Subgroups — #15769210

Order 3328.

970 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88045	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718774	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718771	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718144	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718115	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114532	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6127	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#97	—	2	2	no	—
16	C₂×C₁₃×#97	—	2	2	no	—
17	C₂×C₁₃×#97	—	2	2	no	—
18	#11718774	—	2	2	no	—
19	#11718774	—	2	2	no	—
20	C₂×#88061	C₄	1	2	yes	complemented
21	#11718771	—	2	2	no	—
22	#11718771	C₄	1	4	yes	complemented
23	C₂×#88060	—	2	2	no	—
24	C₂×#88056	C₄	1	2	yes	complemented
25	C₂×#88045	—	2	2	no	—
26	C₂×#88045	—	2	2	no	—
27	C₂×#88045	C₄	1	4	yes	complemented
28	#11718144	—	2	2	no	—
29	#11718142	—	2	2	no	—
30	#11718115	—	2	2	no	—
31	C₂³×C₄×C₁₃	—	2	1	no	—
32	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×C₂²⋊D₁₃	—	2	1	no	—
34	C₂×#6127	—	2	1	no	—
35	C₂×#6127	—	2	1	no	—
36	C₂×#6127	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₂×#6127	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
45	C₂×#6127	C₂×C₄	1	2	yes	—
46	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×D₁₃	—	2	1	no	—
48	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₂²×C₈×C₁₃	—	2	1	no	—
57	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₁₃	D₄	1	2	yes	—
60	C₂²×C₈×C₁₃	D₄	1	2	yes	—
61	C₂²×C₈×C₁₃	D₄	1	2	yes	—
62	C₂²×C₈×C₁₃	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	D₄	1	2	yes	—
69	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
70	#88180	—	2	1	no	—
71	#88180	—	2	1	no	—
72	#88180	—	2	1	no	—
73	#88180	—	2	1	no	—
74	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₁₃	—	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	C₂×C₄	1	2	yes	—
87	C₂×#6099	C₂×C₄	1	2	yes	—
88	C₂²×#1055	—	2	1	no	—
89	C₂²×#1055	—	2	1	no	—
90	C₁₃×#97	—	2	8	no	—
91	#88061	—	2	4	no	—
92	#88060	—	2	8	no	—
93	#88056	—	2	4	no	—
94	#88045	—	2	8	no	—
95	#10930	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₂³×D₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	4	4	no	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₃	—	2	2	no	—
117	C₂×C₂²⋊D₁₃	—	2	2	no	—
118	C₂×C₂²⋊D₁₃	—	4	1	no	—
119	C₂×C₂²⋊D₁₃	—	4	1	no	—
120	C₂×C₂²⋊D₁₃	—	4	1	no	—
121	C₂×C₂²⋊D₁₃	—	4	1	no	—
122	C₂²×Dic₁₃	—	2	1	no	—
123	C₂²×Dic₁₃	—	2	2	no	—
124	#6127	—	2	2	no	—
125	#6127	—	2	2	no	—
126	#6127	—	2	2	no	—
127	#6127	—	2	2	no	—
128	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	4	1	no	—
133	#6127	—	4	1	no	—
134	#6127	—	4	1	no	—
135	#6127	—	4	1	no	—
136	#6127	—	4	1	no	—
137	#6127	—	4	1	no	—
138	#6127	—	4	1	no	—
139	#6127	—	4	1	no	—
140	C₂×D₅₂	—	2	1	no	—
141	C₂×D₅₂	—	2	1	no	—
142	C₂×D₅₂	—	2	1	no	—
143	C₂×D₅₂	—	2	1	no	—
144	C₂×D₅₂	—	2	1	no	—
145	C₂×D₅₂	C₄²	1	2	yes	—
146	C₂×C₄×D₁₃	—	2	2	no	—
147	C₂×C₄×D₁₃	—	2	2	no	—
148	C₂×C₄×D₁₃	—	4	1	no	—
149	C₂×C₄×D₁₃	—	4	1	no	—
150	C₂×C₄×D₁₃	—	4	1	no	—
151	C₂×C₄×D₁₃	—	4	1	no	—
152	C₂×Dic₂₆	—	2	1	no	—
153	C₂×Dic₂₆	—	2	1	no	—
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	—	2	1	no	—
156	C₂×Dic₂₆	—	2	1	no	—
157	C₂×Dic₂₆	C₄²	1	2	yes	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
171	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
176	C₂²⋊Dic₁₃	—	4	1	no	—
177	C₂²⋊Dic₁₃	—	4	1	no	—
178	C₄⋊Dic₁₃	—	2	2	no	—
179	C₄⋊Dic₁₃	—	2	2	no	—
180	C₄×Dic₁₃	—	4	1	no	—
181	C₄×Dic₁₃	—	4	1	no	—
182	#6099	—	2	2	no	—
183	#6099	—	2	2	no	—
184	#6099	—	2	2	no	—
185	#6099	—	2	2	no	—
186	#6099	—	4	1	no	—
187	#6099	—	4	1	no	—
188	#6099	—	4	1	no	—
189	#6099	—	4	1	no	—
190	C₂×#1055	—	2	2	no	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	4	1	no	—
193	C₂×#1055	—	4	1	no	—
194	C₂×#1055	—	4	1	no	—
195	C₂×#1055	—	4	1	no	—
196	C₂²×#104	—	13	1	no	—
197	C₂×#416	—	13	1	no	—
198	C₂×#408	—	13	1	no	—
199	C₂²×#97	D₁₃	1	1	yes	characteristic, complemented
200	C₂×#341	—	13	1	no	—
201	C₂×#339	—	13	1	no	—
202	#1729	—	13	1	no	—
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	#117	1	1	yes	characteristic
205	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₁₃	#121	1	1	yes	characteristic
208	C₂³×C₁₃	#123	1	1	yes	characteristic
209	C₂³×C₁₃	#124	1	1	yes	characteristic
210	C₂³×C₁₃	#126	1	1	yes	characteristic
211	C₂²×D₁₃	—	2	2	no	—
212	C₂²×D₁₃	—	4	1	no	—
213	C₂²×D₁₃	—	4	1	no	—
214	C₂²×D₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
247	C₂²⋊D₁₃	—	4	2	no	—
248	C₂²⋊D₁₃	—	4	2	no	—
249	C₂²⋊D₁₃	—	4	2	no	—
250	C₂²⋊D₁₃	—	4	2	no	—
251	C₂×Dic₁₃	—	2	2	no	—
252	C₂×Dic₁₃	—	4	1	no	—
253	C₂×Dic₁₃	—	4	1	no	—
254	C₂×Dic₁₃	—	4	2	no	—
255	C₂×Dic₁₃	—	4	4	no	—
256	D₅₂	—	2	2	no	—
257	D₅₂	—	2	2	no	—
258	D₅₂	—	4	1	no	—
259	D₅₂	—	4	1	no	—
260	C₄×D₁₃	—	4	2	no	—
261	C₄×D₁₃	—	4	2	no	—
262	C₄×D₁₃	—	4	2	no	—
263	C₄×D₁₃	—	4	2	no	—
264	Dic₂₆	—	2	2	no	—
265	Dic₂₆	—	2	2	no	—
266	Dic₂₆	—	4	1	no	—
267	Dic₂₆	—	4	1	no	—
268	C₈×C₁₃	—	2	4	no	—
269	C₈×C₁₃	—	2	4	no	—
270	#1055	—	4	2	no	—
271	#1055	—	4	2	no	—
272	C₂²×#41	—	13	1	no	—
273	C₂²×M₁₆	—	13	1	no	—
274	C₂²×M₁₆	—	13	1	no	—
275	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
276	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
277	C₂×#117	—	13	1	no	—
278	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
279	C₂×#104	—	13	4	no	—
280	C₂×#104	—	26	2	no	—
281	C₂×#104	—	26	2	no	—
282	#416	—	26	2	no	—
283	#416	—	26	2	no	—
284	C₂×#103	—	13	2	no	—
285	C₂×#102	—	13	2	no	—
286	#408	—	13	4	no	—
287	#408	—	26	2	no	—
288	C₂×C₂²⋊C₈	—	26	2	no	—
289	C₂×#97	—	2	2	no	—
290	C₂×#97	—	2	2	no	—
291	C₂×#97	—	2	2	no	—
292	#341	—	26	2	no	—
293	#339	—	26	2	no	—
294	#336	—	26	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×C₁₃	#386	1	1	yes	characteristic
303	C₂²×C₁₃	#388	1	1	yes	characteristic
304	C₂²×C₁₃	#388	1	1	yes	characteristic
305	C₂²×C₁₃	#388	1	1	yes	characteristic
306	C₂²×C₁₃	#388	1	1	yes	characteristic
307	C₂²×C₁₃	#390	1	1	yes	characteristic
308	C₂²×C₁₃	#444	1	4	yes	—
309	C₂×D₁₃	—	4	2	no	—
310	C₂×D₁₃	—	4	4	no	—
311	C₂×D₁₃	—	8	2	no	—
312	C₂×D₁₃	—	8	2	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
315	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
316	C₄×C₁₃	#386	1	1	yes	characteristic
317	C₄×C₁₃	#386	1	1	yes	characteristic
318	C₄×C₁₃	#388	1	1	yes	characteristic
319	C₄×C₁₃	#388	1	1	yes	characteristic
320	C₄×C₁₃	#390	1	1	yes	characteristic
321	C₄×C₁₃	#390	1	1	yes	characteristic
322	Dic₁₃	—	4	2	no	—
323	Dic₁₃	—	8	2	no	—
324	C₂×#41	—	13	2	no	—
325	C₂×#41	—	13	2	no	—
326	C₂×#41	—	26	1	no	—
327	C₂×#41	—	26	1	no	—
328	C₂×#41	—	26	1	no	—
329	C₂×#41	—	26	1	no	—
330	C₂×#41	—	26	1	no	—
331	C₂×#41	—	26	1	no	—
332	C₂×#41	—	26	1	no	—
333	C₂×#41	—	26	1	no	—
334	C₂×#41	—	26	1	no	—
335	C₂×#41	—	26	1	no	—
336	C₂²×Q₈	—	13	1	no	—
337	C₂²×D₄	—	13	1	no	—
338	C₂²×D₄	—	26	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	26	1	no	—
341	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
342	C₂×M₁₆	—	13	2	no	—
343	C₂×M₁₆	—	13	2	no	—
344	C₂×M₁₆	—	26	1	no	—
345	C₂×M₁₆	—	26	1	no	—
346	C₂×M₁₆	—	26	1	no	—
347	C₂×M₁₆	—	26	1	no	—
348	C₂×M₁₆	—	26	1	no	—
349	C₂×M₁₆	—	26	1	no	—
350	C₂×M₁₆	—	26	1	no	—
351	C₂×M₁₆	—	26	1	no	—
352	C₂×M₁₆	—	26	1	no	—
353	C₂×M₁₆	—	26	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	26	1	no	—
363	C₂²×C₈	—	26	1	no	—
364	C₂²×C₈	C₄×D₁₃	1	2	yes	—
365	C₂²×C₈	C₄×D₁₃	1	2	yes	—
366	C₂²×C₈	D₅₂	1	2	yes	—
367	C₂²×C₈	D₅₂	1	2	yes	—
368	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
369	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
370	#117	—	26	1	no	—
371	#117	—	26	1	no	—
372	#117	—	26	1	no	—
373	#117	—	26	1	no	—
374	C₂×C₄⋊C₄	—	13	2	no	—
375	C₂×C₂²⋊C₄	—	26	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	26	1	no	—
380	C₂×C₄²	C₄×D₁₃	1	2	yes	—
381	C₂×C₄²	D₅₂	1	2	yes	—
382	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
383	#104	—	26	8	no	—
384	#103	—	26	4	no	—
385	#102	—	26	4	no	—
386	C₂²⋊C₈	—	26	8	no	—
387	#97	—	2	8	no	—
388	C₂×C₁₃	—	2	1	no	—
389	C₂×C₁₃	—	2	1	no	—
390	C₂×C₁₃	—	2	1	no	—
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	#1437	1	1	yes	characteristic
393	C₂×C₁₃	#1765	1	2	yes	—
394	C₂×C₁₃	#1938	1	2	yes	—
395	C₂×C₁₃	#1975	1	2	yes	—
396	D₁₃	—	8	2	no	—
397	C₂⁴	—	26	1	no	—
398	C₂⁴	#6127	1	1	yes	characteristic
399	#41	—	26	2	no	—
400	#41	—	26	2	no	—
401	#41	—	26	2	no	—
402	#41	—	26	2	no	—
403	#41	—	26	2	no	—
404	#41	—	26	2	no	—
405	#41	—	26	2	no	—
406	#41	—	26	2	no	—
407	#41	—	52	1	no	—
408	#41	—	52	1	no	—
409	#41	—	52	1	no	—
410	#41	—	52	1	no	—
411	#41	—	52	1	no	—
412	#41	—	52	1	no	—
413	#41	—	52	1	no	—
414	#41	—	52	1	no	—
415	C₂×Q₈	—	13	2	no	—
416	C₂×Q₈	—	26	1	no	—
417	C₂×Q₈	—	26	1	no	—
418	C₂×Q₈	—	26	1	no	—
419	C₂×Q₈	—	26	1	no	—
420	C₂×Q₈	—	26	1	no	—
421	C₂×D₄	—	13	2	no	—
422	C₂×D₄	—	26	2	no	—
423	C₂×D₄	—	26	2	no	—
424	C₂×D₄	—	26	1	no	—
425	C₂×D₄	—	26	1	no	—
426	C₂×D₄	—	26	1	no	—
427	C₂×D₄	—	26	1	no	—
428	C₂×D₄	—	26	1	no	—
429	C₂×D₄	—	52	1	no	—
430	C₂×D₄	—	52	1	no	—
431	C₂×D₄	—	52	1	no	—
432	C₂×D₄	—	52	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	—	26	1	no	—
438	C₂²×C₄	—	26	2	no	—
439	C₂²×C₄	—	26	2	no	—
440	C₂²×C₄	—	26	2	no	—
441	C₂²×C₄	—	52	1	no	—
442	C₂²×C₄	—	52	1	no	—
443	C₂²×C₄	—	52	1	no	—
444	C₂²×C₄	—	52	1	no	—
445	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
451	C₂²×C₄	#6127	1	1	yes	characteristic
452	C₂²×C₄	#6127	1	1	yes	characteristic
453	C₂²×C₄	#6127	1	1	yes	characteristic
454	C₂²×C₄	#6127	1	1	yes	characteristic
455	C₂²×C₄	#6127	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
459	M₁₆	—	26	2	no	—
460	M₁₆	—	26	2	no	—
461	M₁₆	—	26	2	no	—
462	M₁₆	—	26	2	no	—
463	M₁₆	—	52	1	no	—
464	M₁₆	—	52	1	no	—
465	M₁₆	—	52	1	no	—
466	M₁₆	—	52	1	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	26	2	no	—
480	C₂×C₈	—	26	2	no	—
481	C₂×C₈	—	52	1	no	—
482	C₂×C₈	—	52	1	no	—
483	C₂×C₈	—	52	1	no	—
484	C₂×C₈	—	52	1	no	—
485	C₂×C₈	#6103	1	4	yes	—
486	C₂×C₈	#6103	1	4	yes	—
487	C₄⋊C₄	—	26	2	no	—
488	C₄⋊C₄	—	26	2	no	—
489	C₂²⋊C₄	—	52	1	no	—
490	C₂²⋊C₄	—	52	1	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	52	1	no	—
495	C₄²	—	52	1	no	—
496	C₄²	#6103	1	4	yes	—
497	C₁₃	#10930	1	1	yes	characteristic, complemented, Sylow
498	C₂³	—	2	4	no	—
499	C₂³	—	26	2	no	—
500	C₂³	—	52	1	no	—
501	C₂³	—	52	1	no	—
502	C₂³	—	52	4	no	—
503	C₂³	#88126	1	1	yes	characteristic
504	C₂³	C₄×D₅₂	1	1	yes	characteristic
505	C₂³	#88129	1	1	yes	characteristic
506	C₂³	#88130	1	1	yes	characteristic
507	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
508	C₂³	#88183	1	1	yes	characteristic
509	C₂³	#88184	1	1	yes	characteristic
510	Q₈	—	26	2	no	—
511	Q₈	—	26	2	no	—
512	Q₈	—	52	1	no	—
513	Q₈	—	52	1	no	—
514	D₄	—	26	2	no	—
515	D₄	—	26	2	no	—
516	D₄	—	52	2	no	—
517	D₄	—	52	2	no	—
518	D₄	—	52	2	no	—
519	D₄	—	52	2	no	—
520	D₄	—	52	1	no	—
521	D₄	—	52	1	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	26	2	no	—
527	C₂×C₄	—	52	1	no	—
528	C₂×C₄	—	52	1	no	—
529	C₂×C₄	—	52	2	no	—
530	C₂×C₄	—	52	2	no	—
531	C₂×C₄	—	52	2	no	—
532	C₂×C₄	—	52	2	no	—
533	C₂×C₄	—	52	2	no	—
534	C₂×C₄	—	52	4	no	—
535	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
536	C₂×C₄	#88126	1	1	yes	characteristic
537	C₂×C₄	#88126	1	1	yes	characteristic
538	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
539	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
540	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
541	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
542	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
543	C₂×C₄	#88128	1	1	yes	characteristic
544	C₂×C₄	#88129	1	1	yes	characteristic
545	C₂×C₄	#88129	1	1	yes	characteristic
546	C₂×C₄	#88130	1	1	yes	characteristic
547	C₂×C₄	C₂×#6103	1	1	yes	characteristic
548	C₂×C₄	C₂×#6103	1	1	yes	characteristic
549	C₂×C₄	C₂×#6103	1	1	yes	characteristic
550	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
551	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
552	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
553	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
554	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
555	C₂×C₄	#88183	1	1	yes	characteristic
556	C₂×C₄	#88183	1	1	yes	characteristic
557	C₂×C₄	#88184	1	1	yes	characteristic
558	C₂×C₄	#88184	1	1	yes	characteristic
559	C₂×C₄	#88184	1	1	yes	characteristic
560	C₂×C₄	#88184	1	1	yes	characteristic
561	C₂×C₄	#88184	1	1	yes	characteristic
562	C₂×C₄	#88207	1	1	yes	characteristic
563	C₈	—	2	4	no	—
564	C₈	—	2	4	no	—
565	C₈	—	52	2	no	—
566	C₈	—	52	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	52	4	no	—
574	C₂²	—	52	2	no	—
575	C₂²	—	104	2	no	—
576	C₂²	—	104	2	no	—
577	C₂²	#11718378	1	4	yes	—
578	C₂²	C₄×#6103	1	1	yes	characteristic
579	C₂²	#11718600	1	1	yes	characteristic
580	C₂²	#11718601	1	1	yes	characteristic
581	C₂²	#11718601	1	1	yes	characteristic
582	C₂²	#11718601	1	1	yes	characteristic
583	C₂²	#11718601	1	1	yes	characteristic
584	C₂²	#11718874	1	1	yes	characteristic
585	C₄	—	4	4	no	—
586	C₄	—	52	2	no	—
587	C₄	—	104	2	no	—
588	C₄	C₄×#6103	1	1	yes	characteristic
589	C₄	C₄×#6103	1	1	yes	characteristic
590	C₄	#11718600	1	1	yes	characteristic
591	C₄	#11718600	1	1	yes	characteristic
592	C₄	#11718601	1	1	yes	characteristic
593	C₄	#11718601	1	1	yes	characteristic
594	C₄	#11718874	1	1	yes	characteristic
595	C₄	#11718874	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	104	2	no	—
601	C₂	#13113074	1	1	yes	characteristic
602	C₂	#13114680	1	2	yes	—
603	C₂	#13115547	1	2	yes	—
604	C₂	#13115729	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×#6127	C₂²
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#10930
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
4. C₂×#11718144	C₂	semidirect
5. C₂×#11718115	C₂	semidirect
6. #13114532	C₂	semidirect
7. C₂²×C₁₃×#97	C₂	semidirect
20. C₂×#88061	C₄	semidirect
22. #11718771	C₄	semidirect
24. C₂×#88056	C₄	semidirect
27. C₂×#88045	C₄	semidirect
199. C₂²×#97	D₁₃	semidirect
497. C₁₃	#10930	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88045	2
C₂×#11718774	2
C₂×#11718771	2
C₂×#11718144	2
C₂×#11718115	2
#13114532	2
C₂²×C₁₃×#97	2
#10930	13