Subgroups — #15881729

Order 3328.

832 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×#11718489	C₂	1	2	yes	maximal
2	C₄²×Dic₂₆	C₂	1	1	yes	maximal, characteristic
3	#13115557	C₂	1	2	yes	maximal
4	#13115556	C₂	1	2	yes	maximal
5	#13115551	C₂	1	2	yes	maximal
6	#13114987	C₂	1	1	yes	maximal, characteristic
7	#13114987	C₂	1	1	yes	maximal, characteristic
8	#13114691	C₂	1	1	yes	maximal, characteristic
9	#13114689	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₄³×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88055	C₂²	1	2	yes	—
21	C₂×#88054	C₂²	1	2	yes	—
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×#88054	C₂²	1	2	yes	—
24	C₂×#88054	C₂²	1	2	yes	—
25	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
27	C₄×C₄⋊Dic₁₃	C₄	1	1	yes	characteristic
28	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
29	C₄×#6101	C₄	1	1	yes	characteristic
30	C₄×#6101	C₄	1	1	yes	characteristic
31	C₄×#6101	C₄	1	1	yes	characteristic
32	C₄×#6101	C₄	1	1	yes	characteristic
33	C₄×#6101	C₂²	1	1	yes	characteristic
34	C₄×#6101	C₂²	1	1	yes	characteristic
35	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
36	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
39	C₂×#88043	C₂²	1	2	yes	—
40	#11718489	—	2	8	no	—
41	#11718142	C₂²	1	2	yes	—
42	#11718142	C₂²	1	2	yes	—
43	#11718116	C₂²	1	2	yes	—
44	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×#6101	C₂×C₄	1	1	yes	characteristic
58	C₂×#6101	C₂×C₄	1	1	yes	characteristic
59	C₂×#6101	C₂×C₄	1	1	yes	characteristic
60	C₂×#6101	C₂×C₄	1	1	yes	characteristic
61	C₂×#6101	C₂×C₄	1	1	yes	characteristic
62	C₂×#6101	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₂²×#1055	C₂³	1	2	yes	—
77	C₄×Dic₂₆	—	2	4	no	—
78	C₄×Dic₂₆	—	2	4	no	—
79	C₄×Dic₂₆	D₄	1	4	yes	—
80	C₄×Dic₂₆	Q₈	1	4	yes	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×C₄⋊C₈	—	4	2	no	—
85	#88071	C₂×C₄	1	1	yes	characteristic
86	#88071	C₂×C₄	1	1	yes	characteristic
87	#88071	C₂×C₄	1	1	yes	characteristic
88	#88071	C₂×C₄	1	1	yes	characteristic
89	#88071	C₂×C₄	1	1	yes	characteristic
90	#88071	C₂×C₄	1	1	yes	characteristic
91	#88055	—	2	4	no	—
92	#88054	—	2	4	no	—
93	#88054	—	2	4	no	—
94	#88054	—	4	2	no	—
95	#88054	—	4	2	no	—
96	C₈×Dic₁₃	—	2	4	no	—
97	C₄⋊#1055	—	2	2	no	—
98	C₄⋊#1055	Q₈	1	4	yes	complemented
99	#88043	—	2	4	no	—
100	#22722	—	13	1	no	maximal, Sylow
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×Dic₂₆	—	2	2	no	—
117	C₂×Dic₂₆	—	2	2	no	—
118	C₂×Dic₂₆	C₄⋊C₄	1	4	yes	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	4	1	no	—
131	C₄²×C₁₃	C₂×D₄	1	2	yes	—
132	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
133	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
134	C₄²×C₁₃	#41	1	2	yes	—
135	C₄⋊Dic₁₃	—	2	2	no	—
136	C₄⋊Dic₁₃	—	2	2	no	—
137	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	—
138	#6101	—	2	2	no	—
139	#6101	—	2	2	no	—
140	#6101	—	2	2	no	—
141	#6101	C₄⋊C₄	1	4	yes	—
142	#6101	C₄⋊C₄	1	4	yes	—
143	#6101	M₁₆	1	4	yes	—
144	C₄×Dic₁₃	—	2	2	no	—
145	C₄×Dic₁₃	—	2	2	no	—
146	C₄×Dic₁₃	—	2	2	no	—
147	C₄×Dic₁₃	—	2	1	no	—
148	C₄×Dic₁₃	—	2	1	no	—
149	C₄×Dic₁₃	—	2	1	no	—
150	C₄×Dic₁₃	—	2	1	no	—
151	C₄×Dic₁₃	—	2	2	no	—
152	C₄×Dic₁₃	—	2	2	no	—
153	C₄×Dic₁₃	—	4	1	no	—
154	C₄×Dic₁₃	—	4	1	no	—
155	C₄×Dic₁₃	M₁₆	1	4	yes	—
156	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
157	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
158	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
159	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	—	2	2	no	—
163	C₂×#1055	—	2	2	no	—
164	C₂×#1055	—	2	2	no	—
165	C₂×#1055	C₂×Q₈	1	4	yes	—
166	C₂×#446	—	13	2	no	—
167	C₄²×Q₈	—	13	1	no	—
168	#1940	—	13	2	no	—
169	#1940	—	13	2	no	—
170	#1939	—	13	2	no	—
171	#1842	—	13	1	no	—
172	#1842	—	13	1	no	—
173	#1842	D₁₃	1	1	yes	characteristic
174	#1767	—	13	1	no	—
175	#1767	—	13	1	no	—
176	C₄×C₄⋊C₈	—	13	1	no	—
177	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	#131	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×Dic₁₃	—	2	1	no	—
203	C₂×Dic₁₃	—	2	1	no	—
204	C₂×Dic₁₃	—	2	1	no	—
205	C₂×Dic₁₃	—	2	1	no	—
206	C₂×Dic₁₃	—	2	1	no	—
207	C₂×Dic₁₃	—	2	1	no	—
208	C₂×Dic₁₃	—	2	1	no	—
209	C₂×Dic₁₃	—	2	1	no	—
210	C₂×Dic₁₃	—	2	1	no	—
211	C₂×Dic₁₃	—	2	1	no	—
212	C₂×Dic₁₃	—	2	1	no	—
213	C₂×Dic₁₃	—	2	1	no	—
214	C₂×Dic₁₃	—	2	1	no	—
215	C₂×Dic₁₃	—	2	1	no	—
216	C₂×Dic₁₃	—	2	1	no	—
217	C₂×Dic₁₃	—	2	1	no	—
218	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
220	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
221	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
222	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
223	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
224	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
225	C₂×Dic₁₃	C₂×M₁₆	1	2	yes	—
226	Dic₂₆	—	2	8	no	—
227	C₈×C₁₃	—	4	2	no	—
228	C₈×C₁₃	—	4	2	no	—
229	#1055	—	2	4	no	—
230	#1055	—	4	2	no	—
231	C₂×C₄×Q₈	—	13	1	no	—
232	C₂×C₄×Q₈	—	13	1	no	—
233	C₂×C₄×Q₈	—	13	1	no	—
234	#446	—	26	8	no	—
235	C₂×C₄⋊C₈	—	13	1	no	—
236	C₂×C₄⋊C₈	—	13	2	no	—
237	C₂×C₄⋊C₈	—	13	2	no	—
238	C₂×C₄⋊C₈	—	13	1	no	—
239	C₂×C₄⋊C₈	—	13	2	no	—
240	C₂×C₄⋊C₈	—	13	2	no	—
241	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
245	C₂×#97	—	13	2	no	—
246	C₂×#97	—	13	2	no	—
247	C₂×C₄×C₈	—	13	2	no	—
248	C₄×C₄⋊C₄	—	13	1	no	—
249	C₄×C₄⋊C₄	—	13	1	no	—
250	C₄×C₄⋊C₄	—	13	1	no	—
251	C₄×C₄⋊C₄	—	13	1	no	—
252	C₄×C₄⋊C₄	—	13	1	no	—
253	C₄×C₄⋊C₄	—	13	1	no	—
254	C₄×C₄⋊C₄	—	13	1	no	—
255	C₄×C₄⋊C₄	—	13	1	no	—
256	C₄×C₄⋊C₄	—	13	1	no	—
257	C₄³	—	13	1	no	—
258	C₄³	—	13	1	no	—
259	C₄³	C₂×D₁₃	1	1	yes	characteristic
260	#336	—	13	2	no	—
261	#336	—	13	2	no	—
262	#336	—	13	2	no	—
263	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
265	C₂²×C₁₃	#520	1	1	yes	characteristic
266	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
267	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
269	C₂²×C₁₃	#568	1	1	yes	characteristic
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	#446	1	4	yes	complemented
276	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
277	C₄×C₁₃	#550	1	1	yes	characteristic
278	C₄×C₁₃	#557	1	1	yes	characteristic
279	C₄×C₁₃	Q₈²	1	1	yes	characteristic
280	Dic₁₃	—	2	2	no	—
281	Dic₁₃	—	2	2	no	—
282	Dic₁₃	—	2	2	no	—
283	Dic₁₃	—	2	2	no	—
284	Dic₁₃	—	2	2	no	—
285	Dic₁₃	—	4	1	no	—
286	Dic₁₃	—	4	1	no	—
287	Dic₁₃	#423	1	4	yes	—
288	C₂²×Q₈	—	13	1	no	—
289	C₂²×C₈	—	13	2	no	—
290	C₂²×C₈	—	13	2	no	—
291	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
292	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
293	C₄×Q₈	—	13	4	no	—
294	C₄×Q₈	—	13	4	no	—
295	C₄×Q₈	—	26	4	no	—
296	C₄×Q₈	—	26	4	no	—
297	C₂×C₄⋊C₄	—	13	1	no	—
298	C₂×C₄⋊C₄	—	13	1	no	—
299	C₂×C₄⋊C₄	—	13	1	no	—
300	C₂×C₄⋊C₄	—	13	1	no	—
301	C₂×C₄⋊C₄	—	13	1	no	—
302	C₂×C₄⋊C₄	—	13	1	no	—
303	C₂×C₄⋊C₄	—	13	1	no	—
304	C₂×C₄⋊C₄	—	13	1	no	—
305	C₂×C₄⋊C₄	—	13	1	no	—
306	C₂×C₄²	—	13	1	no	—
307	C₂×C₄²	—	13	1	no	—
308	C₂×C₄²	—	13	1	no	—
309	C₂×C₄²	—	13	1	no	—
310	C₂×C₄²	—	13	1	no	—
311	C₂×C₄²	—	13	1	no	—
312	C₂×C₄²	—	13	1	no	—
313	C₂×C₄²	—	13	1	no	—
314	C₂×C₄²	—	13	1	no	—
315	C₂×C₄²	—	13	1	no	—
316	C₂×C₄²	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
320	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
325	C₄⋊C₈	—	2	4	no	—
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	4	2	no	—
329	C₄⋊C₈	—	13	4	no	—
330	C₄⋊C₈	—	26	4	no	—
331	C₄⋊C₈	—	26	4	no	—
332	C₄⋊C₈	—	26	2	no	—
333	C₄⋊C₈	—	52	2	no	—
334	C₄⋊C₈	—	52	2	no	—
335	#97	—	26	4	no	—
336	#97	—	26	4	no	—
337	C₄×C₈	—	26	4	no	—
338	#95	—	13	1	no	—
339	#95	—	13	1	no	—
340	#95	—	13	1	no	—
341	#95	—	13	1	no	—
342	#95	—	13	1	no	—
343	#95	—	13	1	no	—
344	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
346	C₂×C₁₃	#2906	1	1	yes	characteristic
347	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
348	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
349	C₂×C₁₃	#2989	1	1	yes	characteristic
350	C₂×C₁₃	#2990	1	1	yes	characteristic
351	C₂×Q₈	—	13	4	no	—
352	C₂×Q₈	—	26	2	no	—
353	C₂×Q₈	—	26	2	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	13	4	no	—
376	C₂×C₈	—	26	2	no	—
377	C₂×C₈	—	26	2	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	—	26	2	no	—
380	C₂×C₈	—	26	2	no	—
381	C₄⋊C₄	—	13	4	no	—
382	C₄⋊C₄	—	13	4	no	—
383	C₄⋊C₄	—	13	4	no	—
384	C₄⋊C₄	—	13	4	no	—
385	C₄⋊C₄	—	26	2	no	—
386	C₄⋊C₄	—	26	2	no	—
387	C₄⋊C₄	—	26	2	no	—
388	C₄⋊C₄	—	26	2	no	—
389	C₄⋊C₄	—	26	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	13	4	no	—
397	C₄²	—	13	2	no	—
398	C₄²	—	13	2	no	—
399	C₄²	—	13	2	no	—
400	C₄²	—	13	2	no	—
401	C₄²	—	26	2	no	—
402	C₄²	—	26	2	no	—
403	C₄²	—	26	2	no	—
404	C₄²	—	26	2	no	—
405	C₄²	—	26	2	no	—
406	C₄²	—	26	1	no	—
407	C₄²	—	26	1	no	—
408	C₄²	—	26	1	no	—
409	C₄²	—	26	1	no	—
410	C₄²	—	52	1	no	—
411	C₄²	—	52	1	no	—
412	C₄²	D₄×D₁₃	1	2	yes	—
413	C₄²	#6129	1	2	yes	—
414	C₄²	Q₈×D₁₃	1	2	yes	—
415	C₄²	Q₈×D₁₃	1	2	yes	—
416	C₁₃	#22722	1	1	yes	characteristic, complemented, Sylow
417	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
418	Q₈	—	26	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	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	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	13	2	no	—
431	C₂×C₄	—	13	2	no	—
432	C₂×C₄	—	13	2	no	—
433	C₂×C₄	—	13	2	no	—
434	C₂×C₄	—	13	2	no	—
435	C₂×C₄	—	13	2	no	—
436	C₂×C₄	—	13	2	no	—
437	C₂×C₄	—	13	2	no	—
438	C₂×C₄	—	26	1	no	—
439	C₂×C₄	—	26	1	no	—
440	C₂×C₄	—	26	1	no	—
441	C₂×C₄	—	26	1	no	—
442	C₂×C₄	—	26	1	no	—
443	C₂×C₄	—	26	1	no	—
444	C₂×C₄	—	26	1	no	—
445	C₂×C₄	—	26	1	no	—
446	C₂×C₄	—	26	1	no	—
447	C₂×C₄	—	26	1	no	—
448	C₂×C₄	—	26	1	no	—
449	C₂×C₄	—	26	1	no	—
450	C₂×C₄	—	26	1	no	—
451	C₂×C₄	—	26	1	no	—
452	C₂×C₄	—	26	1	no	—
453	C₂×C₄	—	26	1	no	—
454	C₂×C₄	#88141	1	2	yes	—
455	C₂×C₄	#88141	1	2	yes	—
456	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
457	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
458	C₂×C₄	#88155	1	2	yes	—
459	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
460	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
461	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×#6129	1	1	yes	characteristic
463	C₂×C₄	#88251	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
466	C₂×C₄	#88254	1	1	yes	characteristic
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	26	4	no	—
470	C₈	—	52	2	no	—
471	C₂²	C₂×#88141	1	1	yes	characteristic
472	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
473	C₂²	#11719209	1	1	yes	characteristic
474	C₂²	C₂×#88155	1	1	yes	characteristic
475	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
476	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
477	C₂²	#11719450	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	13	4	no	—
484	C₄	—	26	2	no	—
485	C₄	—	26	2	no	—
486	C₄	—	26	2	no	—
487	C₄	—	26	2	no	—
488	C₄	—	26	2	no	—
489	C₄	—	52	1	no	—
490	C₄	—	52	1	no	—
491	C₄	#11718489	1	4	yes	complemented
492	C₄	#11719423	1	1	yes	characteristic
493	C₄	#11719426	1	1	yes	characteristic
494	C₄	#11719427	1	1	yes	characteristic
495	C₄	#11719432	1	1	yes	characteristic
496	C₂	#13117748	1	1	yes	characteristic
497	C₂	D₁₃×#423	1	1	yes	characteristic
498	C₂	#13123401	1	1	yes	characteristic
499	C₂	C₂×#11718489	1	1	yes	characteristic
500	C₂	#13123787	1	1	yes	characteristic
501	C₂	#13123950	1	1	yes	characteristic
502	C₂	#13123958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1842	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1842	D₁₃
hypocenter	C₁₃	#22722
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
98. C₄⋊#1055	Q₈	semidirect
275. C₄×C₁₃	#446	semidirect
416. C₁₃	#22722	semidirect
491. C₄	#11718489	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718489	2
C₄²×Dic₂₆	2
#13115557	2
#13115556	2
#13115551	2
#13114987	2
#13114691	2
#13114689	2
C₄⋊C₈×Dic₁₃	2
C₁₃×#1842	2
#22722	13