Subgroups — #15833892

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123580	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113750	C₂	1	2	yes	maximal, complemented
4	#13113701	C₂	1	2	yes	maximal, complemented
5	#13113701	C₂	1	2	yes	maximal, complemented
6	#13113660	C₂	1	2	yes	maximal, complemented
7	#13113607	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88202	—	2	1	no	—
15	C₂²×#6099	—	2	1	no	—
16	C₁₃×#480	C₄	1	2	yes	—
17	C₁₃×#474	C₄	1	1	yes	characteristic
18	C₁₃×#474	C₄	1	1	yes	characteristic
19	C₁₃×#459	C₄	1	1	yes	characteristic
20	C₁₃×#459	C₄	1	1	yes	characteristic
21	C₁₃×#447	C₄	1	2	yes	—
22	C₄×C₁₃×D₈	C₂²	1	2	yes	—
23	C₄×C₁₃×D₈	C₂²	1	2	yes	—
24	C₁₃×#431	C₂²	1	1	yes	characteristic
25	#11718895	—	2	1	no	—
26	#11718868	—	2	1	no	—
27	#11718673	C₂²	1	2	yes	—
28	#11718673	C₂²	1	2	yes	complemented
29	#11718672	—	2	2	no	—
30	#11718672	—	2	2	no	—
31	D₄×#1055	C₂²	1	2	yes	—
32	D₄×#1055	C₂²	1	2	yes	complemented
33	#11718585	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	C₄×#6099	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	D₄⋊#1055	C₂²	1	1	yes	characteristic
38	D₄⋊#1055	C₂²	1	1	yes	characteristic
39	D₄⋊#1055	C₂²	1	1	yes	characteristic
40	D₄⋊#1055	C₂²	1	1	yes	characteristic
41	D₄⋊#1055	C₂²	1	2	yes	complemented
42	D₄⋊#1055	C₂²	1	2	yes	complemented
43	#11718049	C₂²	1	2	yes	complemented
44	#11718049	C₂²	1	2	yes	complemented
45	#11718047	C₂²	1	2	yes	complemented
46	#11718046	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#124	—	2	1	no	—
55	C₁₃×#121	—	2	1	no	—
56	C₁₃×#121	C₂×C₄	1	2	yes	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₄×D₄×C₁₃	—	2	1	no	—
60	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂³	1	2	yes	—
64	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	#88202	—	4	4	no	—
69	C₂×#6099	—	2	1	no	—
70	C₂×#6099	—	2	2	no	—
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	—	4	4	no	—
73	C₂×#6099	D₄	1	1	yes	characteristic
74	C₂×#6099	D₄	1	1	yes	characteristic
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	—	2	1	no	—
77	C₂²×#1055	—	2	2	no	—
78	C₂²×#1055	—	2	2	no	—
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#107	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×#102	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	2	no	—
90	C₂²⋊#1055	—	2	2	no	—
91	C₂²⋊#1055	—	2	2	no	—
92	C₂²⋊#1055	—	2	2	no	—
93	C₄⋊#1055	—	2	1	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	C₂³	1	2	yes	—
96	C₄⋊#1055	C₂³	1	1	yes	characteristic
97	C₄⋊#1055	C₂³	1	1	yes	characteristic
98	#88043	D₄	1	2	yes	—
99	C₄×#1055	—	2	1	no	—
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	1	yes	characteristic
102	C₄×#1055	C₂³	1	2	yes	—
103	#18001	—	13	1	no	maximal, Sylow
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₁₃×#41	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	4	1	no	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₁₃×D₈	—	2	4	no	—
129	C₁₃×D₈	—	4	2	no	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₁₃×C₂²⋊C₄	—	2	2	no	—
140	C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₁₃×C₂²⋊C₄	—	2	2	no	—
143	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₃	#41	1	1	yes	characteristic
146	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
147	#6099	—	2	2	no	—
148	#6099	—	2	2	no	—
149	#6099	—	4	4	no	—
150	#6099	—	4	4	no	—
151	#6099	—	4	2	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	1	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	4	2	no	—
158	C₂×#1055	—	4	4	no	—
159	C₂×#1055	—	4	4	no	—
160	C₂×#1055	—	4	2	no	—
161	C₂×#1055	C₂×D₄	1	2	yes	—
162	C₂×#1055	C₂×D₄	1	2	yes	—
163	#3100	D₁₃	1	1	yes	characteristic
164	#2935	—	13	1	no	—
165	D₄×M₁₆	—	13	1	no	—
166	#1594	—	13	2	no	—
167	#1586	—	13	2	no	—
168	#1586	—	13	2	no	—
169	#1580	—	13	2	no	—
170	#1570	—	13	1	no	—
171	#1492	—	13	1	no	—
172	C₂×D₄⋊C₈	—	13	1	no	—
173	#1451	—	13	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	8	1	no	—
180	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	1	no	—
184	D₄×C₁₃	—	2	1	no	—
185	D₄×C₁₃	—	2	1	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	4	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	8	1	no	—
191	D₄×C₁₃	#131	1	2	yes	complemented
192	C₂×C₄×C₁₃	—	2	1	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	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	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	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	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	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	—	2	2	no	—
217	#1055	—	2	2	no	—
218	#1055	—	2	2	no	—
219	#1055	—	2	2	no	—
220	#1055	—	4	1	no	—
221	#1055	—	4	1	no	—
222	#1055	—	4	2	no	—
223	#1055	—	4	1	no	—
224	C₂×#131	—	26	1	no	—
225	C₂²×M₁₆	—	26	1	no	—
226	#532	C₂×D₁₃	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
228	#480	Dic₁₃	1	2	yes	—
229	#474	Dic₁₃	1	1	yes	characteristic
230	#474	Dic₁₃	1	1	yes	characteristic
231	#459	Dic₁₃	1	1	yes	characteristic
232	#459	Dic₁₃	1	1	yes	characteristic
233	#447	Dic₁₃	1	2	yes	—
234	C₄×D₈	C₂×D₁₃	1	2	yes	—
235	C₄×D₈	C₂×D₁₃	1	2	yes	—
236	#436	—	13	2	no	—
237	#436	—	13	2	no	—
238	#435	—	26	2	no	—
239	#435	—	26	2	no	—
240	C₈×D₄	—	13	2	no	—
241	C₈×D₄	—	13	2	no	—
242	#431	C₂×D₁₃	1	1	yes	characteristic
243	#423	—	13	1	no	—
244	C₂×C₄⋊C₈	—	13	1	no	—
245	#408	—	26	1	no	—
246	#407	—	26	1	no	—
247	C₄×M₁₆	—	13	1	no	—
248	C₂×C₄×C₈	—	13	1	no	—
249	#334	—	13	2	no	—
250	#334	—	13	2	no	—
251	D₄⋊C₈	—	13	1	no	—
252	D₄⋊C₈	—	13	2	no	—
253	D₄⋊C₈	—	13	1	no	—
254	D₄⋊C₈	—	13	1	no	—
255	D₄⋊C₈	—	13	2	no	—
256	D₄⋊C₈	—	13	1	no	—
257	#322	—	13	2	no	—
258	#322	—	13	2	no	—
259	C₂²×C₁₃	—	2	1	no	—
260	C₂²×C₁₃	—	2	1	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	4	1	no	—
263	C₂²×C₁₃	—	4	1	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	1	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	1	no	—
270	C₂²×C₁₃	—	8	4	no	—
271	C₂²×C₁₃	#442	1	2	yes	—
272	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	1	no	—
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	#442	1	2	yes	—
280	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
281	C₄×C₁₃	#568	1	1	yes	characteristic
282	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂×#41	—	2	1	no	—
285	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
288	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
289	#131	—	52	4	no	—
290	C₂×M₁₆	—	13	1	no	—
291	C₂×M₁₆	—	13	1	no	—
292	C₂×M₁₆	—	26	2	no	—
293	C₂×M₁₆	—	26	2	no	—
294	C₂×M₁₆	—	26	1	no	—
295	C₂×M₁₆	—	52	4	no	—
296	C₂²×C₈	—	26	2	no	—
297	C₂²×C₈	—	26	2	no	—
298	C₂²×C₈	—	26	1	no	—
299	C₂²×C₈	—	26	1	no	—
300	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
301	#127	C₂×Dic₁₃	1	1	yes	characteristic
302	#124	—	2	1	no	—
303	#121	—	2	1	no	—
304	#121	C₂×Dic₁₃	1	2	yes	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
309	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
310	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
311	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
312	C₄×D₄	C₂²×D₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
316	#107	C₂×Dic₁₃	1	2	yes	—
317	#107	C₂×Dic₁₃	1	2	yes	—
318	C₄⋊C₈	—	13	1	no	—
319	C₄⋊C₈	—	13	1	no	—
320	C₄⋊C₈	—	13	2	no	—
321	C₄⋊C₈	—	26	1	no	—
322	C₄⋊C₈	—	26	1	no	—
323	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
324	C₄⋊C₈	C₂×Dic₁₃	1	1	yes	characteristic
325	#102	C₂×Dic₁₃	1	2	yes	—
326	#102	C₂×Dic₁₃	1	2	yes	—
327	#102	C₂×Dic₁₃	1	2	yes	—
328	#102	C₂×Dic₁₃	1	2	yes	—
329	C₂²⋊C₈	—	26	2	no	—
330	C₂²⋊C₈	—	26	2	no	—
331	C₂²⋊C₈	—	26	2	no	—
332	C₂²⋊C₈	—	26	2	no	—
333	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
334	#97	—	13	2	no	—
335	C₄×C₈	—	13	2	no	—
336	C₄×C₈	—	13	1	no	—
337	C₄×C₈	—	13	1	no	—
338	C₄×C₈	—	26	1	no	—
339	C₄×C₈	C₂²×D₁₃	1	2	yes	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	4	2	no	—
342	C₂×C₁₃	—	8	2	no	—
343	C₂×C₁₃	—	8	1	no	—
344	C₂×C₁₃	#2933	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
346	C₂×C₁₃	#2956	1	1	yes	characteristic
347	C₂⁴	—	2	1	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
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	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
369	C₂²×C₄	#6129	1	1	yes	characteristic
370	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
371	D₈	—	2	4	no	—
372	D₈	—	4	2	no	—
373	M₁₆	—	26	2	no	—
374	M₁₆	—	26	2	no	—
375	M₁₆	—	52	4	no	—
376	M₁₆	—	52	4	no	—
377	M₁₆	—	52	2	no	—
378	C₂×C₈	—	13	2	no	—
379	C₂×C₈	—	13	2	no	—
380	C₂×C₈	—	26	1	no	—
381	C₂×C₈	—	26	1	no	—
382	C₂×C₈	—	26	2	no	—
383	C₂×C₈	—	26	1	no	—
384	C₂×C₈	—	26	1	no	—
385	C₂×C₈	—	52	4	no	—
386	C₂×C₈	—	52	4	no	—
387	C₂×C₈	—	52	2	no	—
388	C₂×C₈	—	52	2	no	—
389	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
390	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
394	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₄²	D₄×D₁₃	1	1	yes	characteristic
403	C₄²	#6129	1	1	yes	characteristic
404	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
405	C₄²	C₂³×D₁₃	1	1	yes	characteristic
406	C₁₃	#18001	1	1	yes	characteristic, complemented, Sylow
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	8	1	no	—
413	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	1	no	—
417	D₄	—	2	1	no	—
418	D₄	—	2	1	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	8	1	no	—
424	D₄	#88202	1	2	yes	complemented
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	#88165	1	2	yes	—
441	C₂×C₄	#88165	1	2	yes	—
442	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
443	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂×#6129	1	1	yes	characteristic
447	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	26	2	no	—
451	C₈	—	26	2	no	—
452	C₈	—	26	2	no	—
453	C₈	—	52	1	no	—
454	C₈	—	52	1	no	—
455	C₈	—	52	2	no	—
456	C₈	—	52	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	8	4	no	—
469	C₂²	#11718813	1	2	yes	—
470	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	#11718813	1	2	yes	—
478	C₄	C₂×#88165	1	1	yes	characteristic
479	C₄	C₂×#88165	1	1	yes	characteristic
480	C₄	C₂×#88202	1	1	yes	characteristic
481	C₄	#11719524	1	1	yes	characteristic
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	8	1	no	—
485	C₂	—	8	2	no	—
486	C₂	#13123563	1	1	yes	characteristic
487	C₂	C₂×#11718813	1	1	yes	characteristic
488	C₂	#13123746	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×#3100	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3100	D₁₃
hypocenter	C₁₃	#18001
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. #13123580	C₂	semidirect
2. D₄×#6099	C₂	semidirect
3. #13113750	C₂	semidirect
4. #13113701	C₂	semidirect
5. #13113701	C₂	semidirect
6. #13113660	C₂	semidirect
7. #13113607	C₂	semidirect
8. #13113287	C₂	semidirect
9. C₂×D₄⋊#1055	C₂	semidirect
10. #13113126	C₂	semidirect
28. #11718673	C₂²	semidirect
32. D₄×#1055	C₂²	semidirect
41. D₄⋊#1055	C₂²	semidirect
42. D₄⋊#1055	C₂²	semidirect
43. #11718049	C₂²	semidirect
44. #11718049	C₂²	semidirect
45. #11718047	C₂²	semidirect
46. #11718046	C₂²	semidirect
191. D₄×C₁₃	#131	semidirect
406. C₁₃	#18001	semidirect
424. D₄	#88202	semidirect

Maximal subgroups

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

subgroup	index
#13123580	2
D₄×#6099	2
#13113750	2
#13113701	2
#13113660	2
#13113607	2
#13113287	2
C₂×D₄⋊#1055	2
#13113126	2
C₁₃×#3100	2
#18001	13