Subgroups — #15885177

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718688	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718449	C₂	1	2	yes	maximal, complemented
3	#13117900	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115642	C₂	1	1	yes	maximal, characteristic
6	#13115599	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115520	C₂	1	2	yes	maximal, complemented
8	#13115189	C₂	1	2	yes	maximal, complemented
9	#13115098	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	—
14	C₂²×#6106	C₂²	1	2	yes	—
15	C₂×#88147	C₂²	1	2	yes	—
16	C₂×#88128	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅₂	—	2	1	no	—
18	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×#88061	C₂²	1	2	yes	—
23	C₂×#88061	C₂²	1	2	yes	—
24	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
25	#11718688	C₄	1	8	yes	complemented
26	#11718649	C₂²	1	2	yes	—
27	#11718646	—	2	2	no	—
28	#11718646	C₂²	1	2	yes	—
29	C₂×#88049	C₂²	1	2	yes	—
30	C₂×#88048	C₂²	1	2	yes	—
31	#11718600	—	2	1	no	—
32	#11718596	—	2	1	no	—
33	#11718596	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊Dic₁₃	—	2	1	no	—
35	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	#11718449	—	2	8	no	—
38	#11718326	—	2	2	no	—
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	#11718142	C₂²	1	2	yes	—
42	#11718121	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₅₂	—	2	1	no	—
45	C₂²×D₅₂	—	2	1	no	—
46	C₂²×D₅₂	C₂³	1	2	yes	—
47	C₂²×C₄×D₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	—	2	1	no	—
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	Q₈×Dic₁₃	—	2	4	no	—
60	Q₈×Dic₁₃	—	4	2	no	—
61	C₂×#6106	—	2	4	no	—
62	C₂×#6106	—	2	4	no	—
63	C₂×#6106	C₂×C₄	1	8	yes	complemented
64	C₂×#6103	—	2	2	no	—
65	C₂×#6103	—	2	2	no	—
66	C₂×#6103	—	2	2	no	—
67	C₂×C₄⋊Dic₁₃	—	2	1	no	—
68	C₂×C₄⋊Dic₁₃	—	2	2	no	—
69	C₂×C₄⋊Dic₁₃	—	2	1	no	—
70	C₂×C₄⋊Dic₁₃	—	2	2	no	—
71	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
74	C₂×C₄×Dic₁₃	—	2	2	no	—
75	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
76	C₂²×#1055	C₂³	1	2	yes	—
77	#88147	—	2	4	no	—
78	#88147	—	4	2	no	—
79	#88128	—	2	2	no	—
80	#88128	C₂×C₄	1	4	yes	—
81	C₄×D₅₂	—	4	4	no	—
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#103	D₄	1	4	yes	complemented
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	#88071	—	2	2	no	—
87	#88071	D₄	1	2	yes	—
88	#88061	—	2	4	no	—
89	#88061	—	4	2	no	—
90	C₈×Dic₁₃	—	2	4	no	—
91	#88049	C₂×C₄	1	8	yes	complemented
92	#88048	—	2	4	no	—
93	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
94	#22997	—	13	1	no	maximal, Sylow
95	C₂³×D₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₁₃	—	2	2	no	—
110	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
111	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	2	2	no	—
114	C₂×D₅₂	—	2	2	no	—
115	C₂×D₅₂	—	2	2	no	—
116	C₂×D₅₂	—	2	4	no	—
117	C₂×D₅₂	—	2	2	no	—
118	C₂×D₅₂	—	2	4	no	—
119	C₂×D₅₂	—	4	2	no	—
120	C₂×D₅₂	—	4	2	no	—
121	C₂×D₅₂	—	8	1	no	—
122	C₂×D₅₂	—	8	1	no	—
123	C₂×D₅₂	C₂²×C₄	1	4	yes	—
124	C₂×C₄×D₁₃	—	4	4	no	—
125	C₂×C₄×D₁₃	—	4	4	no	—
126	C₂×C₄×D₁₃	—	8	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
143	C₄²×C₁₃	#41	1	2	yes	—
144	#6106	—	2	16	no	—
145	#6103	—	4	4	no	—
146	#6103	—	4	4	no	—
147	#6103	—	8	2	no	—
148	C₄⋊Dic₁₃	—	2	2	no	—
149	C₄⋊Dic₁₃	—	2	2	no	—
150	C₄⋊Dic₁₃	—	2	2	no	—
151	C₄⋊Dic₁₃	—	4	4	no	—
152	C₄⋊Dic₁₃	—	4	2	no	—
153	C₄⋊Dic₁₃	—	8	2	no	—
154	C₄⋊Dic₁₃	—	8	1	no	—
155	C₄⋊Dic₁₃	SD₁₆	1	4	yes	complemented
156	C₄×Dic₁₃	—	2	2	no	—
157	C₄×Dic₁₃	—	2	2	no	—
158	C₄×Dic₁₃	—	4	4	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	C₂²×C₄	1	4	yes	—
162	C₂×#460	—	13	1	no	—
163	C₂×C₄×SD₁₆	—	13	2	no	—
164	#2366	—	13	1	no	—
165	Q₈×C₄⋊C₄	—	13	1	no	—
166	#1957	—	13	1	no	—
167	#1948	—	13	1	no	—
168	#1934	—	13	2	no	—
169	#1880	—	13	2	no	—
170	#1864	—	13	2	no	—
171	C₈×C₄⋊C₄	—	13	1	no	—
172	C₄×#103	D₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂²×D₁₃	—	2	4	no	—
175	C₂²×D₁₃	—	4	2	no	—
176	C₂²×D₁₃	—	4	2	no	—
177	C₂²×D₁₃	—	4	2	no	—
178	C₂²×D₁₃	—	4	2	no	—
179	C₂²×D₁₃	—	4	2	no	—
180	C₂²×D₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	2	2	no	—
184	Q₈×C₁₃	C₄×D₄	1	4	yes	complemented
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₁₃	#135	1	2	yes	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×Dic₁₃	—	2	2	no	—
210	C₂×Dic₁₃	—	2	2	no	—
211	C₂×Dic₁₃	—	2	2	no	—
212	C₂×Dic₁₃	—	2	2	no	—
213	C₂×Dic₁₃	—	2	2	no	—
214	C₂×Dic₁₃	—	4	2	no	—
215	C₂×Dic₁₃	—	4	2	no	—
216	C₂×Dic₁₃	—	4	2	no	—
217	C₂×Dic₁₃	C₂×SD₁₆	1	4	yes	—
218	D₅₂	—	2	4	no	—
219	D₅₂	—	2	4	no	—
220	D₅₂	—	4	2	no	—
221	D₅₂	—	4	2	no	—
222	D₅₂	—	4	8	no	—
223	D₅₂	—	8	4	no	—
224	C₄×D₁₃	—	8	8	no	—
225	C₈×C₁₃	—	2	2	no	—
226	C₈×C₁₃	—	4	1	no	—
227	#1055	—	2	4	no	—
228	C₂²×SD₁₆	—	13	2	no	—
229	C₂×#127	—	13	1	no	—
230	C₂×C₄×Q₈	—	13	2	no	—
231	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	13	2	no	—
233	C₂×C₄×D₄	—	26	1	no	—
234	#460	—	13	8	no	—
235	C₄×SD₁₆	—	26	8	no	—
236	C₂×#106	—	13	2	no	—
237	C₂×C₄⋊C₈	—	13	1	no	—
238	C₂×#103	C₂×D₁₃	1	1	yes	characteristic
239	C₂×#103	C₂×D₁₃	1	1	yes	characteristic
240	C₂×#102	—	13	2	no	—
241	C₂×#102	—	13	2	no	—
242	C₂×#102	—	13	2	no	—
243	C₂×C₄×C₈	—	13	2	no	—
244	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
245	#390	—	13	2	no	—
246	#390	—	26	1	no	—
247	#389	—	13	2	no	—
248	#389	—	26	2	no	—
249	#386	—	26	2	no	—
250	#384	—	13	1	no	—
251	#384	—	26	1	no	—
252	C₄×C₄⋊C₄	—	13	1	no	—
253	C₄×C₄⋊C₄	—	26	1	no	—
254	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
255	#340	—	13	2	no	—
256	#340	C₂×D₁₃	1	1	yes	characteristic
257	#340	C₂×D₁₃	1	1	yes	characteristic
258	#336	—	13	2	no	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂²×C₁₃	D₄²	1	1	yes	characteristic
261	C₂²×C₁₃	#548	1	1	yes	characteristic
262	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
264	C₂²×C₁₃	#576	1	1	yes	characteristic
265	C₂²×C₁₃	#577	1	1	yes	characteristic
266	C₂×D₁₃	—	4	4	no	—
267	C₂×D₁₃	—	4	4	no	—
268	C₂×D₁₃	—	4	4	no	—
269	C₂×D₁₃	—	8	2	no	—
270	C₂×D₁₃	—	8	2	no	—
271	C₂×D₁₃	—	8	2	no	—
272	C₂×D₁₃	—	8	2	no	—
273	C₄×C₁₃	—	2	4	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	C₄×SD₁₆	1	4	yes	complemented
279	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₁₃	#520	1	1	yes	characteristic
281	C₄×C₁₃	#547	1	1	yes	characteristic
282	C₄×C₁₃	#553	1	1	yes	characteristic
283	Dic₁₃	—	2	4	no	—
284	Dic₁₃	—	4	2	no	—
285	Dic₁₃	—	8	2	no	—
286	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
287	C₂²×D₄	—	13	2	no	—
288	C₂²×D₄	—	26	1	no	—
289	C₂²×D₄	—	26	1	no	—
290	C₂³×C₄	—	26	2	no	—
291	C₂×SD₁₆	—	13	8	no	—
292	C₂×SD₁₆	—	26	4	no	—
293	C₂×SD₁₆	—	26	4	no	—
294	C₂²×C₈	—	13	2	no	—
295	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
297	#127	—	13	4	no	—
298	#127	—	26	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	26	4	no	—
301	C₄×Q₈	—	52	2	no	—
302	C₄×Q₈	C₄×D₁₃	1	4	yes	complemented
303	C₄×D₄	—	26	4	no	—
304	C₄×D₄	—	52	4	no	—
305	C₄×D₄	—	52	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	13	1	no	—
308	C₂×C₄⋊C₄	—	13	1	no	—
309	C₂×C₄⋊C₄	—	13	2	no	—
310	C₂×C₄⋊C₄	—	26	2	no	—
311	C₂×C₄⋊C₄	—	26	1	no	—
312	C₂×C₄⋊C₄	—	26	2	no	—
313	C₂×C₄⋊C₄	—	26	1	no	—
314	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	26	2	no	—
318	C₂×C₂²⋊C₄	—	26	2	no	—
319	C₂×C₂²⋊C₄	—	26	2	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	13	2	no	—
323	C₂×C₄²	—	26	2	no	—
324	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
325	#106	—	26	4	no	—
326	C₄⋊C₈	—	13	4	no	—
327	#103	—	2	2	no	—
328	#103	D₅₂	1	4	yes	complemented
329	#102	—	13	8	no	—
330	#102	—	26	4	no	—
331	#102	—	52	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	26	4	no	—
334	#95	—	2	1	no	—
335	#95	—	13	2	no	—
336	#95	—	26	2	no	—
337	C₂×C₁₃	#2361	1	1	yes	characteristic
338	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
339	C₂×C₁₃	#2946	1	1	yes	characteristic
340	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
341	C₂×C₁₃	#3287	1	1	yes	characteristic
342	C₂×C₁₃	#3362	1	1	yes	characteristic
343	C₂×C₁₃	#3365	1	1	yes	characteristic
344	D₁₃	—	8	4	no	—
345	C₂⁴	—	26	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
350	C₂×Q₈	C₂×D₅₂	1	2	yes	—
351	C₂×Q₈	#6127	1	2	yes	—
352	C₂×D₄	—	13	4	no	—
353	C₂×D₄	—	26	4	no	—
354	C₂×D₄	—	26	4	no	—
355	C₂×D₄	—	26	2	no	—
356	C₂×D₄	—	26	2	no	—
357	C₂×D₄	—	26	2	no	—
358	C₂×D₄	—	26	2	no	—
359	C₂×D₄	—	26	2	no	—
360	C₂×D₄	—	52	2	no	—
361	C₂×D₄	—	52	2	no	—
362	C₂×D₄	—	104	1	no	—
363	C₂×D₄	—	104	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	13	2	no	—
369	C₂²×C₄	—	13	2	no	—
370	C₂²×C₄	—	26	2	no	—
371	C₂²×C₄	—	52	4	no	—
372	C₂²×C₄	—	52	4	no	—
373	C₂²×C₄	—	104	2	no	—
374	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
377	SD₁₆	—	26	16	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	13	4	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	C₂×D₅₂	1	2	yes	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	13	4	no	—
393	C₄⋊C₄	—	26	2	no	—
394	C₄⋊C₄	—	26	2	no	—
395	C₄⋊C₄	—	26	2	no	—
396	C₄⋊C₄	—	52	4	no	—
397	C₄⋊C₄	—	52	2	no	—
398	C₄⋊C₄	—	104	1	no	—
399	C₄⋊C₄	—	104	2	no	—
400	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
401	C₄⋊C₄	C₂×D₅₂	1	2	yes	—
402	C₂²⋊C₄	—	52	4	no	—
403	C₂²⋊C₄	—	52	4	no	—
404	C₂²⋊C₄	—	104	2	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	26	2	no	—
408	C₄²	—	26	2	no	—
409	C₄²	—	52	4	no	—
410	C₄²	C₂×C₄×D₁₃	1	2	yes	—
411	C₄²	#6129	1	2	yes	—
412	C₁₃	#22997	1	1	yes	characteristic, complemented, Sylow
413	C₂³	—	26	4	no	—
414	C₂³	—	52	2	no	—
415	C₂³	—	52	2	no	—
416	C₂³	—	52	2	no	—
417	C₂³	—	52	2	no	—
418	C₂³	—	52	2	no	—
419	C₂³	—	52	2	no	—
420	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	C₄×D₅₂	1	4	yes	complemented
425	D₄	—	26	4	no	—
426	D₄	—	26	4	no	—
427	D₄	—	52	8	no	—
428	D₄	—	52	2	no	—
429	D₄	—	52	2	no	—
430	D₄	—	104	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	13	4	no	—
446	C₂×C₄	—	26	2	no	—
447	C₂×C₄	—	26	2	no	—
448	C₂×C₄	—	26	2	no	—
449	C₂×C₄	—	26	2	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	52	2	no	—
452	C₂×C₄	—	52	2	no	—
453	C₂×C₄	—	52	2	no	—
454	C₂×C₄	—	104	8	no	—
455	C₂×C₄	#88135	1	2	yes	—
456	C₂×C₄	#88135	1	2	yes	—
457	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
458	C₂×C₄	#88173	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
461	C₂×C₄	C₂×#6127	1	1	yes	characteristic
462	C₂×C₄	C₂×#6129	1	1	yes	characteristic
463	C₂×C₄	#88256	1	1	yes	characteristic
464	C₂×C₄	#88257	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	26	4	no	—
468	C₂²	—	52	4	no	—
469	C₂²	—	52	4	no	—
470	C₂²	—	52	4	no	—
471	C₂²	—	104	2	no	—
472	C₂²	—	104	2	no	—
473	C₂²	—	104	2	no	—
474	C₂²	—	104	2	no	—
475	C₂²	C₂×#88135	1	1	yes	characteristic
476	C₂²	D₄×D₅₂	1	1	yes	characteristic
477	C₂²	#11719257	1	1	yes	characteristic
478	C₂²	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
479	C₂²	C₂×#88173	1	1	yes	characteristic
480	C₂²	#11719474	1	1	yes	characteristic
481	C₂²	#11719475	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	26	4	no	—
488	C₄	—	52	2	no	—
489	C₄	—	104	2	no	—
490	C₄	#11718449	1	4	yes	complemented
491	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
492	C₄	#11719228	1	1	yes	characteristic
493	C₄	#11719260	1	1	yes	characteristic
494	C₄	#11719270	1	1	yes	characteristic
495	C₂	—	104	4	no	—
496	C₂	#13117850	1	1	yes	characteristic
497	C₂	C₂×#11718449	1	1	yes	characteristic
498	C₂	#13123671	1	1	yes	characteristic
499	C₂	SD₁₆×D₅₂	1	1	yes	characteristic
500	C₂	#13126595	1	1	yes	characteristic
501	C₂	#13127505	1	1	yes	characteristic
502	C₂	#13127530	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×#103	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂×#88128	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#103	D₁₃
hypocenter	C₁₃	#22997
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
2. C₂×#11718449	C₂	semidirect
4. Q₈×C₄⋊Dic₁₃	C₂	semidirect
6. #13115599	C₂	semidirect
7. #13115520	C₂	semidirect
8. #13115189	C₂	semidirect
9. #13115098	C₂	semidirect
10. C₈×C₄⋊Dic₁₃	C₂	semidirect
11. C₄×C₁₃×#103	C₂	semidirect
25. #11718688	C₄	semidirect
51. C₄×Q₈×C₁₃	C₂×C₄	semidirect
63. C₂×#6106	C₂×C₄	semidirect
83. C₁₃×#103	D₄	semidirect
91. #88049	C₂×C₄	semidirect
93. C₄⋊#1055	C₂×C₄	semidirect
155. C₄⋊Dic₁₃	SD₁₆	semidirect
172. C₄×#103	D₁₃	semidirect
184. Q₈×C₁₃	C₄×D₄	semidirect
278. C₄×C₁₃	C₄×SD₁₆	semidirect
302. C₄×Q₈	C₄×D₁₃	semidirect
328. #103	D₅₂	semidirect
412. C₁₃	#22997	semidirect
424. Q₈	C₄×D₅₂	semidirect
490. C₄	#11718449	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718688	2
C₂×#11718449	2
#13117900	2
Q₈×C₄⋊Dic₁₃	2
#13115642	2
#13115599	2
#13115520	2
#13115189	2
#13115098	2
C₈×C₄⋊Dic₁₃	2
C₄×C₁₃×#103	2
#22997	13