Subgroups — #15832520

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#1055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88203	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718499	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113711	C₂	1	2	yes	maximal, complemented
5	#13113697	C₂	1	2	yes	maximal, complemented
6	#13113676	C₂	1	2	yes	maximal, complemented
7	#13113662	C₂	1	2	yes	maximal, complemented
8	#13113586	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113228	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88203	C₄	1	1	yes	characteristic
14	C₂²×#6094	—	2	1	no	—
15	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	#11718893	C₄	1	1	yes	characteristic
19	C₂×#88060	—	2	1	no	—
20	#11718687	C₄	1	2	yes	—
21	C₄×#6106	C₂²	1	2	yes	—
22	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
23	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
24	#11718675	C₄	1	2	yes	—
25	C₄×#6104	C₂²	1	2	yes	—
26	D₄×#1055	—	2	1	no	—
27	D₄×#1055	—	2	1	no	—
28	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
29	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
30	#11718662	C₄	1	1	yes	characteristic
31	#11718656	C₄	1	1	yes	characteristic
32	#11718586	—	2	1	no	—
33	#11718586	C₂²	1	1	yes	characteristic
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	—	2	1	no	—
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	#11718499	—	2	1	no	—
38	#11718499	—	2	1	no	—
39	#11718499	C₂²	1	2	yes	—
40	#11718499	C₂²	1	2	yes	—
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
43	#11718072	C₂²	1	2	yes	complemented
44	#11718071	C₂²	1	2	yes	complemented
45	#11718051	C₂²	1	2	yes	—
46	#11718051	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	complemented
48	#11718046	C₂²	1	2	yes	complemented
49	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₃	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	#88203	—	2	4	no	—
64	C₂×#6106	C₂×C₄	1	2	yes	—
65	C₂×#6104	C₂×C₄	1	2	yes	—
66	C₂×#6103	—	2	1	no	—
67	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×#6099	C₂×C₄	1	1	yes	characteristic
69	C₂×#6099	C₂×C₄	1	1	yes	characteristic
70	C₂²×#1055	—	2	1	no	—
71	C₂²×#1055	—	2	1	no	—
72	C₂²×#1055	D₄	1	1	yes	characteristic
73	C₂²×#1055	D₄	1	1	yes	characteristic
74	C₂×#6094	—	2	2	no	—
75	C₂×#6094	—	2	2	no	—
76	C₂×#6094	—	4	4	no	—
77	C₄×D₅₂	—	2	1	no	—
78	C₄×D₅₂	—	2	1	no	—
79	C₄×D₅₂	C₂×C₄	1	2	yes	—
80	C₄×D₅₂	C₂³	1	2	yes	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₃×C₂²⋊C₈	—	2	1	no	—
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	#88075	C₂×C₄	1	2	yes	—
87	#88072	C₂×C₄	1	2	yes	—
88	C₂²⋊#1055	—	2	1	no	—
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	#88060	—	2	2	no	—
92	#88060	—	2	2	no	—
93	#88049	C₂×C₄	1	2	yes	—
94	#88049	C₂×C₄	1	2	yes	—
95	#88048	C₂×C₄	1	2	yes	—
96	#88047	C₂×C₄	1	2	yes	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	—	2	1	no	—
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	#88043	C₂×C₄	1	2	yes	—
102	C₄×#1055	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	C₄×#1055	—	2	1	no	—
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	D₄	1	1	yes	characteristic
107	C₄×#1055	C₂³	1	2	yes	—
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	C₄×#1055	C₂³	1	1	yes	characteristic
110	#17871	—	13	1	no	maximal, Sylow
111	C₂³×D₁₃	—	2	1	no	—
112	C₁₃×#41	—	2	2	no	—
113	C₁₃×#41	M₁₆	1	4	yes	complemented
114	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
123	C₂²×Dic₁₃	—	2	1	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	2	2	no	—
126	C₂×D₅₂	—	2	1	no	—
127	C₂×D₅₂	C₂²×C₄	1	2	yes	—
128	C₂×C₄×D₁₃	—	2	2	no	—
129	C₂×C₄×D₁₃	—	2	2	no	—
130	C₂×C₄×D₁₃	—	4	2	no	—
131	C₂×C₄×D₁₃	—	4	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
139	C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₁₃	#41	1	1	yes	characteristic
148	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
149	#6106	—	2	4	no	—
150	#6104	—	2	4	no	—
151	#6103	—	2	2	no	—
152	#6103	—	2	2	no	—
153	C₄⋊Dic₁₃	—	2	1	no	—
154	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
155	#6099	—	2	2	no	—
156	#6099	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	2	1	no	—
159	C₂×#1055	—	2	1	no	—
160	C₂×#1055	—	4	1	no	—
161	C₂×#1055	—	4	2	no	—
162	C₂×#1055	—	4	2	no	—
163	C₂×#1055	C₂²×C₄	1	2	yes	—
164	C₂×#1055	C₂²×C₄	1	2	yes	—
165	C₂×#1055	C₂×D₄	1	1	yes	characteristic
166	C₂×#1055	C₂×D₄	1	1	yes	characteristic
167	C₂×#1055	C₂×D₄	1	1	yes	characteristic
168	C₂×#1055	C₂×D₄	1	1	yes	characteristic
169	#6094	—	4	4	no	—
170	#6094	—	4	4	no	—
171	C₈×#41	—	13	1	no	—
172	C₄×AGL(1,ℤ/8)	—	13	1	no	—
173	C₂×#436	—	13	1	no	—
174	#1588	—	13	2	no	—
175	#1586	—	13	2	no	—
176	#1583	—	13	2	no	—
177	#1581	—	13	2	no	—
178	#1565	—	13	1	no	—
179	#1478	—	13	1	no	—
180	#1477	D₁₃	1	1	yes	characteristic, complemented
181	#1451	—	13	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂²×D₁₃	—	2	2	no	—
185	C₂²×D₁₃	—	4	2	no	—
186	C₂²×D₁₃	—	4	2	no	—
187	C₂²×D₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	2	1	no	—
189	Q₈×C₁₃	C₂×M₁₆	1	2	yes	complemented
190	D₄×C₁₃	—	2	4	no	—
191	D₄×C₁₃	—	2	1	no	—
192	D₄×C₁₃	C₂×M₁₆	1	2	yes	complemented
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₁₃	#131	1	2	yes	—
208	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×Dic₁₃	—	2	2	no	—
212	C₂×Dic₁₃	—	4	2	no	—
213	D₅₂	—	2	2	no	—
214	D₅₂	—	2	2	no	—
215	D₅₂	—	4	2	no	—
216	C₄×D₁₃	—	4	4	no	—
217	C₄×D₁₃	—	4	2	no	—
218	C₄×D₁₃	—	4	2	no	—
219	C₈×C₁₃	—	4	2	no	—
220	C₈×C₁₃	—	4	2	no	—
221	#1055	—	2	2	no	—
222	#1055	—	2	2	no	—
223	#1055	—	2	1	no	—
224	#1055	—	2	1	no	—
225	#1055	—	2	1	no	—
226	#1055	—	4	1	no	—
227	#1055	—	4	1	no	—
228	#1055	AGL(1,ℤ/8)	1	2	yes	complemented
229	C₂×AGL(1,ℤ/8)	—	13	1	no	—
230	C₂²×M₁₆	—	26	1	no	—
231	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	13	1	no	—
233	C₈×Q₈	—	13	1	no	—
234	C₈×Q₈	—	13	1	no	—
235	#442	—	13	2	no	—
236	#440	—	13	2	no	—
237	C₄×SD₁₆	—	13	2	no	—
238	C₄×D₈	—	13	2	no	—
239	#436	—	13	2	no	—
240	#436	—	13	2	no	—
241	#436	—	26	1	no	—
242	#436	—	26	1	no	—
243	C₈×D₄	—	13	1	no	—
244	C₈×D₄	—	13	1	no	—
245	C₈×D₄	—	26	1	no	—
246	C₈×D₄	—	26	1	no	—
247	#431	—	13	1	no	—
248	#431	—	26	1	no	—
249	#431	C₂×D₁₃	1	1	yes	characteristic
250	#428	—	13	1	no	—
251	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
252	#418	—	13	1	no	—
253	#417	—	13	1	no	—
254	C₂×C₂²⋊C₈	—	26	1	no	—
255	C₄×M₁₆	—	13	1	no	—
256	C₂×C₄×C₈	—	13	1	no	—
257	C₂×C₄×C₈	—	26	1	no	—
258	#335	—	13	2	no	—
259	#334	—	13	2	no	—
260	Q₈⋊C₈	C₂×D₁₃	1	2	yes	complemented
261	D₄⋊C₈	—	13	2	no	—
262	D₄⋊C₈	—	13	2	no	—
263	D₄⋊C₈	C₂×D₁₃	1	2	yes	complemented
264	#322	—	13	2	no	—
265	#322	—	13	2	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	—	4	1	no	—
271	C₂²×C₁₃	#435	1	2	yes	—
272	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×D₁₃	—	4	2	no	—
274	C₂×D₁₃	—	4	2	no	—
275	C₂×D₁₃	—	4	2	no	—
276	C₂×D₁₃	—	8	4	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	1	no	—
283	C₄×C₁₃	#435	1	2	yes	—
284	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
285	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
286	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₄×C₁₃	#575	1	1	yes	characteristic
288	Dic₁₃	—	4	2	no	—
289	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
290	C₂²×D₄	—	13	1	no	—
291	C₂³×C₄	—	26	1	no	—
292	AGL(1,ℤ/8)	—	26	4	no	—
293	C₂×SD₁₆	—	13	2	no	—
294	C₂×D₈	—	13	2	no	—
295	C₂×M₁₆	—	13	1	no	—
296	C₂×M₁₆	—	13	1	no	—
297	C₂×M₁₆	—	26	2	no	—
298	C₂×M₁₆	—	26	2	no	—
299	C₂×M₁₆	—	52	4	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	26	1	no	—
304	C₂²×C₈	—	26	1	no	—
305	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
306	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	13	2	no	—
310	C₄×D₄	—	13	2	no	—
311	C₄×D₄	—	26	1	no	—
312	C₄×D₄	—	26	1	no	—
313	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
314	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₄×D₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	—	13	1	no	—
318	C₂×C₂²⋊C₄	—	26	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
321	#107	—	13	2	no	—
322	#106	—	13	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	13	1	no	—
326	C₄⋊C₈	—	13	1	no	—
327	C₄⋊C₈	—	26	1	no	—
328	C₄⋊C₈	—	26	1	no	—
329	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
330	#103	—	13	2	no	—
331	#102	—	13	2	no	—
332	#102	—	13	2	no	—
333	#102	—	13	2	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	26	2	no	—
336	C₂²⋊C₈	—	26	2	no	—
337	C₂²⋊C₈	—	26	1	no	—
338	C₂²⋊C₈	—	26	1	no	—
339	C₂²⋊C₈	—	26	1	no	—
340	#97	—	13	2	no	—
341	C₄×C₈	—	13	1	no	—
342	C₄×C₈	—	13	1	no	—
343	C₄×C₈	—	13	2	no	—
344	C₄×C₈	—	13	1	no	—
345	C₄×C₈	—	13	1	no	—
346	C₄×C₈	—	26	1	no	—
347	C₄×C₈	—	26	1	no	—
348	C₄×C₈	—	26	1	no	—
349	C₄×C₈	C₂²×D₁₃	1	2	yes	—
350	C₂×C₁₃	—	2	2	no	—
351	C₂×C₁₃	—	4	2	no	—
352	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
353	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂×C₁₃	#2955	1	1	yes	characteristic
355	D₁₃	—	8	2	no	—
356	C₂⁴	—	26	1	no	—
357	#41	—	2	2	no	—
358	#41	#6094	1	4	yes	complemented
359	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	13	2	no	—
362	C₂×D₄	—	26	1	no	—
363	C₂×D₄	—	26	2	no	—
364	C₂×D₄	—	26	2	no	—
365	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	26	1	no	—
370	C₂²×C₄	—	26	2	no	—
371	C₂²×C₄	—	26	2	no	—
372	C₂²×C₄	—	52	2	no	—
373	C₂²×C₄	—	52	2	no	—
374	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
376	C₂²×C₄	#6129	1	1	yes	characteristic
377	SD₁₆	—	26	4	no	—
378	D₈	—	26	4	no	—
379	M₁₆	—	26	2	no	—
380	M₁₆	—	26	2	no	—
381	M₁₆	—	52	4	no	—
382	M₁₆	—	52	4	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	2	no	—
386	C₂×C₈	—	13	1	no	—
387	C₂×C₈	—	13	2	no	—
388	C₂×C₈	—	13	2	no	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	13	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	26	2	no	—
393	C₂×C₈	—	26	1	no	—
394	C₂×C₈	—	26	1	no	—
395	C₂×C₈	—	52	2	no	—
396	C₂×C₈	—	52	1	no	—
397	C₂×C₈	—	52	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	13	2	no	—
401	C₄⋊C₄	—	26	1	no	—
402	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
403	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	26	2	no	—
408	C₂²⋊C₄	—	26	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
413	C₄²	D₄×D₁₃	1	1	yes	characteristic
414	C₄²	#6129	1	1	yes	characteristic
415	C₄²	C₂³×D₁₃	1	1	yes	characteristic
416	C₁₃	#17871	1	1	yes	characteristic, complemented, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	26	2	no	—
419	C₂³	—	52	2	no	—
420	C₂³	—	52	2	no	—
421	C₂³	—	52	2	no	—
422	C₂³	#88135	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	C₂×#6094	1	2	yes	complemented
425	D₄	—	2	4	no	—
426	D₄	—	2	1	no	—
427	D₄	—	26	2	no	—
428	D₄	—	26	2	no	—
429	D₄	—	52	2	no	—
430	D₄	C₂×#6094	1	2	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	26	2	no	—
442	C₂×C₄	—	52	4	no	—
443	C₂×C₄	—	52	2	no	—
444	C₂×C₄	—	52	2	no	—
445	C₂×C₄	—	52	2	no	—
446	C₂×C₄	#88135	1	1	yes	characteristic
447	C₂×C₄	#88135	1	1	yes	characteristic
448	C₂×C₄	#88135	1	1	yes	characteristic
449	C₂×C₄	C₂×#6094	1	2	yes	—
450	C₂×C₄	#88161	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#6129	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	13	2	no	—
457	C₈	—	26	2	no	—
458	C₈	—	26	2	no	—
459	C₈	—	26	1	no	—
460	C₈	—	26	1	no	—
461	C₈	—	26	1	no	—
462	C₈	—	52	1	no	—
463	C₈	—	52	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	52	2	no	—
470	C₂²	—	52	2	no	—
471	C₂²	—	52	2	no	—
472	C₂²	—	104	4	no	—
473	C₂²	#11718391	1	2	yes	—
474	C₂²	C₂×#88135	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	52	2	no	—
482	C₄	#11718391	1	2	yes	—
483	C₄	C₂²×#6094	1	1	yes	characteristic
484	C₄	C₂×#88161	1	1	yes	characteristic
485	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	#11719482	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	104	2	no	—
490	C₂	C₂×#11718391	1	1	yes	characteristic
491	C₂	#13123649	1	1	yes	characteristic
492	C₂	#13123735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1477	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88203	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1477	D₁₃
hypocenter	C₁₃	#17871
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
1. #41×#1055	C₂	semidirect
3. C₂×#11718499	C₂	semidirect
4. #13113711	C₂	semidirect
5. #13113697	C₂	semidirect
6. #13113676	C₂	semidirect
7. #13113662	C₂	semidirect
8. #13113586	C₂	semidirect
9. #13113228	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#1477	C₂	semidirect
22. Q₈×#1055	C₂²	semidirect
23. Q₈×#1055	C₂²	semidirect
28. D₄×#1055	C₂²	semidirect
29. D₄×#1055	C₂²	semidirect
41. C₁₃×Q₈⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
43. #11718072	C₂²	semidirect
44. #11718071	C₂²	semidirect
47. #11718047	C₂²	semidirect
48. #11718046	C₂²	semidirect
113. C₁₃×#41	M₁₆	semidirect
180. #1477	D₁₃	semidirect
189. Q₈×C₁₃	C₂×M₁₆	semidirect
192. D₄×C₁₃	C₂×M₁₆	semidirect
228. #1055	AGL(1,ℤ/8)	semidirect
260. Q₈⋊C₈	C₂×D₁₃	semidirect
263. D₄⋊C₈	C₂×D₁₃	semidirect
358. #41	#6094	semidirect
416. C₁₃	#17871	semidirect
424. Q₈	C₂×#6094	semidirect
430. D₄	C₂×#6094	semidirect

Maximal subgroups

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

subgroup	index
#41×#1055	2
C₄×#88203	2
C₂×#11718499	2
#13113711	2
#13113697	2
#13113676	2
#13113662	2
#13113586	2
#13113228	2
#13113126	2
C₁₃×#1477	2
#17871	13