Subgroups — #15873129

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115451	C₂	1	1	yes	maximal, characteristic
2	#13115451	C₂	1	1	yes	maximal, characteristic
3	#13115444	C₂	1	1	yes	maximal, characteristic
4	#13115444	C₂	1	1	yes	maximal, characteristic
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114988	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114953	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114820	C₂	1	1	yes	maximal, characteristic
12	#13114820	C₂	1	1	yes	maximal, characteristic
13	#13114693	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114693	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#388	C₄	1	1	yes	characteristic
18	C₁₃×#388	C₄	1	1	yes	characteristic
19	C₁₃×#388	C₄	1	1	yes	characteristic
20	C₁₃×#388	C₄	1	1	yes	characteristic
21	C₁₃×#387	C₄	1	1	yes	characteristic
22	C₁₃×#387	C₄	1	1	yes	characteristic
23	C₁₃×#387	C₄	1	1	yes	characteristic
24	C₁₃×#387	C₄	1	1	yes	characteristic
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#376	C₂²	1	1	yes	characteristic
30	C₄³×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₂×#88043	C₂²	1	1	yes	characteristic
44	C₂×#88043	C₂²	1	1	yes	characteristic
45	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
46	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
47	#11718116	C₂²	1	1	yes	characteristic
48	#11718116	C₂²	1	1	yes	characteristic
49	#11718116	C₂²	1	1	yes	characteristic
50	#11718116	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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×#1055	C₂³	1	1	yes	characteristic
85	C₂²×#1055	C₂³	1	1	yes	characteristic
86	C₂²×#1055	C₂³	1	1	yes	characteristic
87	C₂²×#1055	C₂³	1	1	yes	characteristic
88	C₂²×#1055	C₂³	1	1	yes	characteristic
89	C₂²×#1055	C₂³	1	1	yes	characteristic
90	C₂²×#1055	C₂³	1	1	yes	characteristic
91	C₂²×#1055	C₂³	1	1	yes	characteristic
92	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊#1055	—	4	1	no	—
105	C₂²⋊#1055	—	4	1	no	—
106	C₂²⋊#1055	—	4	1	no	—
107	C₂²⋊#1055	—	4	1	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	C₄⋊#1055	—	2	2	no	—
111	C₄⋊#1055	—	2	2	no	—
112	C₄⋊#1055	—	4	1	no	—
113	C₄⋊#1055	—	4	1	no	—
114	C₄⋊#1055	—	4	1	no	—
115	C₄⋊#1055	—	4	1	no	—
116	#88043	—	4	1	no	—
117	#88043	—	4	1	no	—
118	C₄×#1055	—	4	1	no	—
119	C₄×#1055	—	4	1	no	—
120	#21929	—	13	1	no	maximal, Sylow
121	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	1	no	—
147	C₁₃×C₄⋊C₄	—	4	1	no	—
148	C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	1	no	—
153	C₁₃×C₂²⋊C₄	—	4	1	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₄²×C₁₃	—	4	1	no	—
167	C₄²×C₁₃	—	4	1	no	—
168	C₄²×C₁₃	#41	1	2	yes	—
169	C₄²×C₁₃	#41	1	2	yes	—
170	C₂×#1055	—	2	1	no	—
171	C₂×#1055	—	2	1	no	—
172	C₂×#1055	—	2	1	no	—
173	C₂×#1055	—	2	1	no	—
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	2	1	no	—
178	C₂×#1055	—	2	1	no	—
179	C₂×#1055	—	2	1	no	—
180	C₂×#1055	—	2	1	no	—
181	C₂×#1055	—	2	1	no	—
182	C₂×#1055	—	2	1	no	—
183	C₂×#1055	—	2	1	no	—
184	C₂×#1055	—	2	1	no	—
185	C₂×#1055	—	2	1	no	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	1	no	—
189	C₂×#1055	—	2	1	no	—
190	C₂×#1055	—	2	1	no	—
191	C₂×#1055	—	2	1	no	—
192	C₂×#1055	—	2	1	no	—
193	C₂×#1055	—	2	1	no	—
194	#2298	D₁₃	1	1	yes	characteristic
195	#1924	—	13	1	no	—
196	#1924	—	13	1	no	—
197	#1923	—	13	1	no	—
198	#1923	—	13	1	no	—
199	#1917	—	13	1	no	—
200	#1917	—	13	1	no	—
201	#1916	—	13	1	no	—
202	#1916	—	13	1	no	—
203	#1842	—	13	1	no	—
204	#1831	—	13	1	no	—
205	#1798	—	13	1	no	—
206	#1798	—	13	1	no	—
207	#1768	—	13	1	no	—
208	#1768	—	13	1	no	—
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	#117	1	2	yes	—
257	C₂×C₄×C₁₃	#117	1	2	yes	—
258	C₂×C₄×C₁₃	#131	1	2	yes	—
259	C₂×C₄×C₁₃	#131	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
266	#1055	—	4	1	no	—
267	#1055	—	4	1	no	—
268	#1055	—	4	1	no	—
269	#1055	—	4	1	no	—
270	#1055	—	4	1	no	—
271	#1055	—	4	1	no	—
272	#1055	—	4	1	no	—
273	#1055	—	4	1	no	—
274	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₈	—	13	1	no	—
276	C₂×C₄⋊C₈	—	13	1	no	—
277	C₂×C₄⋊C₈	—	13	1	no	—
278	C₂×C₄⋊C₈	—	13	1	no	—
279	C₂×C₄⋊C₈	—	13	1	no	—
280	C₂×C₄⋊C₈	—	13	1	no	—
281	C₂×C₄⋊C₈	—	13	1	no	—
282	C₂×C₄⋊C₈	—	13	1	no	—
283	C₂×C₂²⋊C₈	—	13	1	no	—
284	C₂×C₂²⋊C₈	—	13	1	no	—
285	C₂×C₂²⋊C₈	—	13	1	no	—
286	C₂×C₂²⋊C₈	—	13	1	no	—
287	C₂×#97	—	13	1	no	—
288	C₂×#97	—	13	1	no	—
289	C₂×C₄×C₈	—	13	1	no	—
290	C₂×C₄×C₈	—	13	1	no	—
291	#388	Dic₁₃	1	1	yes	characteristic
292	#388	Dic₁₃	1	1	yes	characteristic
293	#388	Dic₁₃	1	1	yes	characteristic
294	#388	Dic₁₃	1	1	yes	characteristic
295	#387	Dic₁₃	1	1	yes	characteristic
296	#387	Dic₁₃	1	1	yes	characteristic
297	#387	Dic₁₃	1	1	yes	characteristic
298	#387	Dic₁₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
303	#376	C₂×D₁₃	1	1	yes	characteristic
304	C₄³	C₂×D₁₃	1	1	yes	characteristic
305	#336	—	13	1	no	—
306	#336	—	13	1	no	—
307	#336	—	13	1	no	—
308	#336	—	13	1	no	—
309	#336	—	13	1	no	—
310	#336	—	13	1	no	—
311	#336	—	13	1	no	—
312	#336	—	13	1	no	—
313	#336	—	13	1	no	—
314	#336	—	13	1	no	—
315	#336	—	13	1	no	—
316	#336	—	13	1	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
325	C₂²×C₁₃	#520	1	1	yes	characteristic
326	C₂²×C₁₃	#520	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
328	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
329	C₂²×C₁₃	#568	1	1	yes	characteristic
330	C₂²×C₁₃	#568	1	1	yes	characteristic
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	#540	1	1	yes	characteristic
345	C₄×C₁₃	#541	1	1	yes	characteristic
346	C₄×C₁₃	#542	1	1	yes	characteristic
347	C₄×C₁₃	#542	1	1	yes	characteristic
348	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	13	1	no	—
353	C₂²×C₈	—	13	1	no	—
354	C₂²×C₈	—	13	1	no	—
355	C₂²×C₈	—	13	1	no	—
356	C₂²×C₈	—	13	1	no	—
357	#117	—	2	2	no	—
358	#117	—	2	2	no	—
359	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₄⋊C₈	—	26	2	no	—
382	C₄⋊C₈	—	26	2	no	—
383	C₄⋊C₈	—	26	2	no	—
384	C₄⋊C₈	—	26	2	no	—
385	C₄⋊C₈	—	52	1	no	—
386	C₄⋊C₈	—	52	1	no	—
387	C₄⋊C₈	—	52	1	no	—
388	C₄⋊C₈	—	52	1	no	—
389	C₂²⋊C₈	—	52	1	no	—
390	C₂²⋊C₈	—	52	1	no	—
391	C₂²⋊C₈	—	52	1	no	—
392	C₂²⋊C₈	—	52	1	no	—
393	#97	—	52	1	no	—
394	#97	—	52	1	no	—
395	C₄×C₈	—	52	1	no	—
396	C₄×C₈	—	52	1	no	—
397	#95	C₂×Dic₁₃	1	1	yes	characteristic
398	#95	C₂×Dic₁₃	1	1	yes	characteristic
399	#95	C₂×Dic₁₃	1	1	yes	characteristic
400	#95	C₂×Dic₁₃	1	1	yes	characteristic
401	#95	C₂×Dic₁₃	1	1	yes	characteristic
402	#95	C₂×Dic₁₃	1	1	yes	characteristic
403	#95	C₂×Dic₁₃	1	1	yes	characteristic
404	#95	C₂×Dic₁₃	1	1	yes	characteristic
405	#95	C₂×Dic₁₃	1	1	yes	characteristic
406	#95	C₂×Dic₁₃	1	1	yes	characteristic
407	#95	C₂×Dic₁₃	1	1	yes	characteristic
408	#95	C₂×Dic₁₃	1	1	yes	characteristic
409	C₂×C₁₃	—	8	1	no	—
410	C₂×C₁₃	#2314	1	1	yes	characteristic
411	C₂×C₁₃	#2925	1	1	yes	characteristic
412	C₂×C₁₃	#2925	1	1	yes	characteristic
413	C₂×C₁₃	#2992	1	1	yes	characteristic
414	C₂×C₁₃	#2993	1	1	yes	characteristic
415	C₂×C₁₃	#2994	1	1	yes	characteristic
416	C₂×C₁₃	#2995	1	1	yes	characteristic
417	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
438	C₂×C₈	—	26	1	no	—
439	C₂×C₈	—	26	1	no	—
440	C₂×C₈	—	26	1	no	—
441	C₂×C₈	—	26	1	no	—
442	C₂×C₈	—	26	1	no	—
443	C₂×C₈	—	26	1	no	—
444	C₂×C₈	—	26	1	no	—
445	C₂×C₈	—	26	1	no	—
446	C₂×C₈	—	26	1	no	—
447	C₂×C₈	—	26	1	no	—
448	C₂×C₈	—	26	1	no	—
449	C₂×C₈	—	26	1	no	—
450	C₂×C₈	—	26	1	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	1	no	—
454	C₂×C₈	—	26	1	no	—
455	C₂×C₈	—	26	1	no	—
456	C₂×C₈	—	26	1	no	—
457	C₂×C₈	—	26	1	no	—
458	C₂×C₈	—	26	1	no	—
459	C₂×C₈	—	26	1	no	—
460	C₂×C₈	—	26	1	no	—
461	C₂×C₈	—	26	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	#6127	1	2	yes	—
489	C₄²	#6127	1	2	yes	—
490	C₁₃	#21929	1	1	yes	characteristic, complemented, Sylow
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	#88180	1	2	yes	—
539	C₂×C₄	#88180	1	2	yes	—
540	C₂×C₄	#88202	1	2	yes	—
541	C₂×C₄	#88202	1	2	yes	—
542	C₂×C₄	C₂×#6127	1	1	yes	characteristic
543	C₂×C₄	C₂×#6127	1	1	yes	characteristic
544	C₂×C₄	#88256	1	1	yes	characteristic
545	C₂×C₄	#88256	1	1	yes	characteristic
546	C₂×C₄	#88257	1	1	yes	characteristic
547	C₂×C₄	#88257	1	1	yes	characteristic
548	C₈	—	52	1	no	—
549	C₈	—	52	1	no	—
550	C₈	—	52	1	no	—
551	C₈	—	52	1	no	—
552	C₈	—	52	1	no	—
553	C₈	—	52	1	no	—
554	C₈	—	52	1	no	—
555	C₈	—	52	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×#88180	1	1	yes	characteristic
564	C₂²	C₂×#88202	1	1	yes	characteristic
565	C₂²	C₂×#88202	1	1	yes	characteristic
566	C₂²	#11719524	1	1	yes	characteristic
567	C₂²	#11719524	1	1	yes	characteristic
568	C₂²	#11719532	1	1	yes	characteristic
569	C₂²	#11719532	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	#11719223	1	1	yes	characteristic
584	C₄	#11719239	1	1	yes	characteristic
585	C₄	#11719239	1	1	yes	characteristic
586	C₄	#11719240	1	1	yes	characteristic
587	C₂	—	8	1	no	—
588	C₂	#13117445	1	1	yes	characteristic
589	C₂	#13123502	1	1	yes	characteristic
590	C₂	#13123502	1	1	yes	characteristic
591	C₂	#13123975	1	1	yes	characteristic
592	C₂	#13123985	1	1	yes	characteristic
593	C₂	#13123996	1	1	yes	characteristic
594	C₂	#13124006	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2298	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2298	D₁₃
hypocenter	C₁₃	#21929
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2298

Complements

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

N	H ≅ G/N	type
5. #13115402	C₂	semidirect
6. #13115402	C₂	semidirect
7. #13115395	C₂	semidirect
8. #13115395	C₂	semidirect
9. #13114988	C₂	semidirect
10. #13114953	C₂	semidirect
13. #13114693	C₂	semidirect
14. #13114693	C₂	semidirect
490. C₁₃	#21929	semidirect

Maximal subgroups

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

subgroup	index
#13115451	2
#13115444	2
#13115402	2
#13115395	2
#13114988	2
#13114953	2
#13114820	2
#13114693	2
C₁₃×#2298	2
#21929	13