Subgroups — #15881155

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718349	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718522	C₂	1	2	yes	maximal, complemented
3	#13117783	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
5	#13115599	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115594	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115038	C₂	1	2	yes	maximal, complemented
8	#13115025	C₂	1	2	yes	maximal, complemented
9	#13114996	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114866	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#6094	C₂²	1	2	yes	—
13	C₂×#88146	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
15	C₂×C₄×D₅₂	—	2	1	no	—
16	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×#88060	C₂²	1	2	yes	—
23	C₂×#88058	C₂²	1	2	yes	—
24	C₂×#88058	C₂²	1	2	yes	—
25	#11718648	C₂²	1	2	yes	—
26	#11718648	C₂²	1	2	yes	—
27	C₂×#88048	C₂²	1	2	yes	—
28	C₂×#88047	C₂²	1	2	yes	—
29	#11718600	—	2	1	no	—
30	#11718596	C₂²	1	1	yes	characteristic
31	#11718596	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₁₃	—	2	1	no	—
33	#11718589	—	2	1	no	—
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	#11718522	—	2	8	no	—
36	#11718349	C₄	1	8	yes	complemented
37	#11718331	—	2	2	no	—
38	#11718329	—	2	2	no	—
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	#11718121	C₂²	1	2	yes	—
42	#11718121	C₂²	1	2	yes	—
43	C₂²×D₅₂	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	—	2	2	no	—
45	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	—	2	1	no	—
53	C₂×C₄²×C₁₃	—	2	1	no	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6103	—	2	2	no	—
56	C₂×#6103	—	2	2	no	—
57	C₂×#6103	—	2	2	no	—
58	C₂×#6103	D₄	1	2	yes	—
59	C₂×C₄⋊Dic₁₃	—	2	1	no	—
60	C₂×C₄⋊Dic₁₃	—	2	1	no	—
61	C₂×C₄⋊Dic₁₃	—	2	1	no	—
62	C₂×C₄⋊Dic₁₃	—	2	1	no	—
63	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
66	C₂×#6101	—	2	2	no	—
67	C₂×C₄×Dic₁₃	—	2	2	no	—
68	C₂²×#1055	C₂³	1	2	yes	—
69	C₂×#6094	—	2	4	no	—
70	C₂×#6094	—	2	4	no	—
71	C₂×#6094	C₂×C₄	1	8	yes	complemented
72	#88146	—	2	4	no	—
73	#88146	—	4	2	no	—
74	C₄⋊C₄×D₁₃	—	2	4	no	—
75	C₄⋊C₄×D₁₃	—	4	2	no	—
76	C₄×D₅₂	—	4	4	no	—
77	C₄×D₅₂	C₂×C₄	1	4	yes	—
78	C₄×D₅₂	Q₈	1	4	yes	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	D₄	1	4	yes	complemented
81	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	#88071	—	2	2	no	—
85	#88071	—	2	2	no	—
86	#88060	C₂×C₄	1	8	yes	complemented
87	#88058	—	2	4	no	—
88	#88058	—	4	2	no	—
89	#88048	—	2	4	no	—
90	#88047	—	2	4	no	—
91	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
92	#22665	—	13	1	no	maximal, Sylow
93	C₂³×D₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₁₃	—	2	2	no	—
102	C₂²×Dic₁₃	—	2	2	no	—
103	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
104	C₂×D₅₂	—	2	2	no	—
105	C₂×D₅₂	—	2	2	no	—
106	C₂×D₅₂	C₄⋊C₄	1	4	yes	—
107	C₂×C₄×D₁₃	—	2	2	no	—
108	C₂×C₄×D₁₃	—	2	2	no	—
109	C₂×C₄×D₁₃	—	2	2	no	—
110	C₂×C₄×D₁₃	—	2	2	no	—
111	C₂×C₄×D₁₃	—	4	4	no	—
112	C₂×C₄×D₁₃	—	4	4	no	—
113	C₂×C₄×D₁₃	—	8	2	no	—
114	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
115	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
130	C₄²×C₁₃	—	4	2	no	—
131	C₄²×C₁₃	—	4	2	no	—
132	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
134	#6103	—	4	4	no	—
135	#6103	—	4	4	no	—
136	#6103	—	8	2	no	—
137	#6103	C₄⋊C₄	1	8	yes	—
138	C₄⋊Dic₁₃	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	2	no	—
140	C₄⋊Dic₁₃	—	2	2	no	—
141	C₄⋊Dic₁₃	—	2	2	no	—
142	C₄⋊Dic₁₃	—	4	2	no	—
143	C₄⋊Dic₁₃	—	4	2	no	—
144	C₄⋊Dic₁₃	—	8	1	no	—
145	C₄⋊Dic₁₃	—	8	1	no	—
146	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	—
147	#6101	—	4	4	no	—
148	C₄×Dic₁₃	—	4	4	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	C₂²×C₄	1	4	yes	—
152	#6094	—	2	16	no	—
153	C₂×#436	—	13	1	no	—
154	C₂×#428	—	13	2	no	—
155	#2354	—	13	1	no	—
156	D₄×C₄⋊C₄	—	13	1	no	—
157	#1948	—	13	1	no	—
158	#1947	—	13	1	no	—
159	#1854	—	13	2	no	—
160	#1852	—	13	2	no	—
161	#1845	—	13	1	no	—
162	#1809	—	13	2	no	—
163	C₄×#106	D₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂²×D₁₃	—	2	2	no	—
166	C₂²×D₁₃	—	2	2	no	—
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	—	2	2	no	—
171	C₂²×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₃	#137	1	2	yes	—
190	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×Dic₁₃	—	2	2	no	—
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	—	4	2	no	—
199	C₂×Dic₁₃	—	4	2	no	—
200	C₂×Dic₁₃	—	4	2	no	—
201	C₂×Dic₁₃	—	4	2	no	—
202	C₂×Dic₁₃	—	4	2	no	—
203	C₂×Dic₁₃	—	4	2	no	—
204	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
205	D₅₂	—	2	8	no	—
206	C₄×D₁₃	—	2	4	no	—
207	C₄×D₁₃	—	2	4	no	—
208	C₄×D₁₃	—	2	4	no	—
209	C₄×D₁₃	—	2	4	no	—
210	C₄×D₁₃	—	8	8	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	C₄×D₄	1	4	yes	complemented
213	#1055	—	2	4	no	—
214	C₂²×M₁₆	—	13	2	no	—
215	C₂×C₄×D₄	—	13	1	no	—
216	C₂×C₄×D₄	—	26	1	no	—
217	C₂×#117	—	13	2	no	—
218	C₂²×C₄⋊C₄	—	13	2	no	—
219	#436	—	13	8	no	—
220	#428	—	26	8	no	—
221	C₂×#107	—	13	2	no	—
222	C₂×#107	—	13	2	no	—
223	C₂×#107	—	13	2	no	—
224	C₂×#106	—	13	2	no	—
225	C₂×#106	C₂×D₁₃	1	1	yes	characteristic
226	C₂×#106	C₂×D₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	13	1	no	—
228	C₂×C₂²⋊C₈	—	13	2	no	—
229	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
230	#390	—	26	1	no	—
231	#389	—	26	1	no	—
232	#388	—	26	2	no	—
233	#385	—	26	2	no	—
234	#384	—	13	1	no	—
235	#384	—	13	1	no	—
236	#380	—	13	2	no	—
237	#380	—	13	2	no	—
238	C₄×C₄⋊C₄	—	26	1	no	—
239	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
241	#340	—	13	2	no	—
242	#340	—	13	2	no	—
243	#340	C₂×D₁₃	1	1	yes	characteristic
244	#340	C₂×D₁₃	1	1	yes	characteristic
245	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
246	C₂²×C₁₃	D₄²	1	1	yes	characteristic
247	C₂²×C₁₃	#547	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
250	C₂²×C₁₃	#576	1	1	yes	characteristic
251	C₂²×C₁₃	#578	1	1	yes	characteristic
252	C₂×D₁₃	—	2	4	no	—
253	C₂×D₁₃	—	2	4	no	—
254	C₂×D₁₃	—	2	4	no	—
255	C₂×D₁₃	—	4	2	no	—
256	C₂×D₁₃	—	4	2	no	—
257	C₂×D₁₃	—	4	2	no	—
258	C₂×D₁₃	—	4	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	#428	1	4	yes	complemented
265	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
266	C₄×C₁₃	#520	1	1	yes	characteristic
267	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
268	C₄×C₁₃	#554	1	1	yes	characteristic
269	Dic₁₃	—	2	4	no	—
270	Dic₁₃	—	8	2	no	—
271	Dic₁₃	—	8	2	no	—
272	C₂²×D₄	—	13	1	no	—
273	C₂³×C₄	—	13	2	no	—
274	C₂³×C₄	—	26	2	no	—
275	C₂×M₁₆	—	13	8	no	—
276	C₂×M₁₆	—	26	4	no	—
277	C₂×M₁₆	—	26	4	no	—
278	C₂²×C₈	—	13	2	no	—
279	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
281	C₄×D₄	—	13	4	no	—
282	C₄×D₄	—	13	4	no	—
283	C₄×D₄	—	52	4	no	—
284	#117	—	26	4	no	—
285	#117	—	52	2	no	—
286	C₂×C₄⋊C₄	—	13	1	no	—
287	C₂×C₄⋊C₄	—	13	2	no	—
288	C₂×C₄⋊C₄	—	13	2	no	—
289	C₂×C₄⋊C₄	—	26	4	no	—
290	C₂×C₄⋊C₄	—	26	2	no	—
291	C₂×C₄⋊C₄	—	26	1	no	—
292	C₂×C₄⋊C₄	—	26	1	no	—
293	C₂×C₄⋊C₄	—	26	1	no	—
294	C₂×C₄⋊C₄	—	26	1	no	—
295	C₂×C₄⋊C₄	—	52	2	no	—
296	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	13	2	no	—
301	C₂×C₂²⋊C₄	—	26	2	no	—
302	C₂×C₂²⋊C₄	—	26	2	no	—
303	C₂×C₂²⋊C₄	—	26	2	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	26	2	no	—
307	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
308	#107	—	26	4	no	—
309	#107	—	26	4	no	—
310	#107	—	52	2	no	—
311	#106	—	2	2	no	—
312	#106	—	26	4	no	—
313	#106	D₅₂	1	4	yes	complemented
314	C₄⋊C₈	—	13	4	no	—
315	C₂²⋊C₈	—	13	8	no	—
316	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	26	2	no	—
320	#95	—	26	2	no	—
321	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
323	C₂×C₁₃	#2913	1	1	yes	characteristic
324	C₂×C₁₃	#3274	1	1	yes	characteristic
325	C₂×C₁₃	#3276	1	1	yes	characteristic
326	C₂×C₁₃	#3353	1	1	yes	characteristic
327	C₂×C₁₃	#3357	1	1	yes	characteristic
328	D₁₃	—	4	4	no	—
329	C₂⁴	—	13	2	no	—
330	C₂×D₄	—	13	4	no	—
331	C₂×D₄	—	26	2	no	—
332	C₂×D₄	—	26	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	13	2	no	—
338	C₂²×C₄	—	13	4	no	—
339	C₂²×C₄	—	13	4	no	—
340	C₂²×C₄	—	26	2	no	—
341	C₂²×C₄	—	26	2	no	—
342	C₂²×C₄	—	26	2	no	—
343	C₂²×C₄	—	26	2	no	—
344	C₂²×C₄	—	26	2	no	—
345	C₂²×C₄	—	26	2	no	—
346	C₂²×C₄	—	52	4	no	—
347	C₂²×C₄	—	52	4	no	—
348	C₂²×C₄	—	104	2	no	—
349	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
352	M₁₆	—	26	16	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	13	4	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
359	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
360	C₂×C₈	C₂×D₅₂	1	2	yes	—
361	C₂×C₈	#6127	1	2	yes	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	13	4	no	—
369	C₄⋊C₄	—	26	2	no	—
370	C₄⋊C₄	—	26	2	no	—
371	C₄⋊C₄	—	26	2	no	—
372	C₄⋊C₄	—	26	2	no	—
373	C₄⋊C₄	—	52	4	no	—
374	C₄⋊C₄	—	52	2	no	—
375	C₄⋊C₄	—	52	2	no	—
376	C₄⋊C₄	—	104	1	no	—
377	C₄⋊C₄	—	104	1	no	—
378	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
379	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
380	C₂²⋊C₄	—	13	8	no	—
381	C₂²⋊C₄	—	52	4	no	—
382	C₂²⋊C₄	—	52	4	no	—
383	C₂²⋊C₄	—	104	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	52	4	no	—
387	C₄²	C₂×C₄×D₁₃	1	2	yes	—
388	C₄²	Q₈×D₁₃	1	2	yes	—
389	C₁₃	#22665	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	13	4	no	—
391	C₂³	—	26	2	no	—
392	C₂³	—	26	2	no	—
393	C₂³	—	26	2	no	—
394	C₂³	—	26	2	no	—
395	C₂³	—	26	2	no	—
396	C₂³	—	26	2	no	—
397	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
398	D₄	—	26	8	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	13	4	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	26	4	no	—
417	C₂×C₄	—	26	4	no	—
418	C₂×C₄	—	26	4	no	—
419	C₂×C₄	—	26	4	no	—
420	C₂×C₄	—	52	2	no	—
421	C₂×C₄	—	52	2	no	—
422	C₂×C₄	—	52	2	no	—
423	C₂×C₄	—	52	2	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	104	8	no	—
427	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
428	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
429	C₂×C₄	#88168	1	2	yes	—
430	C₂×C₄	#88169	1	2	yes	—
431	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
433	C₂×C₄	C₂×#6127	1	1	yes	characteristic
434	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
435	C₂×C₄	#88256	1	1	yes	characteristic
436	C₂×C₄	#88257	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	26	4	no	—
439	C₈	C₄×D₅₂	1	4	yes	complemented
440	C₂²	—	26	4	no	—
441	C₂²	—	26	4	no	—
442	C₂²	—	26	4	no	—
443	C₂²	—	52	2	no	—
444	C₂²	—	52	2	no	—
445	C₂²	—	52	2	no	—
446	C₂²	—	52	2	no	—
447	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
448	C₂²	D₄×D₅₂	1	1	yes	characteristic
449	C₂²	#11719256	1	1	yes	characteristic
450	C₂²	C₂×#88168	1	1	yes	characteristic
451	C₂²	C₂×#88169	1	1	yes	characteristic
452	C₂²	#11719474	1	1	yes	characteristic
453	C₂²	#11719476	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	26	4	no	—
460	C₄	—	104	2	no	—
461	C₄	—	104	2	no	—
462	C₄	#11718522	1	4	yes	complemented
463	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
464	C₄	#11719228	1	1	yes	characteristic
465	C₄	Q₈×D₅₂	1	1	yes	characteristic
466	C₄	#11719284	1	1	yes	characteristic
467	C₂	—	52	4	no	—
468	C₂	C₄⋊C₄×D₅₂	1	1	yes	characteristic
469	C₂	C₂×#11718522	1	1	yes	characteristic
470	C₂	#13123433	1	1	yes	characteristic
471	C₂	#13126457	1	1	yes	characteristic
472	C₂	#13126483	1	1	yes	characteristic
473	C₂	#13127422	1	1	yes	characteristic
474	C₂	#13127464	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₄×C₁₃×#106	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₅₂	D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#106	D₁₃
hypocenter	C₁₃	#22665
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#106

Complements

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

N	H ≅ G/N	type
2. C₂×#11718522	C₂	semidirect
5. #13115599	C₂	semidirect
6. #13115594	C₂	semidirect
7. #13115038	C₂	semidirect
8. #13115025	C₂	semidirect
9. #13114996	C₂	semidirect
10. #13114866	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
36. #11718349	C₄	semidirect
71. C₂×#6094	C₂×C₄	semidirect
80. C₁₃×#106	D₄	semidirect
81. C₄×C₈×C₁₃	C₂×C₄	semidirect
86. #88060	C₂×C₄	semidirect
91. C₄⋊#1055	C₂×C₄	semidirect
163. C₄×#106	D₁₃	semidirect
212. C₈×C₁₃	C₄×D₄	semidirect
264. C₄×C₁₃	#428	semidirect
313. #106	D₅₂	semidirect
316. C₄×C₈	C₄×D₁₃	semidirect
389. C₁₃	#22665	semidirect
439. C₈	C₄×D₅₂	semidirect
462. C₄	#11718522	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718349	2
C₂×#11718522	2
#13117783	2
C₄⋊C₄×D₅₂	2
#13115599	2
#13115594	2
#13115038	2
#13115025	2
#13114996	2
#13114866	2
C₄×C₁₃×#106	2
#22665	13