Subgroups — #15869007

Order 3328.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718673	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718672	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718672	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115635	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115560	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
9	#13115134	C₂	1	1	yes	maximal, characteristic, complemented
10	#13115134	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114816	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×#6099	C₂²	1	1	yes	characteristic
22	C₂²×#6099	C₂²	1	1	yes	characteristic
23	C₂²×#6099	C₂²	1	1	yes	characteristic
24	C₂³×#1055	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₄	1	1	yes	characteristic
26	C₁₃×#389	C₄	1	1	yes	characteristic
27	C₁₃×#388	C₄	1	1	yes	characteristic
28	C₁₃×#388	C₄	1	1	yes	characteristic
29	C₁₃×#386	C₄	1	1	yes	characteristic
30	C₁₃×#386	C₄	1	1	yes	characteristic
31	C₁₃×#380	C₄	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₂²⋊C₄	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	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
43	#11718673	—	2	4	no	—
44	#11718672	—	2	4	no	—
45	#11718672	—	2	4	no	—
46	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
50	C₄×#6099	—	2	4	no	—
51	C₂×#88043	C₂²	1	1	yes	characteristic
52	C₂×#88043	C₂²	1	1	yes	characteristic
53	C₂×#88043	C₂²	1	1	yes	characteristic
54	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
55	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
56	C₂×C₄×#1055	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	#11718116	C₂²	1	1	yes	characteristic
62	#11718116	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#121	—	2	4	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊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×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	—	2	2	no	—
94	C₂×C₄²×C₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×#6099	—	2	2	no	—
102	C₂×#6099	—	2	2	no	—
103	C₂×#6099	—	2	2	no	—
104	C₂×#6099	—	2	2	no	—
105	C₂×#6099	—	2	2	no	—
106	C₂×#6099	—	2	2	no	—
107	C₂×#6099	—	2	2	no	—
108	C₂×#6099	—	2	2	no	—
109	C₂×#6099	D₄	1	4	yes	complemented
110	C₂²×#1055	—	2	2	no	—
111	C₂²×#1055	—	2	2	no	—
112	C₂²×#1055	—	2	2	no	—
113	C₂²×#1055	C₂³	1	1	yes	characteristic
114	C₂²×#1055	C₂³	1	1	yes	characteristic
115	C₂²×#1055	C₂³	1	1	yes	characteristic
116	C₂²×#1055	C₂³	1	1	yes	characteristic
117	C₂²×#1055	C₂³	1	1	yes	characteristic
118	C₂²×#1055	C₂³	1	1	yes	characteristic
119	C₂²×#1055	C₂³	1	1	yes	characteristic
120	C₂²×#1055	C₂³	1	1	yes	characteristic
121	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
122	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
123	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
124	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
125	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
126	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
127	C₂²⋊#1055	—	2	2	no	—
128	C₂²⋊#1055	—	2	2	no	—
129	C₂²⋊#1055	—	2	2	no	—
130	C₂²⋊#1055	—	2	2	no	—
131	C₂²⋊#1055	—	2	2	no	—
132	C₂²⋊#1055	—	2	2	no	—
133	C₂²⋊#1055	—	2	2	no	—
134	C₂²⋊#1055	—	2	2	no	—
135	C₄⋊#1055	—	2	2	no	—
136	C₄⋊#1055	—	2	2	no	—
137	C₄⋊#1055	—	2	2	no	—
138	C₄⋊#1055	—	2	2	no	—
139	#88043	—	2	2	no	—
140	#88043	—	2	2	no	—
141	#88043	D₄	1	4	yes	complemented
142	C₄×#1055	—	2	2	no	—
143	C₄×#1055	—	2	2	no	—
144	C₄×#1055	—	2	2	no	—
145	#21490	—	13	1	no	maximal, Sylow
146	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	—	4	1	no	—
180	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₁₃	#41	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	M₁₆	1	4	yes	complemented
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	#41	1	2	yes	—
219	#6099	—	2	8	no	—
220	#6099	—	2	8	no	—
221	#6099	—	4	4	no	—
222	C₂×#1055	—	2	1	no	—
223	C₂×#1055	—	2	1	no	—
224	C₂×#1055	—	2	1	no	—
225	C₂×#1055	—	2	1	no	—
226	C₂×#1055	—	2	1	no	—
227	C₂×#1055	—	2	1	no	—
228	C₂×#1055	—	2	1	no	—
229	C₂×#1055	—	2	1	no	—
230	C₂×#1055	—	2	1	no	—
231	C₂×#1055	—	2	1	no	—
232	C₂×#1055	—	2	1	no	—
233	C₂×#1055	—	2	1	no	—
234	C₂×#1055	—	2	1	no	—
235	C₂×#1055	—	2	1	no	—
236	C₂×#1055	—	2	1	no	—
237	C₂×#1055	—	2	1	no	—
238	C₂×#1055	—	2	1	no	—
239	C₂×#1055	—	2	1	no	—
240	C₂×#1055	—	4	4	no	—
241	C₂×#1055	C₂×D₄	1	2	yes	—
242	C₂×#1055	C₂×D₄	1	2	yes	—
243	C₂×#1055	C₂×D₄	1	2	yes	—
244	C₂×#1055	C₂×D₄	1	2	yes	—
245	C₂×#1055	#41	1	2	yes	—
246	C₂×#1055	#41	1	2	yes	—
247	C₂×#436	—	13	1	no	—
248	C₂×#435	—	13	1	no	—
249	C₂×#435	—	13	1	no	—
250	C₂×C₄×M₁₆	—	13	1	no	—
251	C₄×#121	D₁₃	1	1	yes	characteristic
252	#1955	—	13	1	no	—
253	#1940	—	13	1	no	—
254	#1923	—	13	1	no	—
255	#1923	—	13	1	no	—
256	#1870	—	13	1	no	—
257	#1870	—	13	1	no	—
258	#1797	—	13	1	no	—
259	#1771	—	13	1	no	—
260	#1753	—	13	1	no	—
261	C₈×C₂²⋊C₄	—	13	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	1	no	—
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	C₄×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
283	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
284	D₄×C₁₃	—	4	4	no	—
285	D₄×C₁₃	—	4	4	no	—
286	D₄×C₁₃	—	4	4	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	4	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
330	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
331	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
332	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
333	C₂×C₄×C₁₃	#131	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
340	#1055	—	2	2	no	—
341	#1055	—	2	2	no	—
342	#1055	—	2	2	no	—
343	#1055	—	4	1	no	—
344	#1055	—	4	1	no	—
345	#1055	—	4	1	no	—
346	#1055	—	4	1	no	—
347	#1055	#121	1	4	yes	complemented
348	C₂²×M₁₆	—	13	1	no	—
349	C₂²×M₁₆	—	13	1	no	—
350	C₂²×M₁₆	—	13	1	no	—
351	C₂³×C₈	—	13	1	no	—
352	C₂×#121	Dic₁₃	1	1	yes	characteristic
353	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
354	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
356	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
357	#436	—	26	4	no	—
358	#435	—	26	4	no	—
359	#435	—	26	4	no	—
360	C₂×C₄⋊C₈	—	13	1	no	—
361	C₂×C₄⋊C₈	—	13	1	no	—
362	C₂×C₄⋊C₈	—	13	1	no	—
363	C₂×C₄⋊C₈	—	13	1	no	—
364	C₂×C₂²⋊C₈	—	13	1	no	—
365	C₂×C₂²⋊C₈	—	13	1	no	—
366	C₂×C₂²⋊C₈	—	13	1	no	—
367	C₂×C₂²⋊C₈	—	13	1	no	—
368	C₂×C₂²⋊C₈	—	13	1	no	—
369	C₂×C₂²⋊C₈	—	13	1	no	—
370	C₂×C₂²⋊C₈	—	13	1	no	—
371	C₂×C₂²⋊C₈	—	13	1	no	—
372	C₄×M₁₆	—	26	4	no	—
373	C₂×#97	—	13	1	no	—
374	C₂×#97	—	13	1	no	—
375	C₂×#97	—	13	1	no	—
376	C₂×C₄×C₈	—	13	1	no	—
377	C₂×C₄×C₈	—	13	1	no	—
378	C₂×C₄×C₈	—	13	1	no	—
379	#390	Dic₁₃	1	1	yes	characteristic
380	#389	Dic₁₃	1	1	yes	characteristic
381	#388	Dic₁₃	1	1	yes	characteristic
382	#388	Dic₁₃	1	1	yes	characteristic
383	#386	Dic₁₃	1	1	yes	characteristic
384	#386	Dic₁₃	1	1	yes	characteristic
385	#380	Dic₁₃	1	1	yes	characteristic
386	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
387	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
388	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
389	#336	—	13	1	no	—
390	#336	—	13	1	no	—
391	#336	—	13	1	no	—
392	#336	—	13	1	no	—
393	#336	—	13	1	no	—
394	#336	—	13	1	no	—
395	C₂²×C₁₃	—	2	2	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	2	2	no	—
400	C₂²×C₁₃	—	2	2	no	—
401	C₂²×C₁₃	—	4	1	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	1	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	1	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	1	no	—
409	C₂²×C₁₃	—	4	1	no	—
410	C₂²×C₁₃	—	4	1	no	—
411	C₂²×C₁₃	—	4	1	no	—
412	C₂²×C₁₃	—	4	1	no	—
413	C₂²×C₁₃	—	4	1	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	1	no	—
416	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
417	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
419	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
420	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
421	C₂²×C₁₃	#568	1	1	yes	characteristic
422	C₂²×C₁₃	#568	1	1	yes	characteristic
423	C₄×C₁₃	—	2	2	no	—
424	C₄×C₁₃	—	2	2	no	—
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	2	2	no	—
427	C₄×C₁₃	—	2	2	no	—
428	C₄×C₁₃	—	2	2	no	—
429	C₄×C₁₃	—	4	1	no	—
430	C₄×C₁₃	—	4	1	no	—
431	C₄×C₁₃	—	4	1	no	—
432	C₄×C₁₃	—	4	1	no	—
433	C₄×C₁₃	—	4	1	no	—
434	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
435	C₄×C₁₃	#525	1	1	yes	characteristic
436	C₄×C₁₃	#529	1	1	yes	characteristic
437	C₄×C₁₃	#532	1	1	yes	characteristic
438	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
439	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
440	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
441	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
442	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
444	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
446	C₂×M₁₆	—	13	4	no	—
447	C₂×M₁₆	—	26	2	no	—
448	C₂×M₁₆	—	26	2	no	—
449	C₂×M₁₆	—	26	2	no	—
450	C₂×M₁₆	—	26	2	no	—
451	C₂×M₁₆	—	26	2	no	—
452	C₂×M₁₆	—	26	2	no	—
453	C₂×M₁₆	—	26	2	no	—
454	C₂×M₁₆	—	26	2	no	—
455	C₂²×C₈	—	13	1	no	—
456	C₂²×C₈	—	13	1	no	—
457	C₂²×C₈	—	13	1	no	—
458	C₂²×C₈	—	13	1	no	—
459	C₂²×C₈	—	13	1	no	—
460	C₂²×C₈	—	13	1	no	—
461	C₂²×C₈	—	13	1	no	—
462	C₂²×C₈	—	13	1	no	—
463	C₂²×C₈	—	26	2	no	—
464	C₂²×C₈	—	26	2	no	—
465	C₂²×C₈	—	26	2	no	—
466	#121	—	2	4	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	2	no	—
473	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
488	C₂×C₄²	—	2	2	no	—
489	C₂×C₄²	—	2	2	no	—
490	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
491	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
492	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
493	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
494	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
495	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
496	C₄⋊C₈	—	26	2	no	—
497	C₄⋊C₈	—	26	2	no	—
498	C₄⋊C₈	—	26	2	no	—
499	C₄⋊C₈	—	26	2	no	—
500	C₂²⋊C₈	—	26	2	no	—
501	C₂²⋊C₈	—	26	2	no	—
502	C₂²⋊C₈	—	26	2	no	—
503	C₂²⋊C₈	—	26	2	no	—
504	C₂²⋊C₈	—	26	2	no	—
505	C₂²⋊C₈	—	26	2	no	—
506	C₂²⋊C₈	—	26	2	no	—
507	C₂²⋊C₈	—	26	2	no	—
508	#97	—	13	4	no	—
509	#97	—	26	2	no	—
510	#97	—	26	2	no	—
511	C₄×C₈	—	26	2	no	—
512	C₄×C₈	—	26	2	no	—
513	C₄×C₈	—	26	2	no	—
514	#95	C₂×Dic₁₃	1	1	yes	characteristic
515	#95	C₂×Dic₁₃	1	1	yes	characteristic
516	#95	C₂×Dic₁₃	1	1	yes	characteristic
517	#95	C₂×Dic₁₃	1	1	yes	characteristic
518	#95	C₂×Dic₁₃	1	1	yes	characteristic
519	#95	C₂×Dic₁₃	1	1	yes	characteristic
520	C₂×C₁₃	—	4	2	no	—
521	C₂×C₁₃	—	4	2	no	—
522	C₂×C₁₃	—	8	1	no	—
523	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
524	C₂×C₁₃	#2933	1	1	yes	characteristic
525	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
526	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
527	C₂×C₁₃	#2935	1	1	yes	characteristic
528	C₂×C₁₃	#2965	1	1	yes	characteristic
529	C₂×C₁₃	#2967	1	1	yes	characteristic
530	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
531	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
532	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	4	1	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	D₄×D₁₃	1	2	yes	—
565	C₂²×C₄	#6129	1	2	yes	—
566	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
569	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
570	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
574	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
575	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
578	M₁₆	—	26	8	no	—
579	M₁₆	—	26	8	no	—
580	M₁₆	—	52	4	no	—
581	C₂×C₈	—	13	2	no	—
582	C₂×C₈	—	13	2	no	—
583	C₂×C₈	—	13	2	no	—
584	C₂×C₈	—	13	2	no	—
585	C₂×C₈	—	13	2	no	—
586	C₂×C₈	—	13	2	no	—
587	C₂×C₈	—	26	1	no	—
588	C₂×C₈	—	26	1	no	—
589	C₂×C₈	—	26	1	no	—
590	C₂×C₈	—	26	1	no	—
591	C₂×C₈	—	26	1	no	—
592	C₂×C₈	—	26	1	no	—
593	C₂×C₈	—	26	1	no	—
594	C₂×C₈	—	26	1	no	—
595	C₂×C₈	—	26	1	no	—
596	C₂×C₈	—	26	1	no	—
597	C₂×C₈	—	26	1	no	—
598	C₂×C₈	—	26	1	no	—
599	C₂×C₈	—	26	1	no	—
600	C₂×C₈	—	26	1	no	—
601	C₂×C₈	—	26	1	no	—
602	C₂×C₈	—	26	1	no	—
603	C₂×C₈	—	26	1	no	—
604	C₂×C₈	—	26	1	no	—
605	C₂×C₈	—	52	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	#6099	1	4	yes	complemented
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	D₄×D₁₃	1	2	yes	—
630	C₄²	#6129	1	2	yes	—
631	C₁₃	#21490	1	1	yes	characteristic, complemented, Sylow
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	C₂×#6099	1	2	yes	—
652	C₂³	D₄×Dic₁₃	1	2	yes	—
653	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
654	D₄	—	4	4	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	C₂×#6099	1	2	yes	—
699	C₂×C₄	C₂×#6099	1	2	yes	—
700	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
701	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
702	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
703	C₂×C₄	#88202	1	2	yes	—
704	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂×#6129	1	1	yes	characteristic
707	C₂×C₄	C₂×#6129	1	1	yes	characteristic
708	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
709	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
710	C₈	—	13	4	no	—
711	C₈	—	26	2	no	—
712	C₈	—	26	2	no	—
713	C₈	—	26	2	no	—
714	C₈	—	52	1	no	—
715	C₈	—	52	1	no	—
716	C₈	—	52	1	no	—
717	C₈	—	52	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	C₂²×#6099	1	1	yes	characteristic
740	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
741	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
742	C₂²	C₂×#88202	1	1	yes	characteristic
743	C₂²	#11719524	1	1	yes	characteristic
744	C₂²	#11719524	1	1	yes	characteristic
745	C₂²	#41×Dic₁₃	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	#11719301	1	1	yes	characteristic
758	C₄	#11719305	1	1	yes	characteristic
759	C₄	D₁₃×#121	1	1	yes	characteristic
760	C₄	#11719311	1	1	yes	characteristic
761	C₂	—	4	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	1	no	—
764	C₂	#121×Dic₁₃	1	1	yes	characteristic
765	C₂	#13123563	1	1	yes	characteristic
766	C₂	D₄×#6099	1	1	yes	characteristic
767	C₂	D₄×#6099	1	1	yes	characteristic
768	C₂	#13123580	1	1	yes	characteristic
769	C₂	#13123803	1	1	yes	characteristic
770	C₂	#13123823	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×#121	C₂
prime radical	C₂×C₁₃×#121	C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#121	D₁₃
hypocenter	C₁₃	#21490
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#11718673	C₂	semidirect
2. C₂×#11718672	C₂	semidirect
3. C₂×#11718672	C₂	semidirect
4. C₂×C₄×#6099	C₂	semidirect
5. #13115635	C₂	semidirect
6. #13115560	C₂	semidirect
7. #13115444	C₂	semidirect
8. #13115444	C₂	semidirect
9. #13115134	C₂	semidirect
10. #13115134	C₂	semidirect
11. #13114816	C₂	semidirect
12. #13114711	C₂	semidirect
13. #13114620	C₂	semidirect
14. C₂²⋊C₄×#1055	C₂	semidirect
109. C₂×#6099	D₄	semidirect
141. #88043	D₄	semidirect
208. C₁₃×C₂²⋊C₄	M₁₆	semidirect
347. #1055	#121	semidirect
620. C₂²⋊C₄	#6099	semidirect
631. C₁₃	#21490	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718673	2
C₂×#11718672	2
C₂×C₄×#6099	2
#13115635	2
#13115560	2
#13115444	2
#13115134	2
#13114816	2
#13114711	2
#13114620	2
C₂²⋊C₄×#1055	2
C₄×C₁₃×#121	2
#21490	13