₁₃×#117	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×#6099	—	2	2	no	—
91	C₂×#6099	—	2	2	no	—
92	C₂×#6099	D₄	1	4	yes	—
93	C₂²×#1055	—	2	2	no	—
94	C₂²×#1055	—	2	2	no	—
95	C₂²×#1055	—	2	2	no	—
96	C₂²×#1055	—	2	2	no	—
97	C₂²×#1055	—	2	2	no	—
98	C₂²×#1055	—	2	2	no	—
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	C₂²×#1055	C₂³	1	1	yes	characteristic
102	C₂²×#1055	C₂³	1	1	yes	characteristic
103	C₂²×#1055	C₂³	1	1	yes	characteristic
104	C₂²×#1055	C₂³	1	1	yes	characteristic
105	C₂²×#1055	C₂³	1	1	yes	characteristic
106	C₂²×#1055	C₂³	1	1	yes	characteristic
107	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#1055	—	2	2	no	—
118	C₂²⋊#1055	—	2	2	no	—
119	C₂²⋊#1055	—	2	2	no	—
120	C₂²⋊#1055	—	2	2	no	—
121	C₂²⋊#1055	—	2	2	no	—
122	C₄⋊#1055	—	2	2	no	—
123	C₄⋊#1055	—	2	2	no	—
124	C₄⋊#1055	—	2	2	no	—
125	#88043	—	2	2	no	—
126	#88043	—	2	2	no	—
127	#88043	—	2	2	no	—
128	#88043	—	2	2	no	—
129	C₄×#1055	—	2	2	no	—
130	C₄×#1055	—	2	2	no	—
131	C₄×#1055	—	2	2	no	—
132	#21568	—	13	1	no	maximal, Sylow
133	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	#41	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	1	no	—
179	C₁₃×C₂²⋊C₄	—	4	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	#6099	—	2	8	no	—
191	C₂×#1055	—	2	8	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	C₂×#1055	—	2	1	no	—
195	C₂×#1055	—	2	1	no	—
196	C₂×#1055	—	2	1	no	—
197	C₂×#1055	—	2	1	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	2	1	no	—
206	C₂×#1055	—	2	1	no	—
207	C₂×#1055	—	2	1	no	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	—	2	1	no	—
210	C₂×#1055	—	4	4	no	—
211	C₂×#1055	C₂×D₄	1	2	yes	—
212	C₂×#1055	C₂×D₄	1	2	yes	—
213	C₂×#1055	#41	1	2	yes	—
214	C₂×#1055	#41	1	2	yes	—
215	C₂×#1055	#41	1	2	yes	—
216	C₂×#1055	#41	1	2	yes	—
217	C₂×#435	—	13	1	no	—
218	C₂×#405	—	13	1	no	—
219	#2395	D₁₃	1	1	yes	characteristic
220	#1924	—	13	1	no	—
221	#1923	—	13	1	no	—
222	#1917	—	13	1	no	—
223	#1916	—	13	1	no	—
224	#1869	—	13	1	no	—
225	#1850	—	13	1	no	—
226	#1818	—	13	1	no	—
227	#1771	—	13	1	no	—
228	#1770	—	13	1	no	—
229	#1753	—	13	1	no	—
230	#1752	—	13	1	no	—
231	C₈×C₂²⋊C₄	—	13	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	C₄×D₄	1	2	yes	—
245	C₂³×C₁₃	#131	1	2	yes	—
246	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
247	D₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₁₃	#131	1	2	yes	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	#1055	—	2	2	no	—
299	#1055	—	2	2	no	—
300	#1055	—	2	2	no	—
301	#1055	—	4	1	no	—
302	#1055	—	4	1	no	—
303	#1055	—	4	1	no	—
304	#1055	—	4	1	no	—
305	#1055	#123	1	4	yes	—
306	C₂²×M₁₆	—	13	1	no	—
307	C₂³×C₈	—	13	1	no	—
308	C₂³×C₈	—	13	1	no	—
309	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
310	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
311	#435	—	26	4	no	—
312	C₂×C₄⋊C₈	—	13	1	no	—
313	C₂×C₄⋊C₈	—	13	1	no	—
314	C₂×C₄⋊C₈	—	13	1	no	—
315	C₂×C₂²⋊C₈	—	13	1	no	—
316	C₂×C₂²⋊C₈	—	13	1	no	—
317	C₂×C₂²⋊C₈	—	13	1	no	—
318	C₂×C₂²⋊C₈	—	13	1	no	—
319	C₂×C₂²⋊C₈	—	13	1	no	—
320	#405	—	26	4	no	—
321	C₂×#97	—	13	1	no	—
322	C₂×#97	—	13	1	no	—
323	C₂×#97	—	13	1	no	—
324	C₂×#97	—	13	1	no	—
325	C₂×C₄×C₈	—	13	1	no	—
326	C₂×C₄×C₈	—	13	1	no	—
327	C₂×C₄×C₈	—	13	1	no	—
328	#400	Dic₁₃	1	1	yes	characteristic
329	#399	Dic₁₃	1	1	yes	characteristic
330	#398	Dic₁₃	1	1	yes	characteristic
331	#397	Dic₁₃	1	1	yes	characteristic
332	#397	Dic₁₃	1	1	yes	characteristic
333	#397	Dic₁₃	1	1	yes	characteristic
334	#394	Dic₁₃	1	1	yes	characteristic
335	#394	Dic₁₃	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
339	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
341	#336	—	13	1	no	—
342	#336	—	13	1	no	—
343	#336	—	13	1	no	—
344	#336	—	13	1	no	—
345	#336	—	13	1	no	—
346	#336	—	13	1	no	—
347	#336	—	13	1	no	—
348	#336	—	13	1	no	—
349	#336	—	13	1	no	—
350	#336	—	13	1	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	—	2	2	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
366	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
367	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
368	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
369	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
370	C₂²×C₁₃	#568	1	1	yes	characteristic
371	C₂²×C₁₃	#568	1	1	yes	characteristic
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	2	2	no	—
374	C₄×C₁₃	—	4	1	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	4	1	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	1	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
385	C₄×C₁₃	#525	1	1	yes	characteristic
386	C₄×C₁₃	#529	1	1	yes	characteristic
387	C₄×C₁₃	#529	1	1	yes	characteristic
388	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
389	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
391	C₂×M₁₆	—	13	4	no	—
392	C₂×M₁₆	—	26	2	no	—
393	C₂×M₁₆	—	26	2	no	—
394	C₂²×C₈	—	13	1	no	—
395	C₂²×C₈	—	13	1	no	—
396	C₂²×C₈	—	13	1	no	—
397	C₂²×C₈	—	13	1	no	—
398	C₂²×C₈	—	13	1	no	—
399	C₂²×C₈	—	13	1	no	—
400	C₂²×C₈	—	13	1	no	—
401	C₂²×C₈	—	13	1	no	—
402	C₂²×C₈	—	26	2	no	—
403	C₂²×C₈	—	26	2	no	—
404	C₂²×C₈	—	26	2	no	—
405	C₂²×C₈	—	26	2	no	—
406	C₂²×C₈	—	26	2	no	—
407	C₂²×C₈	—	26	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
429	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
433	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
434	C₄⋊C₈	—	26	2	no	—
435	C₄⋊C₈	—	26	2	no	—
436	C₄⋊C₈	—	26	2	no	—
437	C₂²⋊C₈	—	26	2	no	—
438	C₂²⋊C₈	—	26	2	no	—
439	C₂²⋊C₈	—	26	2	no	—
440	C₂²⋊C₈	—	26	2	no	—
441	C₂²⋊C₈	—	26	2	no	—
442	#97	—	26	2	no	—
443	#97	—	26	2	no	—
444	#97	—	26	2	no	—
445	#97	—	26	2	no	—
446	C₄×C₈	—	26	2	no	—
447	C₄×C₈	—	26	2	no	—
448	C₄×C₈	—	26	2	no	—
449	#95	C₂×Dic₁₃	1	1	yes	characteristic
450	#95	C₂×Dic₁₃	1	1	yes	characteristic
451	#95	C₂×Dic₁₃	1	1	yes	characteristic
452	#95	C₂×Dic₁₃	1	1	yes	characteristic
453	#95	C₂×Dic₁₃	1	1	yes	characteristic
454	#95	C₂×Dic₁₃	1	1	yes	characteristic
455	#95	C₂×Dic₁₃	1	1	yes	characteristic
456	#95	C₂×Dic₁₃	1	1	yes	characteristic
457	#95	C₂×Dic₁₃	1	1	yes	characteristic
458	#95	C₂×Dic₁₃	1	1	yes	characteristic
459	C₂×C₁₃	—	4	2	no	—
460	C₂×C₁₃	—	4	2	no	—
461	C₂×C₁₃	C₄×#123	1	1	yes	characteristic
462	C₂×C₁₃	#2933	1	1	yes	characteristic
463	C₂×C₁₃	#2935	1	1	yes	characteristic
464	C₂×C₁₃	#2966	1	1	yes	characteristic
465	C₂×C₁₃	#2967	1	1	yes	characteristic
466	C₂×C₁₃	#2968	1	1	yes	characteristic
467	C₂×C₁₃	#2968	1	1	yes	characteristic
468	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
469	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	D₄×D₁₃	1	2	yes	—
484	C₂²×C₄	#6129	1	2	yes	—
485	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
498	M₁₆	—	26	8	no	—
499	C₂×C₈	—	13	2	no	—
500	C₂×C₈	—	13	2	no	—
501	C₂×C₈	—	13	2	no	—
502	C₂×C₈	—	13	2	no	—
503	C₂×C₈	—	13	2	no	—
504	C₂×C₈	—	13	2	no	—
505	C₂×C₈	—	26	8	no	—
506	C₂×C₈	—	26	1	no	—
507	C₂×C₈	—	26	1	no	—
508	C₂×C₈	—	26	1	no	—
509	C₂×C₈	—	26	1	no	—
510	C₂×C₈	—	26	1	no	—
511	C₂×C₈	—	26	1	no	—
512	C₂×C₈	—	26	1	no	—
513	C₂×C₈	—	26	1	no	—
514	C₂×C₈	—	26	1	no	—
515	C₂×C₈	—	26	1	no	—
516	C₂×C₈	—	26	1	no	—
517	C₂×C₈	—	26	1	no	—
518	C₂×C₈	—	26	1	no	—
519	C₂×C₈	—	26	1	no	—
520	C₂×C₈	—	26	1	no	—
521	C₂×C₈	—	26	1	no	—
522	C₂×C₈	—	26	1	no	—
523	C₂×C₈	—	26	1	no	—
524	C₂×C₈	—	52	4	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₁₃	#21568	1	1	yes	characteristic, complemented, Sylow
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	D₄×Dic₁₃	1	2	yes	—
566	C₂³	#88202	1	2	yes	—
567	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
568	D₄	—	4	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
612	C₂×C₄	#88202	1	2	yes	—
613	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂×#6129	1	1	yes	characteristic
615	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
616	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
617	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
618	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
619	C₈	—	13	4	no	—
620	C₈	—	26	2	no	—
621	C₈	—	26	2	no	—
622	C₈	—	26	2	no	—
623	C₈	—	52	1	no	—
624	C₈	—	52	1	no	—
625	C₈	—	52	1	no	—
626	C₈	—	52	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
642	C₂²	C₂×#88202	1	1	yes	characteristic
643	C₂²	C₂×#88202	1	1	yes	characteristic
644	C₂²	#11719524	1	1	yes	characteristic
645	C₂²	#11719524	1	1	yes	characteristic
646	C₂²	#41×Dic₁₃	1	1	yes	characteristic
647	C₂²	#41×Dic₁₃	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	#11719354	1	1	yes	characteristic
661	C₄	#11719354	1	1	yes	characteristic
662	C₄	D₁₃×#123	1	1	yes	characteristic
663	C₄	#11719361	1	1	yes	characteristic
664	C₂	—	4	2	no	—
665	C₂	—	4	2	no	—
666	C₂	#123×Dic₁₃	1	1	yes	characteristic
667	C₂	#13123563	1	1	yes	characteristic
668	C₂	#13123580	1	1	yes	characteristic
669	C₂	#13123812	1	1	yes	characteristic
670	C₂	#13123823	1	1	yes	characteristic
671	C₂	#13123832	1	1	yes	characteristic
672	C₂	#13123832	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2395	C₂
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2395	D₁₃
hypocenter	C₁₃	#21568
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2395

Complements

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

N	H ≅ G/N	type
2. C₂×#11718658	C₂	semidirect
3. #13115451	C₂	semidirect
4. #13115444	C₂	semidirect
5. #13115402	C₂	semidirect
6. #13115395	C₂	semidirect
8. #13115016	C₂	semidirect
9. #13114907	C₂	semidirect
10. #13114711	C₂	semidirect
11. #13114705	C₂	semidirect
12. #13114620	C₂	semidirect
13. #13114614	C₂	semidirect
14. C₂²⋊C₄×#1055	C₂	semidirect
552. C₁₃	#21568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718672	2
C₂×#11718658	2
#13115451	2
#13115444	2
#13115402	2
#13115395	2
#13115129	2
#13115016	2
#13114907	2
#13114711	2
#13114705	2
#13114620	2
#13114614	2
C₂²⋊C₄×#1055	2
C₁₃×#2395	2
#21568	13