Subgroups — #15830867

Order 3328.

1316 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719182	C₂	1	1	yes	maximal, characteristic
2	#13123469	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113446	C₂	1	4	yes	maximal, complemented
4	#13113433	C₂	1	4	yes	maximal, complemented
5	#13113427	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6127	C₄	1	2	yes	—
8	C₂²×C₁₃×M₁₆	—	2	1	no	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88184	—	2	1	no	—
11	C₂×#88184	—	2	1	no	—
12	#11719182	—	2	1	no	—
13	#11719182	—	2	1	no	—
14	#11719182	—	2	1	no	—
15	#11719182	—	2	1	no	—
16	#11719182	C₄	1	2	yes	—
17	#11719182	C₄	1	2	yes	—
18	#11719182	C₂²	1	2	yes	—
19	#11719182	C₂²	1	2	yes	—
20	C₂×#88129	C₂²	1	2	yes	—
21	C₂×#88128	C₄	1	1	yes	characteristic
22	C₂×C₄×D₅₂	—	2	1	no	—
23	C₂×C₄×D₅₂	—	2	1	no	—
24	C₂×#88123	C₄	1	1	yes	characteristic
25	C₄×C₁₃×M₁₆	—	2	1	no	—
26	C₄×C₁₃×M₁₆	—	2	1	no	—
27	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
28	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
30	C₂×C₄×C₈×C₁₃	—	2	1	no	—
31	#11718868	—	2	1	no	—
32	#11718587	C₂²	1	2	yes	—
33	#11718587	C₂²	1	2	yes	complemented
34	#11718586	—	2	1	no	—
35	#11718586	—	2	1	no	—
36	#11718585	—	2	1	no	—
37	C₄×#6099	C₂²	1	2	yes	complemented
38	#11718056	C₂²	1	16	yes	complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₂²⋊D₁₃	—	2	2	no	—
43	C₂×#6127	—	2	2	no	—
44	C₂×#6127	—	2	2	no	—
45	C₂×#6127	—	4	8	no	—
46	C₂×#6127	C₂×C₄	1	4	yes	—
47	C₂×#6127	C₂×C₄	1	4	yes	—
48	C₂²×D₅₂	—	2	1	no	—
49	C₂²×D₅₂	—	2	1	no	—
50	C₂²×D₅₂	C₂×C₄	1	2	yes	—
51	C₂²×C₄×D₁₃	—	2	2	no	—
52	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×M₁₆	—	2	8	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	#88184	—	2	2	no	—
70	#88184	—	2	2	no	—
71	#88184	—	2	2	no	—
72	#88184	—	2	2	no	—
73	#88184	—	2	2	no	—
74	#88184	—	2	2	no	—
75	#88184	—	2	2	no	—
76	#88184	—	2	2	no	—
77	C₂×#6103	—	2	2	no	—
78	C₂×#6103	—	2	2	no	—
79	C₂×C₄⋊Dic₁₃	—	2	1	no	—
80	C₂×C₄⋊Dic₁₃	—	2	1	no	—
81	C₂×#6099	—	2	2	no	—
82	#88129	—	2	2	no	—
83	#88129	—	2	2	no	—
84	#88129	C₂×C₄	1	4	yes	—
85	#88129	C₂³	1	4	yes	—
86	#88128	—	2	1	no	—
87	#88128	—	2	1	no	—
88	#88128	C₂×C₄	1	2	yes	—
89	#88128	C₂×C₄	1	2	yes	—
90	C₄×D₅₂	—	2	2	no	—
91	C₄×D₅₂	—	2	2	no	—
92	C₄×D₅₂	—	2	2	no	—
93	C₄×D₅₂	—	2	2	no	—
94	C₄×D₅₂	—	2	2	no	—
95	C₄×D₅₂	—	2	2	no	—
96	C₄×D₅₂	—	2	2	no	—
97	C₄×D₅₂	—	2	2	no	—
98	#88123	—	2	1	no	—
99	#88123	—	2	1	no	—
100	#88123	C₂×C₄	1	2	yes	—
101	#88123	C₂×C₄	1	2	yes	—
102	C₁₃×#97	—	2	2	no	—
103	C₁₃×#97	C₂³	1	4	yes	—
104	C₄×C₈×C₁₃	—	2	2	no	—
105	C₄×C₈×C₁₃	—	2	2	no	—
106	C₂²⋊#1055	—	2	2	no	—
107	C₂²⋊#1055	—	2	2	no	—
108	C₄⋊#1055	—	2	2	no	—
109	C₄⋊#1055	—	2	2	no	—
110	#88043	C₂³	1	4	yes	—
111	C₄×#1055	—	2	2	no	—
112	#17647	—	13	1	no	maximal, Sylow
113	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×D₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	—	2	4	no	—
137	C₂×C₂²⋊D₁₃	—	2	4	no	—
138	C₂×C₂²⋊D₁₃	—	4	8	no	—
139	C₂²×Dic₁₃	—	2	2	no	—
140	#6127	—	4	8	no	—
141	#6127	—	4	8	no	—
142	#6127	—	4	8	no	—
143	#6127	—	4	8	no	—
144	C₂×D₅₂	—	2	2	no	—
145	C₂×D₅₂	—	2	2	no	—
146	C₂×D₅₂	—	2	2	no	—
147	C₂×D₅₂	—	2	2	no	—
148	C₂×D₅₂	—	2	2	no	—
149	C₂×D₅₂	—	4	4	no	—
150	C₂×D₅₂	—	4	4	no	—
151	C₂×D₅₂	—	4	4	no	—
152	C₂×D₅₂	C₂²×C₄	1	4	yes	—
153	C₂×C₄×D₁₃	—	2	4	no	—
154	C₂×C₄×D₁₃	—	2	4	no	—
155	C₂×C₄×D₁₃	—	4	8	no	—
156	C₂×Dic₂₆	—	2	2	no	—
157	C₂×Dic₂₆	—	4	4	no	—
158	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
159	C₁₃×M₁₆	—	2	8	no	—
160	C₁₃×M₁₆	—	2	8	no	—
161	C₂×C₈×C₁₃	—	2	8	no	—
162	C₂×C₈×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	#6103	—	2	4	no	—
180	#6103	—	2	4	no	—
181	#6103	—	2	4	no	—
182	#6103	—	2	4	no	—
183	C₄⋊Dic₁₃	—	2	2	no	—
184	C₄⋊Dic₁₃	—	2	2	no	—
185	C₄⋊Dic₁₃	—	2	2	no	—
186	C₄⋊Dic₁₃	—	2	2	no	—
187	#6099	—	4	4	no	—
188	C₂×#1055	—	2	4	no	—
189	C₂×#532	—	13	1	no	—
190	#2920	—	13	1	no	—
191	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic, complemented
192	#1530	—	13	4	no	—
193	#1527	—	13	4	no	—
194	#1525	—	13	4	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×D₁₃	—	2	4	no	—
202	C₂²×D₁₃	—	4	4	no	—
203	C₂²×D₁₃	—	4	4	no	—
204	C₂²×D₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	#100	1	4	yes	—
222	C₂×C₄×C₁₃	#104	1	4	yes	—
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂²⋊D₁₃	—	4	8	no	—
236	C₂²⋊D₁₃	—	4	8	no	—
237	C₂×Dic₁₃	—	2	4	no	—
238	C₂×Dic₁₃	—	4	4	no	—
239	D₅₂	—	4	4	no	—
240	D₅₂	—	4	4	no	—
241	D₅₂	—	4	4	no	—
242	D₅₂	—	4	4	no	—
243	D₅₂	—	4	4	no	—
244	D₅₂	—	4	4	no	—
245	C₄×D₁₃	—	4	8	no	—
246	C₄×D₁₃	—	4	8	no	—
247	Dic₂₆	—	4	4	no	—
248	Dic₂₆	—	4	4	no	—
249	C₈×C₁₃	—	2	8	no	—
250	#1055	—	4	4	no	—
251	C₂²×#41	—	13	2	no	—
252	C₂²×M₁₆	—	2	1	no	—
253	#532	—	13	2	no	—
254	#532	—	13	2	no	—
255	#532	—	13	2	no	—
256	#532	—	13	2	no	—
257	#532	—	26	1	no	—
258	#532	—	26	1	no	—
259	#532	—	26	1	no	—
260	#532	—	26	1	no	—
261	C₂×C₄⋊Q₈	—	13	1	no	—
262	C₂×#127	—	13	1	no	—
263	C₂×#124	—	13	2	no	—
264	C₂×#121	—	26	1	no	—
265	C₂×#121	—	26	1	no	—
266	C₂×C₄×D₄	—	26	1	no	—
267	C₂×C₄×D₄	—	26	1	no	—
268	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
269	#432	—	13	2	no	—
270	#432	—	13	2	no	—
271	#431	—	26	1	no	—
272	#431	—	26	1	no	—
273	#423	—	26	1	no	—
274	#407	—	26	1	no	—
275	C₄×M₁₆	—	2	1	no	—
276	C₄×M₁₆	—	2	1	no	—
277	C₄×M₁₆	—	13	2	no	—
278	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
279	C₄×M₁₆	C₂×D₁₃	1	2	yes	complemented
280	C₂×#97	C₂×D₁₃	1	2	yes	complemented
281	C₂×C₄×C₈	—	2	1	no	—
282	#329	—	13	16	no	—
283	C₂²×C₁₃	—	2	1	no	—
284	C₂²×C₁₃	—	2	1	no	—
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	C₂×#100	1	2	yes	—
292	C₂²×C₁₃	C₂×#104	1	2	yes	—
293	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×D₁₃	—	4	4	no	—
295	C₂×D₁₃	—	4	4	no	—
296	C₂×D₁₃	—	4	4	no	—
297	C₂×D₁₃	—	8	8	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	C₂×#100	1	2	yes	—
306	C₄×C₁₃	C₂×#100	1	2	yes	—
307	C₄×C₁₃	C₂×#104	1	2	yes	—
308	C₄×C₁₃	C₂×#104	1	2	yes	—
309	C₄×C₁₃	#421	1	2	yes	—
310	Dic₁₃	—	4	4	no	—
311	C₂×#41	—	13	4	no	—
312	C₂×#41	—	13	4	no	—
313	C₂×#41	—	26	2	no	—
314	C₂×#41	—	26	2	no	—
315	C₂×#41	—	52	8	no	—
316	C₂²×Q₈	—	13	2	no	—
317	C₂²×D₄	—	13	2	no	—
318	C₂²×D₄	—	26	2	no	—
319	C₂²×D₄	—	26	1	no	—
320	C₂²×D₄	—	26	1	no	—
321	C₂³×C₄	—	26	2	no	—
322	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
323	C₂³×C₄	D₅₂	1	1	yes	characteristic
324	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
325	C₂×M₁₆	—	2	8	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	26	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₄⋊Q₈	—	13	2	no	—
331	C₄⋊Q₈	—	13	2	no	—
332	C₄⋊Q₈	—	26	1	no	—
333	C₄⋊Q₈	—	26	1	no	—
334	#127	—	13	2	no	—
335	#127	—	13	2	no	—
336	#127	—	26	1	no	—
337	#127	—	26	1	no	—
338	#124	—	13	4	no	—
339	#124	—	13	4	no	—
340	#124	—	26	2	no	—
341	#124	—	26	2	no	—
342	#121	—	26	2	no	—
343	#121	—	26	2	no	—
344	#121	—	26	2	no	—
345	#121	—	26	2	no	—
346	#121	—	26	2	no	—
347	#121	—	26	2	no	—
348	#121	—	26	2	no	—
349	#121	—	26	2	no	—
350	C₄×D₄	—	26	2	no	—
351	C₄×D₄	—	26	2	no	—
352	C₄×D₄	—	26	2	no	—
353	C₄×D₄	—	26	2	no	—
354	C₄×D₄	—	26	2	no	—
355	C₄×D₄	—	26	2	no	—
356	C₄×D₄	—	26	2	no	—
357	C₄×D₄	—	26	2	no	—
358	C₂×C₄⋊C₄	—	26	1	no	—
359	C₂×C₄⋊C₄	—	26	1	no	—
360	C₂×C₂²⋊C₄	—	26	2	no	—
361	C₂×C₂²⋊C₄	—	26	2	no	—
362	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
363	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
365	C₂×C₄²	D₅₂	1	1	yes	characteristic
366	C₂×C₄²	D₅₂	1	1	yes	characteristic
367	C₂×C₄²	D₅₂	1	1	yes	characteristic
368	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
374	C₄⋊C₈	—	26	2	no	—
375	C₄⋊C₈	—	26	2	no	—
376	C₂²⋊C₈	—	26	2	no	—
377	C₂²⋊C₈	—	26	2	no	—
378	#97	—	2	2	no	—
379	#97	—	13	4	no	—
380	#97	C₂²×D₁₃	1	4	yes	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	2	2	no	—
383	C₄×C₈	—	26	2	no	—
384	C₂×C₁₃	—	2	2	no	—
385	C₂×C₁₃	—	2	2	no	—
386	C₂×C₁₃	—	4	1	no	—
387	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
388	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
389	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
390	D₁₃	—	8	4	no	—
391	C₂⁴	—	26	2	no	—
392	C₂⁴	#6103	1	1	yes	characteristic
393	#41	—	52	8	no	—
394	#41	—	52	8	no	—
395	#41	—	52	8	no	—
396	#41	—	52	8	no	—
397	C₂×Q₈	—	13	4	no	—
398	C₂×Q₈	—	26	2	no	—
399	C₂×Q₈	—	52	4	no	—
400	C₂×D₄	—	13	4	no	—
401	C₂×D₄	—	26	4	no	—
402	C₂×D₄	—	26	4	no	—
403	C₂×D₄	—	26	2	no	—
404	C₂×D₄	—	26	2	no	—
405	C₂×D₄	—	26	2	no	—
406	C₂×D₄	—	26	2	no	—
407	C₂×D₄	—	26	2	no	—
408	C₂×D₄	—	52	4	no	—
409	C₂×D₄	—	52	4	no	—
410	C₂×D₄	—	52	8	no	—
411	C₂×D₄	—	52	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	26	2	no	—
416	C₂²×C₄	—	26	4	no	—
417	C₂²×C₄	—	26	4	no	—
418	C₂²×C₄	—	52	8	no	—
419	C₂²×C₄	#6103	1	1	yes	characteristic
420	C₂²×C₄	#6103	1	1	yes	characteristic
421	C₂²×C₄	#6103	1	1	yes	characteristic
422	C₂²×C₄	#6103	1	1	yes	characteristic
423	C₂²×C₄	#6103	1	1	yes	characteristic
424	C₂²×C₄	#6103	1	1	yes	characteristic
425	C₂²×C₄	#6103	1	1	yes	characteristic
426	C₂²×C₄	#6103	1	1	yes	characteristic
427	C₂²×C₄	#6103	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
437	M₁₆	—	2	8	no	—
438	M₁₆	—	2	8	no	—
439	M₁₆	—	52	4	no	—
440	C₂×C₈	—	2	8	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	26	4	no	—
443	C₄⋊C₄	—	26	2	no	—
444	C₄⋊C₄	—	26	2	no	—
445	C₄⋊C₄	—	26	2	no	—
446	C₄⋊C₄	—	26	2	no	—
447	C₂²⋊C₄	—	26	4	no	—
448	C₂²⋊C₄	—	26	4	no	—
449	C₂²⋊C₄	—	26	4	no	—
450	C₂²⋊C₄	—	26	4	no	—
451	C₄²	#6103	1	1	yes	characteristic
452	C₄²	#6103	1	1	yes	characteristic
453	C₄²	#6103	1	1	yes	characteristic
454	C₄²	#6103	1	1	yes	characteristic
455	C₄²	#6103	1	1	yes	characteristic
456	C₄²	#6103	1	1	yes	characteristic
457	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
458	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
459	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
460	C₄²	C₂×D₅₂	1	1	yes	characteristic
461	C₄²	C₂×D₅₂	1	1	yes	characteristic
462	C₄²	C₂×D₅₂	1	1	yes	characteristic
463	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
464	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
465	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
466	C₄²	C₂³×D₁₃	1	1	yes	characteristic
467	C₁₃	#17647	1	1	yes	characteristic, complemented, Sylow
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	26	4	no	—
472	C₂³	—	52	4	no	—
473	C₂³	—	52	4	no	—
474	C₂³	—	52	4	no	—
475	C₂³	C₂×#6103	1	1	yes	characteristic
476	C₂³	C₂×#6103	1	1	yes	characteristic
477	C₂³	C₂×#6103	1	1	yes	characteristic
478	Q₈	—	52	4	no	—
479	Q₈	—	52	4	no	—
480	D₄	—	52	4	no	—
481	D₄	—	52	4	no	—
482	D₄	—	52	8	no	—
483	D₄	—	52	8	no	—
484	D₄	—	52	4	no	—
485	D₄	—	52	4	no	—
486	D₄	—	52	4	no	—
487	D₄	—	52	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	26	4	no	—
505	C₂×C₄	—	52	8	no	—
506	C₂×C₄	—	52	4	no	—
507	C₂×C₄	—	52	8	no	—
508	C₂×C₄	#88045	1	4	yes	—
509	C₂×C₄	#88063	1	4	yes	—
510	C₂×C₄	C₂×#6103	1	1	yes	characteristic
511	C₂×C₄	C₂×#6103	1	1	yes	characteristic
512	C₂×C₄	C₂×#6103	1	1	yes	characteristic
513	C₂×C₄	C₂×#6103	1	1	yes	characteristic
514	C₂×C₄	C₂×#6103	1	1	yes	characteristic
515	C₂×C₄	C₂×#6103	1	1	yes	characteristic
516	C₂×C₄	C₂×#6103	1	1	yes	characteristic
517	C₂×C₄	C₂×#6103	1	1	yes	characteristic
518	C₂×C₄	C₂×#6103	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
522	C₈	—	2	8	no	—
523	C₈	—	52	4	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	52	4	no	—
533	C₂²	—	52	4	no	—
534	C₂²	—	52	4	no	—
535	C₂²	—	104	8	no	—
536	C₂²	C₂×#88045	1	2	yes	—
537	C₂²	C₂×#88063	1	2	yes	—
538	C₂²	C₂²×#6103	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	52	4	no	—
547	C₄	C₂×#88045	1	2	yes	—
548	C₄	C₂×#88045	1	2	yes	—
549	C₄	C₂×#88063	1	2	yes	—
550	C₄	C₂×#88063	1	2	yes	—
551	C₄	#11718800	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	1	no	—
555	C₂	—	104	4	no	—
556	C₂	C₂²×#88063	1	1	yes	characteristic
557	C₂	C₂²×#88045	1	1	yes	characteristic
558	C₂	C₂×#11718800	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6103
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×#11719182	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	#17647
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13123469	C₂	semidirect
3. #13113446	C₂	semidirect
4. #13113433	C₂	semidirect
5. #13113427	C₂	semidirect
6. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
28. C₄×C₁₃×M₁₆	C₂²	semidirect
29. C₂×C₁₃×#97	C₂²	semidirect
33. #11718587	C₂²	semidirect
37. C₄×#6099	C₂²	semidirect
38. #11718056	C₂²	semidirect
191. C₂×C₄×M₁₆	D₁₃	semidirect
279. C₄×M₁₆	C₂×D₁₃	semidirect
280. C₂×#97	C₂×D₁₃	semidirect
467. C₁₃	#17647	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719182	2
#13123469	2
#13113446	2
#13113433	2
#13113427	2
C₂×C₄×C₁₃×M₁₆	2
#17647	13