Subgroups — #15879882

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718895	C₂	1	1	yes	maximal, characteristic
3	#13115451	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115021	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115016	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114904	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114820	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114748	C₂	1	1	yes	maximal, characteristic
12	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114602	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×#6099	C₂²	1	1	yes	characteristic
20	C₂³×#1055	C₂²	1	1	yes	characteristic
21	C₁₃×#391	C₄	1	1	yes	characteristic
22	C₁₃×#391	C₄	1	1	yes	characteristic
23	C₁₃×#390	C₄	1	1	yes	characteristic
24	C₁₃×#390	C₄	1	1	yes	characteristic
25	C₁₃×#386	C₄	1	1	yes	characteristic
26	C₁₃×#386	C₄	1	1	yes	characteristic
27	C₁₃×#386	C₄	1	1	yes	characteristic
28	C₁₃×#386	C₄	1	1	yes	characteristic
29	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₂²⋊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	#11718895	—	2	4	no	—
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	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	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
44	#11718586	—	2	4	no	—
45	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
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×#88043	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	#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	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	—	4	1	no	—
67	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#117	—	4	1	no	—
77	C₁₃×#117	—	4	1	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×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×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×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	—	2	2	no	—
92	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×#6099	—	2	2	no	—
99	C₂×#6099	—	2	2	no	—
100	C₂×#6099	—	4	1	no	—
101	C₂²×#1055	—	2	2	no	—
102	C₂²×#1055	—	2	2	no	—
103	C₂²×#1055	—	4	1	no	—
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	C₂²×#1055	C₂³	1	1	yes	characteristic
108	C₂²×#1055	C₂³	1	1	yes	characteristic
109	C₂²×#1055	C₂³	1	1	yes	characteristic
110	C₂²×#1055	C₂³	1	1	yes	characteristic
111	C₂²×#1055	C₂³	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	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊#1055	—	2	2	no	—
121	C₂²⋊#1055	—	2	2	no	—
122	C₂²⋊#1055	—	2	2	no	—
123	C₂²⋊#1055	—	2	2	no	—
124	C₂²⋊#1055	—	2	2	no	—
125	C₂²⋊#1055	—	2	2	no	—
126	C₂²⋊#1055	—	2	2	no	—
127	C₂²⋊#1055	—	4	1	no	—
128	C₂²⋊#1055	—	4	1	no	—
129	C₂²⋊#1055	D₄	1	4	yes	—
130	C₄⋊#1055	—	2	2	no	—
131	C₄⋊#1055	—	2	2	no	—
132	C₄⋊#1055	—	4	1	no	—
133	C₄⋊#1055	—	4	1	no	—
134	#88043	—	4	1	no	—
135	C₄×#1055	—	2	2	no	—
136	C₄×#1055	—	2	2	no	—
137	C₄×#1055	—	4	1	no	—
138	#22556	—	13	1	no	maximal, Sylow
139	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×#41	—	4	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	4	1	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	—	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	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	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	—	4	1	no	—
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	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	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₁₃	#41	1	2	yes	—
191	C₂²×C₄×C₁₃	#41	1	2	yes	—
192	C₂²×C₄×C₁₃	#41	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	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	—	4	1	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	2	no	—
207	C₄²×C₁₃	—	2	2	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	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	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	—	2	1	no	—
238	C₂×#1055	—	2	1	no	—
239	C₂×#1055	—	4	4	no	—
240	C₂×#1055	C₂×D₄	1	2	yes	—
241	C₂×#1055	C₂×D₄	1	2	yes	—
242	C₂×#431	—	13	1	no	—
243	C₂×#408	—	13	1	no	—
244	#2297	D₁₃	1	1	yes	characteristic
245	#1924	—	13	1	no	—
246	#1923	—	13	1	no	—
247	#1923	—	13	1	no	—
248	#1923	—	13	1	no	—
249	#1851	—	13	1	no	—
250	#1850	—	13	1	no	—
251	#1817	—	13	1	no	—
252	#1798	—	13	1	no	—
253	#1780	—	13	1	no	—
254	#1753	—	13	1	no	—
255	C₈×C₂²⋊C₄	—	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	#117	1	2	yes	—
277	C₂³×C₁₃	C₄×D₄	1	2	yes	—
278	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
279	Q₈×C₁₃	—	4	4	no	—
280	D₄×C₁₃	—	4	4	no	—
281	D₄×C₁₃	—	4	4	no	—
282	D₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	2	8	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	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	2	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	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	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	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	4	4	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	#117	1	2	yes	—
326	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
327	C₂×C₄×C₁₃	#131	1	2	yes	—
328	C₂×C₄×C₁₃	#131	1	2	yes	—
329	C₂×C₄×C₁₃	#131	1	2	yes	—
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
336	#1055	—	2	2	no	—
337	#1055	—	2	2	no	—
338	#1055	—	4	1	no	—
339	#1055	—	4	1	no	—
340	#1055	—	4	1	no	—
341	#1055	—	4	1	no	—
342	#1055	—	4	1	no	—
343	#1055	—	4	1	no	—
344	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
345	C₂²×M₁₆	—	13	1	no	—
346	C₂³×C₈	—	13	1	no	—
347	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
348	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
349	#431	—	26	4	no	—
350	C₂×C₄⋊C₈	—	13	1	no	—
351	C₂×C₄⋊C₈	—	13	1	no	—
352	C₂×C₄⋊C₈	—	13	1	no	—
353	C₂×C₄⋊C₈	—	13	1	no	—
354	#408	—	26	4	no	—
355	C₂×C₂²⋊C₈	—	13	1	no	—
356	C₂×C₂²⋊C₈	—	13	1	no	—
357	C₂×C₂²⋊C₈	—	13	1	no	—
358	C₂×C₂²⋊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×#97	—	13	1	no	—
366	C₂×C₄×C₈	—	13	1	no	—
367	C₂×C₄×C₈	—	13	1	no	—
368	C₂×C₄×C₈	—	13	1	no	—
369	#391	Dic₁₃	1	1	yes	characteristic
370	#391	Dic₁₃	1	1	yes	characteristic
371	#390	Dic₁₃	1	1	yes	characteristic
372	#390	Dic₁₃	1	1	yes	characteristic
373	#386	Dic₁₃	1	1	yes	characteristic
374	#386	Dic₁₃	1	1	yes	characteristic
375	#386	Dic₁₃	1	1	yes	characteristic
376	#386	Dic₁₃	1	1	yes	characteristic
377	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
381	#336	—	13	1	no	—
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	#336	—	13	1	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	2	2	no	—
393	C₂²×C₁₃	—	2	2	no	—
394	C₂²×C₁₃	—	2	2	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	—	4	1	no	—
410	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
411	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
412	C₂²×C₁₃	#518	1	1	yes	characteristic
413	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
414	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
415	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
416	C₂²×C₁₃	#568	1	1	yes	characteristic
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	2	2	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	2	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	—	4	1	no	—
428	C₄×C₁₃	#546	1	1	yes	characteristic
429	C₄×C₁₃	#546	1	1	yes	characteristic
430	C₄×C₁₃	#551	1	1	yes	characteristic
431	C₄×C₁₃	#551	1	1	yes	characteristic
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	4	1	no	—
437	C₂×#41	—	4	1	no	—
438	C₂²×Q₈	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	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
442	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
444	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
445	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
447	C₂×M₁₆	—	26	2	no	—
448	C₂×M₁₆	—	26	2	no	—
449	C₂×M₁₆	—	52	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	—	13	1	no	—
455	C₂²×C₈	—	13	1	no	—
456	C₂²×C₈	—	13	1	no	—
457	C₂²×C₈	—	13	1	no	—
458	C₂²×C₈	—	26	2	no	—
459	C₂²×C₈	—	26	2	no	—
460	C₂²×C₈	—	52	1	no	—
461	#117	—	4	1	no	—
462	#117	—	4	1	no	—
463	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
471	C₂×C₂²⋊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×C₄²	—	2	2	no	—
476	C₂×C₄²	—	2	2	no	—
477	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
478	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
479	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
480	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
481	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
483	C₄⋊C₈	—	26	2	no	—
484	C₄⋊C₈	—	26	2	no	—
485	C₄⋊C₈	—	52	1	no	—
486	C₄⋊C₈	—	52	1	no	—
487	C₂²⋊C₈	—	13	4	no	—
488	C₂²⋊C₈	—	26	2	no	—
489	C₂²⋊C₈	—	26	2	no	—
490	C₂²⋊C₈	—	26	2	no	—
491	C₂²⋊C₈	—	26	2	no	—
492	C₂²⋊C₈	—	26	2	no	—
493	C₂²⋊C₈	—	26	2	no	—
494	C₂²⋊C₈	—	26	2	no	—
495	C₂²⋊C₈	—	52	1	no	—
496	C₂²⋊C₈	—	52	1	no	—
497	#97	—	52	1	no	—
498	C₄×C₈	—	26	2	no	—
499	C₄×C₈	—	26	2	no	—
500	C₄×C₈	—	52	1	no	—
501	#95	C₂×Dic₁₃	1	1	yes	characteristic
502	#95	C₂×Dic₁₃	1	1	yes	characteristic
503	#95	C₂×Dic₁₃	1	1	yes	characteristic
504	#95	C₂×Dic₁₃	1	1	yes	characteristic
505	#95	C₂×Dic₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	4	2	no	—
510	C₂×C₁₃	—	4	2	no	—
511	C₂×C₁₃	—	8	1	no	—
512	C₂×C₁₃	#2342	1	1	yes	characteristic
513	C₂×C₁₃	#2922	1	1	yes	characteristic
514	C₂×C₁₃	#2925	1	1	yes	characteristic
515	C₂×C₁₃	#2929	1	1	yes	characteristic
516	C₂×C₁₃	#2933	1	1	yes	characteristic
517	C₂×C₁₃	#2979	1	1	yes	characteristic
518	C₂×C₁₃	#2981	1	1	yes	characteristic
519	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
520	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
521	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
522	#41	—	4	4	no	—
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	4	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	4	1	no	—
536	C₂×D₄	—	4	1	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	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	2	no	—
550	C₂²×C₄	—	2	2	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	—	4	1	no	—
558	C₂²×C₄	#6127	1	2	yes	—
559	C₂²×C₄	#6127	1	2	yes	—
560	C₂²×C₄	D₄×D₁₃	1	2	yes	—
561	C₂²×C₄	#6129	1	2	yes	—
562	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
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	C₂³×D₁₃	1	1	yes	characteristic
574	M₁₆	—	52	4	no	—
575	C₂×C₈	—	13	2	no	—
576	C₂×C₈	—	13	2	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	—	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	—	52	4	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	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	C₂²⋊C₄	—	4	1	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₁₃	#22556	1	1	yes	characteristic, complemented, Sylow
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	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	#88180	1	2	yes	—
643	C₂³	D₄×Dic₁₃	1	2	yes	—
644	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
645	Q₈	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	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	—	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	—	4	4	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	#88180	1	2	yes	—
692	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
693	C₂×C₄	#88202	1	2	yes	—
694	C₂×C₄	#88202	1	2	yes	—
695	C₂×C₄	#88202	1	2	yes	—
696	C₂×C₄	C₂×#6127	1	1	yes	characteristic
697	C₂×C₄	C₂×#6127	1	1	yes	characteristic
698	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂×#6129	1	1	yes	characteristic
700	C₂×C₄	#88251	1	1	yes	characteristic
701	C₂×C₄	#88251	1	1	yes	characteristic
702	C₈	—	26	2	no	—
703	C₈	—	26	2	no	—
704	C₈	—	52	1	no	—
705	C₈	—	52	1	no	—
706	C₈	—	52	1	no	—
707	C₈	—	52	1	no	—
708	C₈	—	52	1	no	—
709	C₈	—	52	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	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	—	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	C₂×#88180	1	1	yes	characteristic
732	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
733	C₂²	#11719503	1	1	yes	characteristic
734	C₂²	C₂×#88202	1	1	yes	characteristic
735	C₂²	C₂×#88202	1	1	yes	characteristic
736	C₂²	C₂×#88202	1	1	yes	characteristic
737	C₂²	#11719524	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	#11719195	1	1	yes	characteristic
750	C₄	#11719195	1	1	yes	characteristic
751	C₄	#11719200	1	1	yes	characteristic
752	C₄	#11719200	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	1	no	—
756	C₂	#13117685	1	1	yes	characteristic
757	C₂	#13123480	1	1	yes	characteristic
758	C₂	#13123502	1	1	yes	characteristic
759	C₂	#13123531	1	1	yes	characteristic
760	C₂	#13123563	1	1	yes	characteristic
761	C₂	#13123903	1	1	yes	characteristic
762	C₂	#13123912	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2297	C₂
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2297	D₁₃
hypocenter	C₁₃	#22556
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2297

Complements

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

N	H ≅ G/N	type
1. C₂×#11718586	C₂	semidirect
3. #13115451	C₂	semidirect
4. #13115444	C₂	semidirect
5. #13115444	C₂	semidirect
6. #13115444	C₂	semidirect
7. #13115021	C₂	semidirect
8. #13115016	C₂	semidirect
9. #13114904	C₂	semidirect
10. #13114820	C₂	semidirect
12. #13114620	C₂	semidirect
13. C₂²⋊C₄×#1055	C₂	semidirect
14. #13114602	C₂	semidirect
622. C₁₃	#22556	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
C₂×#11718895	2
#13115451	2
#13115444	2
#13115021	2
#13115016	2
#13114904	2
#13114820	2
#13114748	2
#13114620	2
C₂²⋊C₄×#1055	2
#13114602	2
C₁₃×#2297	2
#22556	13