Subgroups — #15863764

Order 3328.

1296 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719450	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718793	C₂	1	1	yes	maximal, characteristic
4	#13123280	C₂	1	1	yes	maximal, characteristic
5	#13115054	C₂	1	8	yes	maximal, complemented
6	#13114562	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114562	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	#11719450	—	2	2	no	—
17	#11719450	—	2	2	no	—
18	#11719450	—	2	2	no	—
19	#11719450	C₂²	1	4	yes	—
20	C₂×#88161	—	2	2	no	—
21	C₂×M₁₆×D₁₃	—	2	2	no	—
22	C₂×#88155	—	2	2	no	—
23	C₁₃×#430	—	2	2	no	—
24	C₁₃×#430	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#108	—	2	2	no	—
26	C₂×#88064	C₄	1	2	yes	—
27	#11718793	C₄	1	4	yes	—
28	#11718793	C₂²	1	4	yes	—
29	C₂×#88063	C₄	1	2	yes	—
30	#11718790	C₂²	1	4	yes	—
31	#11718787	—	2	2	no	—
32	#11718785	—	2	2	no	—
33	#11718785	C₂²	1	4	yes	complemented
34	C₂×#88062	—	2	2	no	—
35	#11718771	—	2	2	no	—
36	#11718150	C₂²	1	4	yes	complemented
37	#11718150	C₂²	1	4	yes	complemented
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₂²⋊D₁₃	Q₈	1	2	yes	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	—	2	1	no	—
47	C₂×#6127	—	2	1	no	—
48	C₂×#6127	C₂×C₄	1	2	yes	—
49	C₂×#6127	D₄	1	2	yes	—
50	C₂×#6127	Q₈	1	2	yes	—
51	C₂×#6127	C₂³	1	2	yes	—
52	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₁₃	D₄	1	2	yes	—
54	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
69	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	C₂×C₄	1	2	yes	—
89	C₂×#6099	C₂×C₄	1	2	yes	—
90	C₂×#6099	D₄	1	2	yes	—
91	C₂×#6099	D₄	1	2	yes	—
92	C₂×#6099	C₂³	1	2	yes	—
93	C₂×#6099	C₂³	1	2	yes	—
94	C₂²×#1055	—	2	1	no	—
95	C₂²×#1055	—	2	1	no	—
96	C₂²×#1055	C₂³	1	2	yes	—
97	#88161	—	2	8	no	—
98	#88161	—	2	8	no	—
99	M₁₆×D₁₃	—	2	8	no	—
100	M₁₆×D₁₃	—	2	8	no	—
101	#88155	—	2	8	no	—
102	#88155	—	2	8	no	—
103	C₂×#6094	—	2	4	no	—
104	C₂×C₈×D₁₃	—	2	4	no	—
105	C₁₃×#108	—	2	8	no	—
106	#88064	C₂×C₄	1	8	yes	—
107	#88063	C₂×C₄	1	8	yes	—
108	#88062	—	2	8	no	—
109	#88060	—	2	8	no	—
110	#20860	—	13	1	no	maximal, Sylow
111	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂³×D₁₃	C₄⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₃	—	2	2	no	—
128	C₂×C₂²⋊D₁₃	—	2	2	no	—
129	C₂×C₂²⋊D₁₃	—	2	2	no	—
130	C₂×C₂²⋊D₁₃	—	2	2	no	—
131	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	4	yes	—
132	C₂×C₂²⋊D₁₃	C₂×Q₈	1	4	yes	—
133	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
134	#6127	—	2	2	no	—
135	#6127	—	2	2	no	—
136	#6127	—	2	2	no	—
137	#6127	—	2	2	no	—
138	#6127	—	2	2	no	—
139	#6127	—	2	2	no	—
140	#6127	—	2	2	no	—
141	#6127	—	2	2	no	—
142	#6127	—	2	2	no	—
143	#6127	—	2	2	no	—
144	#6127	—	2	2	no	—
145	#6127	—	2	2	no	—
146	#6127	—	2	2	no	—
147	#6127	—	2	2	no	—
148	#6127	—	2	2	no	—
149	#6127	—	2	2	no	—
150	C₂×D₅₂	—	2	1	no	—
151	C₂×D₅₂	—	2	1	no	—
152	C₂×D₅₂	—	2	1	no	—
153	C₂×D₅₂	—	2	1	no	—
154	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
155	C₂×D₅₂	C₂²×C₄	1	2	yes	—
156	C₂×C₄×D₁₃	—	2	2	no	—
157	C₂×C₄×D₁₃	—	2	2	no	—
158	C₂×C₄×D₁₃	—	2	2	no	—
159	C₂×C₄×D₁₃	—	2	2	no	—
160	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
161	C₂×C₄×D₁₃	C₂×D₄	1	4	yes	—
162	C₂×Dic₂₆	—	2	1	no	—
163	C₂×Dic₂₆	—	2	1	no	—
164	C₂×Dic₂₆	—	2	1	no	—
165	C₂×Dic₂₆	—	2	1	no	—
166	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
167	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	4	1	no	—
177	C₁₃×M₁₆	—	4	1	no	—
178	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
179	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	4	1	no	—
188	C₂×C₈×C₁₃	—	4	1	no	—
189	#6099	—	2	2	no	—
190	#6099	—	2	2	no	—
191	#6099	—	2	2	no	—
192	#6099	—	2	2	no	—
193	#6099	—	2	2	no	—
194	#6099	—	2	2	no	—
195	#6099	—	4	1	no	—
196	#6099	—	4	1	no	—
197	#6099	—	4	1	no	—
198	#6099	—	4	1	no	—
199	#6099	C₂²×C₄	1	4	yes	—
200	#6099	C₂×D₄	1	4	yes	—
201	C₂×#1055	—	2	2	no	—
202	C₂×#1055	—	2	2	no	—
203	C₂×#1055	—	2	2	no	—
204	C₂×#1055	—	2	2	no	—
205	C₂×#1055	—	2	2	no	—
206	C₂×#1055	—	2	2	no	—
207	C₂×#1055	—	2	2	no	—
208	C₂×#1055	—	2	2	no	—
209	C₂×#1055	—	2	2	no	—
210	#6094	—	2	16	no	—
211	C₈×D₁₃	—	2	16	no	—
212	C₂×#568	—	13	1	no	—
213	C₂×#430	—	13	1	no	—
214	C₂×#430	D₁₃	1	1	yes	characteristic, complemented
215	C₂×#413	—	13	1	no	—
216	#2879	—	13	1	no	—
217	#1858	—	13	8	no	—
218	#1738	—	13	1	no	—
219	#1738	—	13	1	no	—
220	C₂³×C₁₃	—	8	1	no	—
221	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	2	2	no	—
230	C₂²×D₁₃	—	8	2	no	—
231	C₂²×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
232	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	2	4	no	—
262	C₂²⋊D₁₃	—	2	4	no	—
263	C₂²⋊D₁₃	—	2	4	no	—
264	C₂×Dic₁₃	—	2	2	no	—
265	C₂×Dic₁₃	—	2	2	no	—
266	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
267	D₅₂	—	2	2	no	—
268	D₅₂	—	2	2	no	—
269	D₅₂	—	2	2	no	—
270	D₅₂	—	2	2	no	—
271	C₄×D₁₃	—	2	4	no	—
272	C₄×D₁₃	—	2	4	no	—
273	C₄×D₁₃	—	2	4	no	—
274	C₄×D₁₃	—	2	4	no	—
275	Dic₂₆	—	2	2	no	—
276	Dic₂₆	—	2	2	no	—
277	Dic₂₆	—	2	2	no	—
278	Dic₂₆	—	2	2	no	—
279	C₈×C₁₃	—	2	4	no	—
280	C₈×C₁₃	—	2	4	no	—
281	C₈×C₁₃	—	4	2	no	—
282	#1055	—	2	4	no	—
283	#1055	—	2	4	no	—
284	#1055	—	4	2	no	—
285	C₂²×#41	—	13	1	no	—
286	#568	—	13	4	no	—
287	#568	—	26	2	no	—
288	#568	—	26	2	no	—
289	#568	—	26	2	no	—
290	C₂×#131	—	26	2	no	—
291	C₂×#131	—	26	2	no	—
292	C₂²×M₁₆	—	13	1	no	—
293	C₂²×M₁₆	—	13	1	no	—
294	C₂²×M₁₆	—	13	1	no	—
295	C₂²×M₁₆	—	26	2	no	—
296	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
297	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
298	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
299	#430	—	2	2	no	—
300	#430	—	13	4	no	—
301	#430	—	26	2	no	—
302	#430	C₂×D₁₃	1	4	yes	complemented
303	C₂×#108	—	2	2	no	—
304	C₂×#108	—	26	2	no	—
305	#413	—	13	4	no	—
306	#413	—	13	4	no	—
307	C₂×#101	—	13	2	no	—
308	C₂×#100	—	13	2	no	—
309	#408	—	13	4	no	—
310	#408	—	26	2	no	—
311	#407	—	26	2	no	—
312	#341	—	13	4	no	—
313	#341	—	13	4	no	—
314	C₂²×C₁₃	—	4	1	no	—
315	C₂²×C₁₃	—	4	1	no	—
316	C₂²×C₁₃	—	4	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	#385	1	1	yes	characteristic
322	C₂²×C₁₃	#385	1	1	yes	characteristic
323	C₂²×C₁₃	#385	1	1	yes	characteristic
324	C₂²×C₁₃	#385	1	1	yes	characteristic
325	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
328	C₂×D₁₃	—	2	4	no	—
329	C₂×D₁₃	—	4	4	no	—
330	C₂×D₁₃	—	4	4	no	—
331	C₂×D₁₃	—	8	2	no	—
332	C₄×C₁₃	#385	1	1	yes	characteristic
333	C₄×C₁₃	#385	1	1	yes	characteristic
334	C₄×C₁₃	#385	1	1	yes	characteristic
335	C₄×C₁₃	#385	1	1	yes	characteristic
336	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
339	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
340	Dic₁₃	—	2	4	no	—
341	C₂×#41	—	13	2	no	—
342	C₂×#41	—	13	2	no	—
343	C₂×#41	—	13	2	no	—
344	C₂×#41	—	13	2	no	—
345	C₂×#41	—	26	1	no	—
346	C₂×#41	—	26	1	no	—
347	C₂×#41	—	26	1	no	—
348	C₂×#41	—	26	1	no	—
349	C₂×#41	—	26	1	no	—
350	C₂×#41	—	26	1	no	—
351	C₂×#41	—	26	1	no	—
352	C₂×#41	—	26	1	no	—
353	C₂²×Q₈	—	13	1	no	—
354	C₂²×D₄	—	13	2	no	—
355	C₂²×D₄	—	13	1	no	—
356	C₂³×C₄	—	13	2	no	—
357	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
358	#131	—	26	8	no	—
359	#131	—	26	8	no	—
360	#131	—	26	8	no	—
361	#131	—	26	8	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	13	2	no	—
374	C₂×M₁₆	—	13	2	no	—
375	C₂×M₁₆	—	13	2	no	—
376	C₂×M₁₆	—	13	2	no	—
377	C₂×M₁₆	—	13	2	no	—
378	C₂×M₁₆	—	13	2	no	—
379	C₂×M₁₆	—	26	4	no	—
380	C₂×M₁₆	—	26	8	no	—
381	C₂×M₁₆	—	26	8	no	—
382	C₂×M₁₆	—	26	1	no	—
383	C₂×M₁₆	—	26	1	no	—
384	C₂×M₁₆	—	26	1	no	—
385	C₂×M₁₆	—	26	1	no	—
386	C₂×M₁₆	—	26	1	no	—
387	C₂×M₁₆	—	26	1	no	—
388	C₂×M₁₆	—	26	1	no	—
389	C₂×M₁₆	—	26	1	no	—
390	C₂×M₁₆	—	26	1	no	—
391	C₂×M₁₆	—	26	1	no	—
392	C₂×M₁₆	—	26	1	no	—
393	C₂×M₁₆	—	26	1	no	—
394	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
395	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
396	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
397	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
398	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
399	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
400	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	13	2	no	—
405	C₂²×C₈	—	26	4	no	—
406	C₂²×C₈	—	26	1	no	—
407	C₂²×C₈	—	26	1	no	—
408	#108	—	2	8	no	—
409	#108	—	26	8	no	—
410	#101	—	13	8	no	—
411	#100	—	13	8	no	—
412	C₂²⋊C₈	—	26	8	no	—
413	C₂×C₁₃	—	2	1	no	—
414	C₂×C₁₃	—	2	1	no	—
415	C₂×C₁₃	—	2	1	no	—
416	C₂×C₁₃	—	2	1	no	—
417	C₂×C₁₃	—	2	1	no	—
418	C₂×C₁₃	—	2	1	no	—
419	C₂×C₁₃	—	2	1	no	—
420	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
421	D₁₃	—	4	4	no	—
422	C₂⁴	—	13	2	no	—
423	C₂⁴	Q₈×D₁₃	1	1	yes	characteristic
424	#41	—	26	2	no	—
425	#41	—	26	2	no	—
426	#41	—	26	2	no	—
427	#41	—	26	2	no	—
428	#41	—	26	2	no	—
429	#41	—	26	2	no	—
430	#41	—	26	2	no	—
431	#41	—	26	2	no	—
432	#41	—	26	2	no	—
433	#41	—	26	2	no	—
434	#41	—	26	2	no	—
435	#41	—	26	2	no	—
436	#41	—	26	2	no	—
437	#41	—	26	2	no	—
438	#41	—	26	2	no	—
439	#41	—	26	2	no	—
440	C₂×Q₈	—	13	2	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×Q₈	—	26	1	no	—
443	C₂×Q₈	—	26	1	no	—
444	C₂×Q₈	—	26	1	no	—
445	C₂×Q₈	—	26	1	no	—
446	C₂×D₄	—	13	4	no	—
447	C₂×D₄	—	13	4	no	—
448	C₂×D₄	—	13	2	no	—
449	C₂×D₄	—	13	2	no	—
450	C₂×D₄	—	26	2	no	—
451	C₂×D₄	—	26	2	no	—
452	C₂×D₄	—	26	2	no	—
453	C₂×D₄	—	26	2	no	—
454	C₂×D₄	—	26	1	no	—
455	C₂×D₄	—	26	1	no	—
456	C₂×D₄	—	26	1	no	—
457	C₂×D₄	—	26	1	no	—
458	C₂²×C₄	—	13	2	no	—
459	C₂²×C₄	—	13	4	no	—
460	C₂²×C₄	—	13	4	no	—
461	C₂²×C₄	—	26	2	no	—
462	C₂²×C₄	—	26	2	no	—
463	C₂²×C₄	—	26	2	no	—
464	C₂²×C₄	—	26	2	no	—
465	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
467	C₂²×C₄	#6127	1	1	yes	characteristic
468	C₂²×C₄	#6127	1	1	yes	characteristic
469	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
473	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	#6131	1	1	yes	characteristic
475	C₂²×C₄	#6131	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	13	4	no	—
490	M₁₆	—	13	4	no	—
491	M₁₆	—	26	16	no	—
492	M₁₆	—	26	2	no	—
493	M₁₆	—	26	2	no	—
494	M₁₆	—	26	2	no	—
495	M₁₆	—	26	2	no	—
496	M₁₆	—	26	2	no	—
497	M₁₆	—	26	2	no	—
498	M₁₆	—	52	1	no	—
499	M₁₆	—	52	1	no	—
500	M₁₆	—	52	1	no	—
501	M₁₆	—	52	1	no	—
502	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
503	M₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	26	16	no	—
514	C₂×C₈	—	26	2	no	—
515	C₂×C₈	—	26	2	no	—
516	C₂×C₈	—	26	2	no	—
517	C₂×C₈	—	26	2	no	—
518	C₂×C₈	—	26	2	no	—
519	C₂×C₈	—	26	2	no	—
520	C₂×C₈	—	26	2	no	—
521	C₂×C₈	—	26	2	no	—
522	C₂×C₈	—	26	2	no	—
523	C₁₃	#20860	1	1	yes	characteristic, complemented, Sylow
524	C₂³	—	8	1	no	—
525	C₂³	—	13	4	no	—
526	C₂³	—	26	2	no	—
527	C₂³	—	26	2	no	—
528	C₂³	—	104	2	no	—
529	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
530	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
531	C₂³	#88150	1	1	yes	characteristic
532	C₂³	#88150	1	1	yes	characteristic
533	C₂³	#88200	1	1	yes	characteristic
534	C₂³	#88200	1	1	yes	characteristic
535	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
536	Q₈	—	26	2	no	—
537	Q₈	—	26	2	no	—
538	Q₈	—	26	2	no	—
539	Q₈	—	26	2	no	—
540	D₄	—	26	4	no	—
541	D₄	—	26	4	no	—
542	D₄	—	26	4	no	—
543	D₄	—	26	4	no	—
544	D₄	—	26	2	no	—
545	D₄	—	26	2	no	—
546	D₄	—	26	2	no	—
547	D₄	—	26	2	no	—
548	C₂×C₄	—	13	4	no	—
549	C₂×C₄	—	26	2	no	—
550	C₂×C₄	—	26	2	no	—
551	C₂×C₄	—	26	4	no	—
552	C₂×C₄	—	26	4	no	—
553	C₂×C₄	—	26	4	no	—
554	C₂×C₄	—	26	4	no	—
555	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
557	C₂×C₄	#88147	1	1	yes	characteristic
558	C₂×C₄	#88147	1	1	yes	characteristic
559	C₂×C₄	#88147	1	1	yes	characteristic
560	C₂×C₄	#88147	1	1	yes	characteristic
561	C₂×C₄	#88148	1	1	yes	characteristic
562	C₂×C₄	#88148	1	1	yes	characteristic
563	C₂×C₄	#88148	1	1	yes	characteristic
564	C₂×C₄	#88148	1	1	yes	characteristic
565	C₂×C₄	#88150	1	1	yes	characteristic
566	C₂×C₄	#88150	1	1	yes	characteristic
567	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
568	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
569	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
570	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
571	C₂×C₄	#88191	1	1	yes	characteristic
572	C₂×C₄	#88191	1	1	yes	characteristic
573	C₂×C₄	#88191	1	1	yes	characteristic
574	C₂×C₄	#88191	1	1	yes	characteristic
575	C₂×C₄	#88200	1	1	yes	characteristic
576	C₂×C₄	#88200	1	1	yes	characteristic
577	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂×#6127	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂×#6131	1	1	yes	characteristic
582	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	2	4	no	—
585	C₈	—	4	2	no	—
586	C₈	—	26	4	no	—
587	C₈	—	26	4	no	—
588	C₈	—	52	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	26	4	no	—
597	C₂²	—	52	4	no	—
598	C₂²	—	52	4	no	—
599	C₂²	—	104	2	no	—
600	C₂²	#11718650	1	1	yes	characteristic
601	C₂²	#11718650	1	1	yes	characteristic
602	C₂²	#11718650	1	1	yes	characteristic
603	C₂²	#11718650	1	1	yes	characteristic
604	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
605	C₂²	C₂×#88150	1	1	yes	characteristic
606	C₂²	C₂×#88200	1	1	yes	characteristic
607	C₄	—	26	4	no	—
608	C₄	#11718650	1	1	yes	characteristic
609	C₄	#11718650	1	1	yes	characteristic
610	C₄	#11718650	1	1	yes	characteristic
611	C₄	#11718650	1	1	yes	characteristic
612	C₄	C₂×#88147	1	1	yes	characteristic
613	C₄	C₂×#88148	1	1	yes	characteristic
614	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
615	C₄	C₂×#88191	1	1	yes	characteristic
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	52	4	no	—
624	C₂	C₂×#11718650	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#88191
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#430	C₂
socle	C₂×C₁₃	C₂×#385
prime radical	C₂²×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#430	D₁₃
hypocenter	C₁₃	#20860
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
2. C₂×#11718785	C₂	semidirect
5. #13115054	C₂	semidirect
6. #13114562	C₂	semidirect
7. #13114562	C₂	semidirect
8. C₂×C₁₃×#430	C₂	semidirect
24. C₁₃×#430	C₂²	semidirect
33. #11718785	C₂²	semidirect
36. #11718150	C₂²	semidirect
37. #11718150	C₂²	semidirect
214. C₂×#430	D₁₃	semidirect
302. #430	C₂×D₁₃	semidirect
523. C₁₃	#20860	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719450	2
C₂×#11718785	2
C₂×#11718793	2
#13123280	2
#13115054	2
#13114562	2
C₂×C₁₃×#430	2
#20860	13