Subgroups — #15870366

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718340	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#88178	C₂	1	1	yes	maximal, characteristic
3	#13115772	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115554	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115400	C₂	1	2	yes	maximal, complemented
6	#13115019	C₂	1	2	yes	maximal
7	#13114816	C₂	1	1	yes	maximal, characteristic
8	#13114704	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114617	C₂	1	2	yes	maximal
11	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×#88178	C₄	1	1	yes	characteristic
16	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×M₁₆	—	2	4	no	—
18	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	#11718873	C₄	1	1	yes	characteristic
23	#11718871	C₄	1	2	yes	—
24	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
26	C₂×#88055	C₂²	1	2	yes	—
27	C₂×#88054	C₂²	1	2	yes	—
28	C₂×#88054	C₂²	1	2	yes	—
29	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
31	#11718594	C₄	1	2	yes	—
32	C₄×#6101	C₂²	1	2	yes	—
33	#11718590	C₄	1	1	yes	characteristic
34	#11718589	C₄	1	1	yes	characteristic
35	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	#11718340	—	2	4	no	—
38	#11718142	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718142	C₂²	1	2	yes	—
41	#11718142	C₂²	1	2	yes	—
42	#11718116	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
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	#88178	—	2	4	no	—
69	C₂×#6101	C₂×C₄	1	2	yes	—
70	C₂×#6101	C₂×C₄	1	2	yes	—
71	C₂×#6101	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
73	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
74	C₂²×#1055	C₂³	1	2	yes	—
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₄×Dic₂₆	—	2	2	no	—
77	C₄×Dic₂₆	—	2	2	no	—
78	C₁₃×#97	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	D₄	1	4	yes	—
82	#88071	C₂×C₄	1	2	yes	—
83	#88071	C₂×C₄	1	2	yes	—
84	#88071	C₂×C₄	1	2	yes	—
85	#88071	C₂×C₄	1	2	yes	—
86	#88071	C₂×C₄	1	2	yes	—
87	C₂²⋊#1055	—	2	4	no	—
88	#88055	—	2	4	no	—
89	#88054	—	2	4	no	—
90	#88054	—	2	4	no	—
91	C₈×Dic₁₃	—	2	4	no	—
92	C₄⋊#1055	—	2	2	no	—
93	C₄⋊#1055	—	2	2	no	—
94	#21598	—	13	1	no	maximal, Sylow
95	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₁₃	#41	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
117	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
118	C₂×Dic₂₆	—	2	2	no	—
119	C₂×Dic₂₆	—	2	2	no	—
120	C₂×Dic₂₆	—	2	2	no	—
121	C₁₃×M₁₆	—	2	8	no	—
122	C₁₃×M₁₆	—	2	8	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
132	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂×C₈×C₁₃	#41	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂×D₄	1	2	yes	—
140	C₄²×C₁₃	#41	1	2	yes	—
141	C₂²⋊Dic₁₃	—	2	4	no	—
142	C₂²⋊Dic₁₃	—	4	2	no	—
143	C₄⋊Dic₁₃	—	2	2	no	—
144	C₄⋊Dic₁₃	—	2	2	no	—
145	C₄⋊Dic₁₃	M₁₆	1	4	yes	complemented
146	#6101	—	2	4	no	—
147	#6101	—	2	4	no	—
148	#6101	—	4	2	no	—
149	C₄×Dic₁₃	—	2	2	no	—
150	C₄×Dic₁₃	—	2	2	no	—
151	C₄×Dic₁₃	—	2	2	no	—
152	C₄×Dic₁₃	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#446	—	13	1	no	—
160	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
161	C₄×C₂²⋊Q₈	—	13	1	no	—
162	#1984	—	13	1	no	—
163	#1939	—	13	1	no	—
164	#1917	—	13	2	no	—
165	#1851	—	13	2	no	—
166	#1797	—	13	1	no	—
167	#1770	—	13	2	no	—
168	C₈×C₄⋊C₄	—	13	1	no	—
169	#1753	—	13	2	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
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	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₁₃	#131	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×Dic₁₃	—	2	2	no	—
206	C₂×Dic₁₃	—	2	2	no	—
207	C₂×Dic₁₃	—	2	2	no	—
208	C₂×Dic₁₃	—	2	2	no	—
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	—	2	2	no	—
215	C₂×Dic₁₃	—	2	2	no	—
216	C₂×Dic₁₃	C₂×M₁₆	1	4	yes	—
217	Dic₂₆	—	4	4	no	—
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	—	2	2	no	—
221	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
222	#1055	—	4	2	no	—
223	#1055	—	4	2	no	—
224	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
225	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	—	13	1	no	—
227	C₂×C₄×Q₈	—	13	1	no	—
228	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
229	#446	—	26	4	no	—
230	C₂×C₄⋊C₈	—	13	2	no	—
231	C₂×C₄⋊C₈	—	13	2	no	—
232	C₂×C₄⋊C₈	—	13	1	no	—
233	C₂×C₄⋊C₈	—	13	1	no	—
234	C₂×C₂²⋊C₈	—	13	2	no	—
235	C₄×M₁₆	—	2	4	no	—
236	C₂×#97	—	13	2	no	—
237	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
238	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₄×C₈	—	13	2	no	—
240	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
242	#391	—	13	1	no	—
243	#389	—	13	1	no	—
244	#387	—	13	2	no	—
245	#385	—	13	2	no	—
246	#380	—	13	1	no	—
247	C₄×C₄⋊C₄	—	13	2	no	—
248	C₄×C₄⋊C₄	—	13	1	no	—
249	C₄×C₂²⋊C₄	—	13	2	no	—
250	#336	—	13	2	no	—
251	#336	—	13	2	no	—
252	#336	—	13	2	no	—
253	#336	—	13	2	no	—
254	#336	—	13	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
264	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
265	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
267	C₂²×C₁₃	#568	1	1	yes	characteristic
268	C₂²×C₁₃	#568	1	1	yes	characteristic
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	#436	1	4	yes	—
274	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
275	C₄×C₁₃	#525	1	1	yes	characteristic
276	C₄×C₁₃	#529	1	1	yes	characteristic
277	C₄×C₁₃	#533	1	1	yes	characteristic
278	Dic₁₃	—	2	4	no	—
279	Dic₁₃	—	4	2	no	—
280	Dic₁₃	—	4	2	no	—
281	Dic₁₃	—	4	2	no	—
282	C₂²×Q₈	—	13	1	no	—
283	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	Dic₂₆	1	4	yes	complemented
292	C₂²×C₈	—	13	2	no	—
293	C₂²×C₈	—	13	2	no	—
294	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₂²⋊Q₈	—	26	4	no	—
299	C₄×Q₈	—	26	2	no	—
300	C₄×Q₈	—	26	2	no	—
301	C₂×C₄⋊C₄	—	13	1	no	—
302	C₂×C₄⋊C₄	—	13	2	no	—
303	C₂×C₄⋊C₄	—	13	1	no	—
304	C₂×C₄⋊C₄	—	13	2	no	—
305	C₂×C₄⋊C₄	—	13	1	no	—
306	C₂×C₄⋊C₄	—	13	2	no	—
307	C₂×C₂²⋊C₄	—	13	2	no	—
308	C₂×C₂²⋊C₄	—	13	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	13	2	no	—
312	C₂×C₄²	—	13	2	no	—
313	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
315	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
317	C₄⋊C₈	—	26	4	no	—
318	C₄⋊C₈	—	26	4	no	—
319	C₄⋊C₈	—	26	2	no	—
320	C₄⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	—	26	4	no	—
322	#97	—	2	2	no	—
323	#97	—	2	2	no	—
324	#97	—	26	4	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	26	4	no	—
327	C₄×C₈	C₂²⋊D₁₃	1	4	yes	—
328	#95	—	13	2	no	—
329	#95	—	13	2	no	—
330	#95	—	13	2	no	—
331	#95	—	13	2	no	—
332	#95	—	13	2	no	—
333	C₂×C₁₃	—	4	2	no	—
334	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
335	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
336	C₂×C₁₃	#2930	1	1	yes	characteristic
337	C₂×C₁₃	#2962	1	1	yes	characteristic
338	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
339	C₂×C₁₃	#2969	1	1	yes	characteristic
340	C₂×C₁₃	#2970	1	1	yes	characteristic
341	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
342	C₂×Q₈	—	26	2	no	—
343	C₂×Q₈	—	26	2	no	—
344	C₂×Q₈	—	26	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	13	2	no	—
356	C₂²×C₄	—	13	2	no	—
357	C₂²×C₄	—	13	2	no	—
358	C₂²×C₄	—	13	2	no	—
359	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
360	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
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	#6127	1	2	yes	—
366	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
367	M₁₆	—	2	8	no	—
368	M₁₆	—	2	8	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	26	2	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	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
382	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
383	C₂×C₈	#6127	1	2	yes	—
384	C₂×C₈	#6127	1	2	yes	—
385	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
386	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
387	C₄⋊C₄	—	13	4	no	—
388	C₄⋊C₄	—	26	4	no	—
389	C₄⋊C₄	—	26	2	no	—
390	C₄⋊C₄	—	26	4	no	—
391	C₄⋊C₄	—	26	2	no	—
392	C₄⋊C₄	—	52	2	no	—
393	C₂²⋊C₄	—	26	4	no	—
394	C₂²⋊C₄	—	52	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	26	2	no	—
400	C₄²	—	26	2	no	—
401	C₄²	—	26	2	no	—
402	C₄²	—	26	2	no	—
403	C₄²	#6127	1	2	yes	—
404	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
405	C₁₃	#21598	1	1	yes	characteristic, complemented, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	C₄×Dic₂₆	1	2	yes	—
413	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
414	Q₈	—	52	4	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	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	—	4	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	13	4	no	—
432	C₂×C₄	—	26	2	no	—
433	C₂×C₄	—	26	2	no	—
434	C₂×C₄	—	26	2	no	—
435	C₂×C₄	—	26	2	no	—
436	C₂×C₄	—	26	2	no	—
437	C₂×C₄	—	26	2	no	—
438	C₂×C₄	—	26	2	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	2	no	—
442	C₂×C₄	—	26	2	no	—
443	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
444	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
445	C₂×C₄	#88161	1	2	yes	—
446	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
447	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
448	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
449	C₂×C₄	C₂×#6127	1	1	yes	characteristic
450	C₂×C₄	C₂×#6127	1	1	yes	characteristic
451	C₂×C₄	C₂×#6127	1	1	yes	characteristic
452	C₂×C₄	C₂×#6127	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	52	2	no	—
458	C₈	—	52	2	no	—
459	C₈	#88178	1	4	yes	complemented
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	C₂×C₄×Dic₂₆	1	1	yes	characteristic
468	C₂²	C₄×#6127	1	1	yes	characteristic
469	C₂²	C₂×M₁₆×D₁₃	1	1	yes	characteristic
470	C₂²	C₂×#88161	1	1	yes	characteristic
471	C₂²	#11719450	1	1	yes	characteristic
472	C₂²	#11719450	1	1	yes	characteristic
473	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	26	4	no	—
479	C₄	—	52	2	no	—
480	C₄	—	52	2	no	—
481	C₄	—	52	2	no	—
482	C₄	#11718789	1	4	yes	—
483	C₄	#11719175	1	1	yes	characteristic
484	C₄	#11719184	1	1	yes	characteristic
485	C₄	C₂×#88178	1	1	yes	characteristic
486	C₄	#11719496	1	1	yes	characteristic
487	C₂	—	4	2	no	—
488	C₂	C₄×#88178	1	1	yes	characteristic
489	C₂	C₂×#11718789	1	1	yes	characteristic
490	C₂	#13123539	1	1	yes	characteristic
491	C₂	#13123783	1	1	yes	characteristic
492	C₂	M₁₆×Dic₂₆	1	1	yes	characteristic
493	C₂	#13123840	1	1	yes	characteristic
494	C₂	#13123851	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	#21598
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11718340	C₂	semidirect
3. #13115772	C₂	semidirect
4. #13115554	C₂	semidirect
5. #13115400	C₂	semidirect
8. #13114704	C₂	semidirect
9. C₈×C₄⋊Dic₁₃	C₂	semidirect
52. C₂×C₁₃×M₁₆	Q₈	semidirect
145. C₄⋊Dic₁₃	M₁₆	semidirect
221. C₈×C₁₃	C₂²⋊Q₈	semidirect
291. C₂×M₁₆	Dic₂₆	semidirect
405. C₁₃	#21598	semidirect
459. C₈	#88178	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718340	2
C₄×#88178	2
#13115772	2
#13115554	2
#13115400	2
#13115019	2
#13114816	2
#13114704	2
C₈×C₄⋊Dic₁₃	2
#13114617	2
C₂×C₄×C₁₃×M₁₆	2
#21598	13