Subgroups — #15832968

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124896	C₂	1	1	yes	maximal, characteristic
2	#13123549	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113679	C₂	1	2	yes	maximal, complemented
4	#13113665	C₂	1	2	yes	maximal, complemented
5	#13113658	C₂	1	2	yes	maximal, complemented
6	#13113646	C₂	1	2	yes	maximal, complemented
7	#13113624	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113252	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88155	—	2	1	no	—
14	#11719182	C₂²	1	1	yes	characteristic
15	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₃	—	2	1	no	—
18	C₈×D₄×C₁₃	—	2	1	no	—
19	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#431	—	2	1	no	—
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	—	2	1	no	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	#11718899	C₄	1	2	yes	—
26	#11718771	—	2	1	no	—
27	#11718688	C₄	1	1	yes	characteristic
28	C₄×#6106	C₂²	1	2	yes	—
29	#11718682	C₄	1	1	yes	characteristic
30	#11718676	C₄	1	1	yes	characteristic
31	C₄×#6104	C₂²	1	2	yes	—
32	#11718669	C₄	1	1	yes	characteristic
33	#11718664	C₄	1	2	yes	—
34	#11718586	C₂²	1	1	yes	characteristic
35	#11718585	C₂²	1	1	yes	characteristic
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	#11718349	—	2	1	no	—
38	#11718349	C₂²	1	2	yes	—
39	C₈×D₅₂	—	2	1	no	—
40	C₈×D₅₂	C₂²	1	2	yes	—
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	2	yes	—
43	#11718075	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×#6127	—	2	1	no	—
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×#6106	C₂×C₄	1	2	yes	—
66	C₂×#6104	C₂×C₄	1	2	yes	—
67	#88184	—	2	1	no	—
68	#88184	C₂×C₄	1	2	yes	—
69	C₂×#6099	—	2	1	no	—
70	C₂×#6099	—	2	1	no	—
71	#88155	—	4	4	no	—
72	C₂×#6094	—	2	2	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	#88129	—	2	1	no	—
75	#88128	C₂×C₄	1	1	yes	characteristic
76	C₄×D₅₂	—	2	1	no	—
77	C₄×D₅₂	C₂³	1	2	yes	—
78	#88123	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₂²⋊C₈	—	2	1	no	—
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₁₃×C₂²⋊C₈	—	2	1	no	—
86	C₄×C₈×C₁₃	—	2	1	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	—	2	1	no	—
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	#88075	C₂×C₄	1	2	yes	—
94	#88072	C₂×C₄	1	2	yes	—
95	C₂²⋊#1055	C₂×C₄	1	2	yes	—
96	#88060	—	2	2	no	—
97	#88060	—	2	2	no	—
98	#88049	C₂×C₄	1	2	yes	—
99	#88049	C₂×C₄	1	2	yes	—
100	#88048	C₂×C₄	1	2	yes	—
101	#88047	C₂×C₄	1	2	yes	—
102	C₄⋊#1055	—	2	1	no	—
103	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
104	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
105	C₄⋊#1055	C₂³	1	2	yes	—
106	#88043	—	2	1	no	—
107	C₄×#1055	C₂³	1	2	yes	—
108	C₄×#1055	C₂³	1	2	yes	—
109	#17917	—	13	1	no	maximal, Sylow
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₁₃	—	2	2	no	—
122	#6127	—	4	2	no	—
123	#6127	—	4	2	no	—
124	C₂×D₅₂	—	2	1	no	—
125	C₂×D₅₂	—	2	1	no	—
126	C₂×D₅₂	C₂²×C₄	1	2	yes	—
127	C₂×C₄×D₁₃	—	2	2	no	—
128	C₂×Dic₂₆	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₂×C₈×C₁₃	—	4	2	no	—
134	C₂×C₈×C₁₃	—	4	2	no	—
135	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	#6106	—	2	4	no	—
154	#6104	—	2	4	no	—
155	#6103	—	2	2	no	—
156	#6103	—	2	2	no	—
157	C₄⋊Dic₁₃	—	2	1	no	—
158	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
159	#6099	—	4	2	no	—
160	#6099	—	4	2	no	—
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	—	2	2	no	—
163	C₂×#1055	C₂²×C₄	1	2	yes	—
164	C₂×#1055	C₂²×C₄	1	2	yes	—
165	#6094	—	4	4	no	—
166	C₈×D₁₃	—	4	4	no	—
167	#3106	—	13	1	no	—
168	C₈×#41	D₁₃	1	1	yes	characteristic, complemented
169	#2931	—	13	1	no	—
170	#1583	—	13	2	no	—
171	#1581	—	13	2	no	—
172	#1580	—	13	2	no	—
173	SD₁₆⋊C₈	—	13	2	no	—
174	#1574	—	13	1	no	—
175	#1489	—	13	1	no	—
176	#1484	—	13	1	no	—
177	#1451	—	13	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
180	C₂²×D₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	2	1	no	—
182	Q₈×C₁₃	#131	1	2	yes	complemented
183	D₄×C₁₃	—	2	4	no	—
184	D₄×C₁₃	—	2	1	no	—
185	D₄×C₁₃	#131	1	2	yes	complemented
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂²⋊D₁₃	—	4	4	no	—
205	C₂×Dic₁₃	—	2	2	no	—
206	D₅₂	—	2	2	no	—
207	D₅₂	—	2	2	no	—
208	D₅₂	—	4	2	no	—
209	D₅₂	—	4	2	no	—
210	C₄×D₁₃	—	4	2	no	—
211	C₄×D₁₃	—	4	2	no	—
212	Dic₂₆	—	4	2	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	—	2	1	no	—
215	C₈×C₁₃	—	2	1	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₈×C₁₃	—	4	1	no	—
218	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
219	#1055	—	2	2	no	—
220	#1055	—	2	2	no	—
221	#1055	—	4	2	no	—
222	#1055	—	4	2	no	—
223	C₂×#131	—	26	1	no	—
224	#532	—	13	1	no	—
225	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
226	#482	—	13	2	no	—
227	#477	—	13	1	no	—
228	#476	—	13	1	no	—
229	#460	—	13	1	no	—
230	#459	—	13	1	no	—
231	#449	—	13	2	no	—
232	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
233	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
234	C₄×SD₁₆	—	13	2	no	—
235	C₄×D₈	—	13	2	no	—
236	#436	—	13	2	no	—
237	#436	—	26	1	no	—
238	C₈×D₄	—	2	1	no	—
239	C₈×D₄	—	2	1	no	—
240	C₈×D₄	—	13	2	no	—
241	C₈×D₄	—	26	1	no	—
242	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
243	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
244	#431	—	2	1	no	—
245	#431	—	13	1	no	—
246	#431	C₂×D₁₃	1	1	yes	characteristic
247	#423	—	13	1	no	—
248	#408	—	26	1	no	—
249	C₄×M₁₆	—	13	1	no	—
250	C₂×C₄×C₈	—	2	1	no	—
251	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
252	#335	—	13	2	no	—
253	#334	—	13	2	no	—
254	Q₈⋊C₈	—	13	2	no	—
255	D₄⋊C₈	—	13	2	no	—
256	D₄⋊C₈	—	13	2	no	—
257	D₄⋊C₈	—	13	2	no	—
258	#322	—	13	2	no	—
259	#322	—	13	2	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	—	4	1	no	—
266	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂×D₁₃	—	4	2	no	—
268	C₂×D₁₃	—	4	2	no	—
269	C₂×D₁₃	—	4	2	no	—
270	C₄×C₁₃	—	2	1	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	1	no	—
276	C₄×C₁₃	#444	1	2	yes	—
277	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
278	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
279	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₄×C₁₃	#575	1	1	yes	characteristic
281	Dic₁₃	—	4	2	no	—
282	C₂×#41	—	26	1	no	—
283	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
284	C₂×SD₁₆	—	13	2	no	—
285	C₂×D₈	—	13	2	no	—
286	#131	—	52	4	no	—
287	C₂×M₁₆	—	26	1	no	—
288	C₂×M₁₆	—	26	1	no	—
289	C₂×M₁₆	—	26	2	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	26	2	no	—
293	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
294	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	—	13	1	no	—
296	#127	—	13	1	no	—
297	#124	—	26	1	no	—
298	#121	—	13	2	no	—
299	#121	—	26	1	no	—
300	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
301	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	13	2	no	—
305	C₄×D₄	—	26	1	no	—
306	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
307	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#117	C₄×D₁₃	1	1	yes	characteristic
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
312	#107	—	13	2	no	—
313	#106	—	13	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	13	1	no	—
317	C₄⋊C₈	—	13	1	no	—
318	C₄⋊C₈	—	13	2	no	—
319	C₄⋊C₈	—	26	1	no	—
320	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
322	#103	—	13	2	no	—
323	#102	—	13	2	no	—
324	#102	—	13	2	no	—
325	#102	—	13	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	13	2	no	—
330	C₂²⋊C₈	—	26	2	no	—
331	C₂²⋊C₈	—	26	2	no	—
332	#97	—	26	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	2	1	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	—	13	2	no	—
337	C₄×C₈	—	13	2	no	—
338	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
339	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
342	C₂×C₁₃	—	4	1	no	—
343	C₂×C₁₃	—	4	2	no	—
344	C₂×C₁₃	#2929	1	1	yes	characteristic
345	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
347	D₁₃	—	8	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	52	2	no	—
351	#41	—	52	2	no	—
352	C₂×Q₈	—	26	1	no	—
353	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	13	2	no	—
356	C₂×D₄	—	26	2	no	—
357	C₂×D₄	—	26	1	no	—
358	C₂×D₄	—	26	1	no	—
359	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	26	2	no	—
364	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	#6127	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
367	SD₁₆	—	26	4	no	—
368	D₈	—	26	4	no	—
369	M₁₆	—	52	2	no	—
370	M₁₆	—	52	2	no	—
371	M₁₆	—	52	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	13	2	no	—
379	C₂×C₈	—	13	2	no	—
380	C₂×C₈	—	26	2	no	—
381	C₂×C₈	—	26	2	no	—
382	C₂×C₈	—	52	4	no	—
383	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	13	2	no	—
390	C₄⋊C₄	—	26	1	no	—
391	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
392	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	26	2	no	—
397	C₂²⋊C₄	—	26	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
402	C₄²	#6127	1	1	yes	characteristic
403	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
404	C₄²	C₂³×D₁₃	1	1	yes	characteristic
405	C₁₃	#17917	1	1	yes	characteristic, complemented, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	—	26	2	no	—
408	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	52	2	no	—
411	Q₈	#88155	1	2	yes	complemented
412	D₄	—	2	4	no	—
413	D₄	—	2	1	no	—
414	D₄	—	26	2	no	—
415	D₄	—	26	2	no	—
416	D₄	—	52	2	no	—
417	D₄	—	52	4	no	—
418	D₄	—	52	2	no	—
419	D₄	#88155	1	2	yes	complemented
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	26	2	no	—
433	C₂×C₄	—	52	2	no	—
434	C₂×C₄	—	52	2	no	—
435	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
437	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#6127	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	26	2	no	—
447	C₈	—	26	2	no	—
448	C₈	—	52	2	no	—
449	C₈	—	52	2	no	—
450	C₈	#88203	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	52	2	no	—
458	C₂²	—	52	2	no	—
459	C₂²	—	52	2	no	—
460	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	52	2	no	—
468	C₄	#11718806	1	2	yes	—
469	C₄	C₂×#88155	1	1	yes	characteristic
470	C₄	C₂×#88155	1	1	yes	characteristic
471	C₄	C₂×#88203	1	1	yes	characteristic
472	C₄	#11719527	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	104	2	no	—
476	C₂	#13123530	1	1	yes	characteristic
477	C₂	C₄×#88203	1	1	yes	characteristic
478	C₂	C₂×#11718806	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×#41	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13124896	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	#17917
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #13123549	C₂	semidirect
3. #13113679	C₂	semidirect
4. #13113665	C₂	semidirect
5. #13113658	C₂	semidirect
6. #13113646	C₂	semidirect
7. #13113624	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113252	C₂	semidirect
10. #13113125	C₂	semidirect
11. C₈×C₁₃×#41	C₂	semidirect
168. C₈×#41	D₁₃	semidirect
182. Q₈×C₁₃	#131	semidirect
185. D₄×C₁₃	#131	semidirect
405. C₁₃	#17917	semidirect
411. Q₈	#88155	semidirect
419. D₄	#88155	semidirect

Maximal subgroups

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

subgroup	index
#13124896	2
#13123549	2
#13113679	2
#13113665	2
#13113658	2
#13113646	2
#13113624	2
#13113275	2
#13113252	2
#13113125	2
C₈×C₁₃×#41	2
#17917	13