Subgroups — #15885148

Order 3328.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 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×#11718673	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718672	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718660	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115635	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115451	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	#13115129	C₂	1	1	yes	maximal, characteristic, complemented
11	#13115021	C₂	1	1	yes	maximal, characteristic, complemented
12	#13115021	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114602	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2392	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	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×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂²×#6099	C₂²	1	1	yes	characteristic
21	C₂²×#6099	C₂²	1	1	yes	characteristic
22	C₂²×#6099	C₂²	1	1	yes	characteristic
23	C₂³×#1055	C₂²	1	1	yes	characteristic
24	C₁₃×#398	C₄	1	1	yes	characteristic
25	C₁₃×#397	C₄	1	1	yes	characteristic
26	C₁₃×#396	C₄	1	1	yes	characteristic
27	C₁₃×#396	C₄	1	1	yes	characteristic
28	C₁₃×#394	C₄	1	1	yes	characteristic
29	C₁₃×#394	C₄	1	1	yes	characteristic
30	C₁₃×#394	C₄	1	1	yes	characteristic
31	C₁₃×#392	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	#11718673	—	2	4	no	—
45	#11718672	—	2	4	no	—
46	#11718660	—	2	4	no	—
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	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
53	C₂×#88043	C₂²	1	1	yes	characteristic
54	C₂×#88043	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	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₄⋊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×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	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×#6099	—	2	2	no	—
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	—	4	1	no	—
107	C₂×#6099	—	4	1	no	—
108	C₂×#6099	—	4	1	no	—
109	C₂²×#1055	—	2	2	no	—
110	C₂²×#1055	—	2	2	no	—
111	C₂²×#1055	—	4	1	no	—
112	C₂²×#1055	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂×C₄	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	C₂²⋊#1055	—	2	2	no	—
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	—	4	1	no	—
132	C₂²⋊#1055	—	4	1	no	—
133	C₂²⋊#1055	D₄	1	4	yes	complemented
134	C₄⋊#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	C₄⋊#1055	D₄	1	4	yes	complemented
140	#88043	—	2	2	no	—
141	#88043	—	2	2	no	—
142	C₄×#1055	—	2	2	no	—
143	C₄×#1055	—	2	2	no	—
144	#22994	—	13	1	no	maximal, Sylow
145	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₃	—	2	2	no	—
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	—	4	1	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	—	4	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂²×C₄×C₁₃	—	2	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	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₃	#41	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	C₂×D₄	1	2	yes	—
213	C₄²×C₁₃	#41	1	2	yes	—
214	#6099	—	4	4	no	—
215	#6099	—	4	4	no	—
216	#6099	—	4	4	no	—
217	C₂×#1055	—	2	1	no	—
218	C₂×#1055	—	2	1	no	—
219	C₂×#1055	—	2	1	no	—
220	C₂×#1055	—	2	1	no	—
221	C₂×#1055	—	2	1	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	—	4	4	no	—
238	C₂×#1055	C₂×D₄	1	2	yes	—
239	C₂×#1055	C₂×D₄	1	2	yes	—
240	C₂×#1055	C₂×D₄	1	2	yes	—
241	C₂×#1055	C₂×D₄	1	2	yes	—
242	C₂×#436	—	13	1	no	—
243	C₂×#436	—	13	1	no	—
244	C₂×#435	—	13	1	no	—
245	C₂×#424	—	13	1	no	—
246	#2392	D₁₃	1	1	yes	characteristic
247	#1955	—	13	1	no	—
248	#1939	—	13	1	no	—
249	#1924	—	13	1	no	—
250	#1923	—	13	1	no	—
251	#1870	—	13	1	no	—
252	#1869	—	13	1	no	—
253	#1851	—	13	1	no	—
254	#1851	—	13	1	no	—
255	#1771	—	13	1	no	—
256	#1750	—	13	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	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	C₄×D₄	1	2	yes	—
278	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
279	D₄×C₁₃	—	4	4	no	—
280	D₄×C₁₃	—	4	4	no	—
281	D₄×C₁₃	—	4	4	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	—	2	1	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	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	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	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	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	C₄×D₄	1	2	yes	—
324	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
325	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
326	C₂×C₄×C₁₃	#131	1	2	yes	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
333	#1055	—	2	2	no	—
334	#1055	—	2	2	no	—
335	#1055	—	2	2	no	—
336	#1055	—	2	2	no	—
337	#1055	—	4	1	no	—
338	#1055	—	4	1	no	—
339	#1055	—	4	1	no	—
340	#1055	—	4	1	no	—
341	C₂²×M₁₆	—	13	1	no	—
342	C₂²×M₁₆	—	13	1	no	—
343	C₂²×M₁₆	—	13	1	no	—
344	C₂³×C₈	—	13	1	no	—
345	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
348	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
349	#436	—	26	4	no	—
350	#436	—	26	4	no	—
351	#435	—	26	4	no	—
352	#424	—	26	4	no	—
353	C₂×C₄⋊C₈	—	13	1	no	—
354	C₂×C₄⋊C₈	—	13	1	no	—
355	C₂×C₄⋊C₈	—	13	1	no	—
356	C₂×C₄⋊C₈	—	13	1	no	—
357	C₂×C₄⋊C₈	—	13	1	no	—
358	C₂×C₄⋊C₈	—	13	1	no	—
359	C₂×C₂²⋊C₈	—	13	1	no	—
360	C₂×C₂²⋊C₈	—	13	1	no	—
361	C₂×C₂²⋊C₈	—	13	1	no	—
362	C₂×C₂²⋊C₈	—	13	1	no	—
363	C₂×C₂²⋊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×#97	—	13	1	no	—
368	C₂×#97	—	13	1	no	—
369	C₂×C₄×C₈	—	13	1	no	—
370	C₂×C₄×C₈	—	13	1	no	—
371	#398	Dic₁₃	1	1	yes	characteristic
372	#397	Dic₁₃	1	1	yes	characteristic
373	#396	Dic₁₃	1	1	yes	characteristic
374	#396	Dic₁₃	1	1	yes	characteristic
375	#394	Dic₁₃	1	1	yes	characteristic
376	#394	Dic₁₃	1	1	yes	characteristic
377	#394	Dic₁₃	1	1	yes	characteristic
378	#392	Dic₁₃	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
382	#336	—	13	1	no	—
383	#336	—	13	1	no	—
384	#336	—	13	1	no	—
385	#336	—	13	1	no	—
386	#336	—	13	1	no	—
387	#336	—	13	1	no	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	4	1	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	1	no	—
397	C₂²×C₁₃	—	4	1	no	—
398	C₂²×C₁₃	—	4	1	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	1	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	C₂×C₄×D₄	1	1	yes	characteristic
410	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂²×C₁₃	#520	1	1	yes	characteristic
412	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
413	C₂²×C₁₃	#568	1	1	yes	characteristic
414	C₂²×C₁₃	#568	1	1	yes	characteristic
415	C₂²×C₁₃	#568	1	1	yes	characteristic
416	C₄×C₁₃	—	2	2	no	—
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	2	2	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	4	1	no	—
421	C₄×C₁₃	—	4	1	no	—
422	C₄×C₁₃	—	4	1	no	—
423	C₄×C₁₃	—	4	1	no	—
424	C₄×C₁₃	—	4	1	no	—
425	C₄×C₁₃	—	4	1	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	D₄²	1	1	yes	characteristic
428	C₄×C₁₃	#547	1	1	yes	characteristic
429	C₄×C₁₃	#548	1	1	yes	characteristic
430	C₄×C₁₃	#553	1	1	yes	characteristic
431	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
432	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
433	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
435	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
436	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
437	C₂×M₁₆	—	26	2	no	—
438	C₂×M₁₆	—	26	2	no	—
439	C₂×M₁₆	—	26	2	no	—
440	C₂×M₁₆	—	26	2	no	—
441	C₂×M₁₆	—	26	2	no	—
442	C₂×M₁₆	—	26	2	no	—
443	C₂×M₁₆	—	52	1	no	—
444	C₂×M₁₆	—	52	1	no	—
445	C₂×M₁₆	—	52	1	no	—
446	C₂²×C₈	—	13	1	no	—
447	C₂²×C₈	—	13	1	no	—
448	C₂²×C₈	—	13	1	no	—
449	C₂²×C₈	—	13	1	no	—
450	C₂²×C₈	—	13	1	no	—
451	C₂²×C₈	—	13	1	no	—
452	C₂²×C₈	—	13	1	no	—
453	C₂²×C₈	—	13	1	no	—
454	C₂²×C₈	—	26	2	no	—
455	C₂²×C₈	—	26	2	no	—
456	C₂²×C₈	—	52	1	no	—
457	C₄×D₄	—	2	2	no	—
458	C₄×D₄	—	2	2	no	—
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	#117	—	2	2	no	—
464	#117	—	2	2	no	—
465	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
477	C₂×C₂²⋊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×C₄²	C₂²×D₁₃	1	1	yes	characteristic
485	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
486	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
487	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
488	C₄⋊C₈	—	13	4	no	—
489	C₄⋊C₈	—	26	2	no	—
490	C₄⋊C₈	—	26	2	no	—
491	C₄⋊C₈	—	26	2	no	—
492	C₄⋊C₈	—	26	2	no	—
493	C₄⋊C₈	—	26	2	no	—
494	C₂²⋊C₈	—	13	4	no	—
495	C₂²⋊C₈	—	26	2	no	—
496	C₂²⋊C₈	—	26	2	no	—
497	C₂²⋊C₈	—	26	2	no	—
498	C₂²⋊C₈	—	26	2	no	—
499	C₂²⋊C₈	—	26	2	no	—
500	C₂²⋊C₈	—	52	1	no	—
501	C₂²⋊C₈	—	52	1	no	—
502	#97	—	26	2	no	—
503	#97	—	26	2	no	—
504	C₄×C₈	—	26	2	no	—
505	C₄×C₈	—	26	2	no	—
506	#95	C₂×Dic₁₃	1	1	yes	characteristic
507	#95	C₂×Dic₁₃	1	1	yes	characteristic
508	#95	C₂×Dic₁₃	1	1	yes	characteristic
509	#95	C₂×Dic₁₃	1	1	yes	characteristic
510	#95	C₂×Dic₁₃	1	1	yes	characteristic
511	#95	C₂×Dic₁₃	1	1	yes	characteristic
512	C₂×C₁₃	—	4	2	no	—
513	C₂×C₁₃	—	8	1	no	—
514	C₂×C₁₃	—	8	1	no	—
515	C₂×C₁₃	#2361	1	1	yes	characteristic
516	C₂×C₁₃	#2930	1	1	yes	characteristic
517	C₂×C₁₃	#2930	1	1	yes	characteristic
518	C₂×C₁₃	#2933	1	1	yes	characteristic
519	C₂×C₁₃	#2935	1	1	yes	characteristic
520	C₂×C₁₃	#2993	1	1	yes	characteristic
521	C₂×C₁₃	#2995	1	1	yes	characteristic
522	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
523	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
524	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	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	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	D₄×D₁₃	1	2	yes	—
551	C₂²×C₄	#6129	1	2	yes	—
552	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
553	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
557	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
560	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
562	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
564	M₁₆	—	52	4	no	—
565	M₁₆	—	52	4	no	—
566	M₁₆	—	52	4	no	—
567	C₂×C₈	—	13	2	no	—
568	C₂×C₈	—	13	2	no	—
569	C₂×C₈	—	13	2	no	—
570	C₂×C₈	—	13	2	no	—
571	C₂×C₈	—	26	1	no	—
572	C₂×C₈	—	26	1	no	—
573	C₂×C₈	—	26	1	no	—
574	C₂×C₈	—	26	1	no	—
575	C₂×C₈	—	26	1	no	—
576	C₂×C₈	—	26	1	no	—
577	C₂×C₈	—	26	1	no	—
578	C₂×C₈	—	26	1	no	—
579	C₂×C₈	—	26	1	no	—
580	C₂×C₈	—	26	1	no	—
581	C₂×C₈	—	26	1	no	—
582	C₂×C₈	—	26	1	no	—
583	C₂×C₈	—	26	1	no	—
584	C₂×C₈	—	26	1	no	—
585	C₂×C₈	—	26	1	no	—
586	C₂×C₈	—	26	1	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	—	52	4	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	D₄×D₁₃	1	2	yes	—
618	C₄²	#6129	1	2	yes	—
619	C₁₃	#22994	1	1	yes	characteristic, complemented, Sylow
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
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	D₄×Dic₁₃	1	2	yes	—
641	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	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	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	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	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
687	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
688	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
689	C₂×C₄	#88202	1	2	yes	—
690	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
691	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
692	C₂×C₄	C₂×#6129	1	1	yes	characteristic
693	C₂×C₄	C₂×#6129	1	1	yes	characteristic
694	C₂×C₄	#88256	1	1	yes	characteristic
695	C₂×C₄	#88257	1	1	yes	characteristic
696	C₈	—	26	2	no	—
697	C₈	—	26	2	no	—
698	C₈	—	26	2	no	—
699	C₈	—	26	2	no	—
700	C₈	—	52	1	no	—
701	C₈	—	52	1	no	—
702	C₈	—	52	1	no	—
703	C₈	—	52	1	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
726	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
727	C₂²	C₂×#88202	1	1	yes	characteristic
728	C₂²	#11719524	1	1	yes	characteristic
729	C₂²	#11719524	1	1	yes	characteristic
730	C₂²	#11719524	1	1	yes	characteristic
731	C₂²	#11719532	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	#11719303	1	1	yes	characteristic
744	C₄	#11719314	1	1	yes	characteristic
745	C₄	#11719316	1	1	yes	characteristic
746	C₄	#11719323	1	1	yes	characteristic
747	C₂	—	4	2	no	—
748	C₂	—	8	1	no	—
749	C₂	—	8	1	no	—
750	C₂	#13117856	1	1	yes	characteristic
751	C₂	#13123540	1	1	yes	characteristic
752	C₂	#13123540	1	1	yes	characteristic
753	C₂	#13123563	1	1	yes	characteristic
754	C₂	#13123580	1	1	yes	characteristic
755	C₂	#13123985	1	1	yes	characteristic
756	C₂	#13124006	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2392	C₂
prime radical	C₁₃×#392	C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2392	D₁₃
hypocenter	C₁₃	#22994
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2392

Complements

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

N	H ≅ G/N	type
1. C₂×#11718673	C₂	semidirect
2. C₂×#11718673	C₂	semidirect
3. C₂×#11718672	C₂	semidirect
4. C₂×#11718660	C₂	semidirect
5. #13115635	C₂	semidirect
6. #13115555	C₂	semidirect
7. #13115451	C₂	semidirect
8. #13115444	C₂	semidirect
9. #13115134	C₂	semidirect
10. #13115129	C₂	semidirect
11. #13115021	C₂	semidirect
12. #13115021	C₂	semidirect
13. #13114711	C₂	semidirect
14. #13114602	C₂	semidirect
133. C₂²⋊#1055	D₄	semidirect
139. C₄⋊#1055	D₄	semidirect
619. C₁₃	#22994	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×#11718660	2
#13115635	2
#13115555	2
#13115451	2
#13115444	2
#13115134	2
#13115129	2
#13115021	2
#13114711	2
#13114602	2
C₁₃×#2392	2
#22994	13