Subgroups — #15832969

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	#41×#1055	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123548	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113680	C₂	1	2	yes	maximal, complemented
4	#13113666	C₂	1	2	yes	maximal, complemented
5	#13113660	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13113625	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113253	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×#88202	—	2	1	no	—
15	C₁₃×#482	C₄	1	2	yes	—
16	C₁₃×#477	C₄	1	1	yes	characteristic
17	C₁₃×#476	C₄	1	1	yes	characteristic
18	C₁₃×#460	C₄	1	1	yes	characteristic
19	C₁₃×#459	C₄	1	1	yes	characteristic
20	C₁₃×#449	C₄	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₄×C₁₃×D₈	C₂²	1	2	yes	—
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	#11718895	—	2	1	no	—
25	Q₈×#1055	C₂²	1	1	yes	characteristic
26	Q₈×#1055	C₂²	1	1	yes	characteristic
27	#11718673	—	2	1	no	—
28	#11718673	C₂²	1	2	yes	—
29	D₄×#1055	—	2	1	no	—
30	D₄×#1055	—	2	1	no	—
31	D₄×#1055	—	2	1	no	—
32	D₄×#1055	C₂²	1	2	yes	—
33	D₄×#1055	C₂²	1	1	yes	characteristic
34	D₄×#1055	C₂²	1	1	yes	characteristic
35	#11718586	—	2	1	no	—
36	#11718586	C₂²	1	1	yes	characteristic
37	#11718585	C₂²	1	1	yes	characteristic
38	C₄×#6099	C₂²	1	1	yes	characteristic
39	C₂×C₄×#1055	—	2	1	no	—
40	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	D₄⋊#1055	C₂²	1	2	yes	—
43	D₄⋊#1055	C₂²	1	2	yes	—
44	D₄⋊#1055	C₂²	1	2	yes	—
45	#11718050	C₂²	1	2	yes	—
46	#11718049	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#121	—	2	1	no	—
57	C₁₃×#121	C₂×C₄	1	2	yes	—
58	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	1	no	—
61	C₄×D₄×C₁₃	—	2	1	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	#88202	—	4	4	no	—
71	C₂×#6099	—	2	1	no	—
72	C₂×#6099	—	2	1	no	—
73	C₂×#6099	—	2	2	no	—
74	C₂²×#1055	—	2	2	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	1	no	—
77	C₂²×#1055	D₄	1	1	yes	characteristic
78	C₂²×#1055	D₄	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#103	C₂×C₄	1	2	yes	—
84	C₁₃×#102	C₂×C₄	1	2	yes	—
85	C₁₃×#102	C₂×C₄	1	2	yes	—
86	C₁₃×#102	C₂×C₄	1	2	yes	—
87	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₄×C₈×C₁₃	C₂³	1	2	yes	—
89	C₂²⋊#1055	—	2	1	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	C₂²⋊#1055	—	2	1	no	—
92	C₂²⋊#1055	—	2	2	no	—
93	C₂²⋊#1055	—	2	2	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	C₂³	1	2	yes	—
98	C₄⋊#1055	C₂³	1	1	yes	characteristic
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	#88043	—	2	1	no	—
101	C₄×#1055	—	2	1	no	—
102	C₄×#1055	—	2	1	no	—
103	C₄×#1055	—	2	1	no	—
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	#17917	—	13	1	no	maximal, Sylow
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	4	2	no	—
113	C₁₃×#41	—	4	2	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₁₃×SD₁₆	—	2	4	no	—
130	C₁₃×D₈	—	2	4	no	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
137	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃	#41	1	1	yes	characteristic
150	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
151	#6099	—	4	2	no	—
152	#6099	—	4	2	no	—
153	#6099	—	4	4	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	1	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	4	1	no	—
160	C₂×#1055	—	4	2	no	—
161	C₂×#1055	—	4	4	no	—
162	C₂×#1055	—	4	2	no	—
163	C₂×#1055	C₂×D₄	1	1	yes	characteristic
164	C₂×#1055	C₂×D₄	1	1	yes	characteristic
165	C₂×#1055	C₂×D₄	1	1	yes	characteristic
166	C₂×#1055	C₂×D₄	1	1	yes	characteristic
167	#3106	D₁₃	1	1	yes	characteristic
168	C₈×#41	—	13	1	no	—
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	—	2	2	no	—
180	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	2	1	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	#131	1	2	yes	complemented
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	2	1	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	4	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	#131	1	2	yes	complemented
192	C₂×C₄×C₁₃	—	2	4	no	—
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	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	2	2	no	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	#1055	—	2	1	no	—
218	#1055	—	4	2	no	—
219	#1055	—	4	1	no	—
220	#1055	—	4	2	no	—
221	#1055	—	4	1	no	—
222	#1055	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×#131	—	26	1	no	—
224	#532	C₂×D₁₃	1	1	yes	characteristic
225	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
226	#482	Dic₁₃	1	2	yes	—
227	#477	Dic₁₃	1	1	yes	characteristic
228	#476	Dic₁₃	1	1	yes	characteristic
229	#460	Dic₁₃	1	1	yes	characteristic
230	#459	Dic₁₃	1	1	yes	characteristic
231	#449	Dic₁₃	1	2	yes	—
232	C₈×Q₈	—	13	1	no	—
233	C₈×Q₈	—	13	1	no	—
234	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
235	C₄×D₈	C₂×D₁₃	1	2	yes	—
236	#436	—	13	2	no	—
237	#436	—	26	1	no	—
238	C₈×D₄	—	13	2	no	—
239	C₈×D₄	—	13	1	no	—
240	C₈×D₄	—	13	1	no	—
241	C₈×D₄	—	26	1	no	—
242	C₈×D₄	—	26	1	no	—
243	C₈×D₄	—	26	1	no	—
244	#431	—	13	1	no	—
245	#431	—	26	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	—	13	1	no	—
251	C₂×C₄×C₈	—	26	1	no	—
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	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
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	2	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	#444	1	2	yes	—
278	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
279	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
280	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₁₃	#575	1	1	yes	characteristic
282	C₂×#41	—	2	1	no	—
283	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
284	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
285	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
286	#131	—	52	4	no	—
287	C₂×M₁₆	—	26	2	no	—
288	C₂×M₁₆	—	26	1	no	—
289	C₂×M₁₆	—	26	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	26	2	no	—
293	C₂²×C₈	—	26	1	no	—
294	C₂²×C₈	—	26	1	no	—
295	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
296	#127	C₂×Dic₁₃	1	1	yes	characteristic
297	#124	—	2	1	no	—
298	#121	—	2	1	no	—
299	#121	C₂×Dic₁₃	1	2	yes	—
300	C₄×Q₈	C₂×Dic₁₃	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	—	2	1	no	—
305	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
307	C₄×D₄	C₂²×D₁₃	1	2	yes	—
308	#117	—	2	1	no	—
309	#117	C₂×Dic₁₃	1	1	yes	characteristic
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
312	#107	C₂×Dic₁₃	1	2	yes	—
313	#106	C₂×Dic₁₃	1	2	yes	—
314	C₄⋊C₈	—	13	1	no	—
315	C₄⋊C₈	—	13	1	no	—
316	C₄⋊C₈	—	13	2	no	—
317	C₄⋊C₈	—	26	1	no	—
318	C₄⋊C₈	—	26	1	no	—
319	C₄⋊C₈	—	26	1	no	—
320	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
321	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
322	#103	C₂×Dic₁₃	1	2	yes	—
323	#102	C₂×Dic₁₃	1	2	yes	—
324	#102	C₂×Dic₁₃	1	2	yes	—
325	#102	C₂×Dic₁₃	1	2	yes	—
326	C₂²⋊C₈	—	26	2	no	—
327	C₂²⋊C₈	—	26	2	no	—
328	C₂²⋊C₈	—	26	1	no	—
329	C₂²⋊C₈	—	26	1	no	—
330	C₂²⋊C₈	—	26	1	no	—
331	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
332	#97	—	26	1	no	—
333	C₄×C₈	—	13	1	no	—
334	C₄×C₈	—	13	1	no	—
335	C₄×C₈	—	13	1	no	—
336	C₄×C₈	—	13	1	no	—
337	C₄×C₈	—	13	2	no	—
338	C₄×C₈	—	26	1	no	—
339	C₄×C₈	—	26	1	no	—
340	C₄×C₈	—	26	1	no	—
341	C₄×C₈	C₂²×D₁₃	1	2	yes	—
342	C₂×C₁₃	—	4	1	no	—
343	C₂×C₁₃	—	4	2	no	—
344	C₂×C₁₃	—	8	2	no	—
345	C₂×C₁₃	#2929	1	1	yes	characteristic
346	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
359	C₂×D₄	C₂²×Dic₁₃	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	—	2	2	no	—
364	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	#6129	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
367	SD₁₆	—	2	4	no	—
368	D₈	—	2	4	no	—
369	M₁₆	—	52	4	no	—
370	M₁₆	—	52	2	no	—
371	M₁₆	—	52	2	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	13	1	no	—
376	C₂×C₈	—	26	2	no	—
377	C₂×C₈	—	26	1	no	—
378	C₂×C₈	—	26	1	no	—
379	C₂×C₈	—	26	2	no	—
380	C₂×C₈	—	26	2	no	—
381	C₂×C₈	—	52	2	no	—
382	C₂×C₈	—	52	1	no	—
383	C₂×C₈	—	52	4	no	—
384	C₂×C₈	—	52	2	no	—
385	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
386	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
391	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
392	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	D₄×D₁₃	1	1	yes	characteristic
402	C₄²	#6129	1	1	yes	characteristic
403	C₄²	C₂²×Dic₁₃	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	—	2	2	no	—
408	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
409	Q₈	—	2	1	no	—
410	Q₈	—	4	2	no	—
411	Q₈	#88202	1	2	yes	complemented
412	D₄	—	2	4	no	—
413	D₄	—	2	1	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	#88202	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	—	2	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
436	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
437	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#6129	1	1	yes	characteristic
440	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	13	2	no	—
444	C₈	—	26	1	no	—
445	C₈	—	26	1	no	—
446	C₈	—	26	1	no	—
447	C₈	—	52	2	no	—
448	C₈	—	52	1	no	—
449	C₈	—	52	2	no	—
450	C₈	—	52	1	no	—
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	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₂×D₄×Dic₁₃	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	2	no	—
467	C₄	—	4	1	no	—
468	C₄	#11718858	1	2	yes	—
469	C₄	D₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₄	#11719478	1	1	yes	characteristic
471	C₄	C₂×#88202	1	1	yes	characteristic
472	C₄	C₂×#88202	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	8	2	no	—
476	C₂	#13123531	1	1	yes	characteristic
477	C₂	AGL(1,ℤ/8)×Dic₁₃	1	1	yes	characteristic
478	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3106	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3106	D₁₃
hypocenter	C₁₃	#17917
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
1. #41×#1055	C₂	semidirect
2. #13123548	C₂	semidirect
3. #13113680	C₂	semidirect
4. #13113666	C₂	semidirect
5. #13113660	C₂	semidirect
6. SD₁₆⋊#1055	C₂	semidirect
7. #13113625	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113253	C₂	semidirect
10. #13113126	C₂	semidirect
183. Q₈×C₁₃	#131	semidirect
191. D₄×C₁₃	#131	semidirect
405. C₁₃	#17917	semidirect
411. Q₈	#88202	semidirect
419. D₄	#88202	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
#13123548	2
#13113680	2
#13113666	2
#13113660	2
SD₁₆⋊#1055	2
#13113625	2
#13113275	2
#13113253	2
#13113126	2
C₁₃×#3106	2
#17917	13