Subgroups — #15880730

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115560	C₂	1	2	yes	maximal, complemented
2	#13115402	C₂	1	2	yes	maximal, complemented
3	#13115395	C₂	1	2	yes	maximal, complemented
4	#13114816	C₂	1	1	yes	maximal, characteristic
5	#13114816	C₂	1	1	yes	maximal, characteristic
6	#13114816	C₂	1	1	yes	maximal, characteristic
7	#13114711	C₂	1	2	yes	maximal, complemented
8	#13114598	C₂	1	1	yes	maximal, characteristic
9	#13114598	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
18	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
26	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
27	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#1055	C₂²	1	2	yes	—
32	C₂×C₄⋊#1055	C₂²	1	2	yes	—
33	C₂×C₄⋊#1055	C₂²	1	2	yes	—
34	C₂×#88043	C₂²	1	2	yes	—
35	C₂×#88043	C₂²	1	2	yes	—
36	C₂×C₄×#1055	C₂²	1	2	yes	—
37	#11718116	C₂²	1	2	yes	—
38	#11718116	C₂²	1	2	yes	—
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	#11718116	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	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	—	4	2	no	—
62	C₂×C₄²×C₁₃	—	4	2	no	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₂²×#1055	C₂³	1	2	yes	—
77	C₂²×#1055	C₂³	1	2	yes	—
78	C₂²×#1055	C₂³	1	2	yes	—
79	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#1055	—	2	2	no	—
88	C₂²⋊#1055	—	2	2	no	—
89	C₂²⋊#1055	—	2	2	no	—
90	C₂²⋊#1055	Q₈	1	4	yes	—
91	C₄⋊#1055	—	2	4	no	—
92	C₄⋊#1055	—	4	2	no	—
93	C₄⋊#1055	—	4	2	no	—
94	#88043	—	2	4	no	—
95	#88043	—	4	2	no	—
96	C₄×#1055	—	4	2	no	—
97	#22627	—	13	1	no	maximal, Sylow
98	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	2	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	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₃	#41	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	4	1	no	—
151	C₄²×C₁₃	—	4	1	no	—
152	C₄²×C₁₃	—	4	1	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	#41	1	4	yes	—
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×#1055	—	2	2	no	—
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	—	2	2	no	—
166	C₂×#1055	C₂×Q₈	1	4	yes	—
167	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
168	#1940	—	13	2	no	—
169	#1917	—	13	2	no	—
170	#1916	—	13	2	no	—
171	#1797	—	13	1	no	—
172	#1797	—	13	1	no	—
173	#1797	—	13	1	no	—
174	#1771	—	13	2	no	—
175	#1749	—	13	1	no	—
176	#1749	—	13	1	no	—
177	C₄×C₂²⋊C₈	—	13	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
183	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
184	C₂³×C₁₃	#131	1	2	yes	—
185	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	—	2	8	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	—	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	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	#117	1	2	yes	—
226	C₂×C₄×C₁₃	#117	1	2	yes	—
227	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
228	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	#1055	—	2	4	no	—
238	#1055	—	4	2	no	—
239	#1055	—	4	2	no	—
240	#1055	—	4	2	no	—
241	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
243	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
244	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
245	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	13	2	no	—
247	C₂×C₄⋊C₈	—	13	2	no	—
248	C₂×C₄⋊C₈	—	13	2	no	—
249	C₂×C₂²⋊C₈	—	13	1	no	—
250	C₂×C₂²⋊C₈	—	13	1	no	—
251	C₂×C₂²⋊C₈	—	13	1	no	—
252	C₂×C₂²⋊C₈	—	13	1	no	—
253	C₂×#97	—	13	2	no	—
254	C₂×#97	—	13	2	no	—
255	C₂×C₄×C₈	—	13	2	no	—
256	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
257	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
259	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
264	C₂×#95	Dic₁₃	1	1	yes	characteristic
265	C₂×#95	Dic₁₃	1	1	yes	characteristic
266	#336	—	13	2	no	—
267	#336	—	13	2	no	—
268	#336	—	13	2	no	—
269	#336	—	13	2	no	—
270	#336	—	13	2	no	—
271	#336	—	13	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	#446	1	4	yes	—
279	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
281	C₂²×C₁₃	#518	1	1	yes	characteristic
282	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
283	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
285	C₂²×C₁₃	#568	1	1	yes	characteristic
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	4	1	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	#553	1	2	yes	—
300	C₄×C₁₃	#554	1	2	yes	—
301	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
307	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
308	C₂²×C₈	—	13	2	no	—
309	C₂²×C₈	—	13	2	no	—
310	C₂²×C₈	—	13	2	no	—
311	C₂²×C₈	—	13	2	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
322	C₂×C₄²	—	2	4	no	—
323	C₂×C₄²	—	4	2	no	—
324	C₂×C₄²	—	4	2	no	—
325	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
336	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
337	C₄⋊C₈	—	26	4	no	—
338	C₄⋊C₈	—	52	2	no	—
339	C₄⋊C₈	—	52	2	no	—
340	C₂²⋊C₈	—	13	4	no	—
341	C₂²⋊C₈	—	26	2	no	—
342	C₂²⋊C₈	—	26	2	no	—
343	C₂²⋊C₈	—	26	2	no	—
344	#97	—	26	4	no	—
345	#97	—	52	2	no	—
346	C₄×C₈	—	52	2	no	—
347	#95	C₂×Dic₁₃	1	1	yes	characteristic
348	#95	C₂×Dic₁₃	1	1	yes	characteristic
349	#95	C₂×Dic₁₃	1	1	yes	characteristic
350	#95	C₂×Dic₁₃	1	1	yes	characteristic
351	#95	C₂×Dic₁₃	1	1	yes	characteristic
352	#95	C₂×Dic₁₃	1	1	yes	characteristic
353	#95	C₂×Dic₁₃	1	1	yes	characteristic
354	#95	C₂×Dic₁₃	1	1	yes	characteristic
355	C₂×C₁₃	—	2	4	no	—
356	C₂×C₁₃	#2345	1	1	yes	characteristic
357	C₂×C₁₃	#2920	1	1	yes	characteristic
358	C₂×C₁₃	#2924	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
360	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
361	C₂×C₁₃	#2973	1	1	yes	characteristic
362	C₂×C₁₃	#2974	1	1	yes	characteristic
363	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	#6099	1	4	yes	—
384	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
385	C₂²×C₄	#6131	1	2	yes	—
386	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
400	C₂×C₈	—	13	4	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	2	no	—
404	C₂×C₈	—	26	2	no	—
405	C₂×C₈	—	26	2	no	—
406	C₂×C₈	—	26	2	no	—
407	C₂×C₈	—	26	2	no	—
408	C₂×C₈	—	26	2	no	—
409	C₂×C₈	—	26	2	no	—
410	C₂×C₈	—	26	2	no	—
411	C₂×C₈	—	26	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	#6099	1	4	yes	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	#6127	1	4	yes	—
432	C₁₃	#22627	1	1	yes	characteristic, complemented, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	C₂×#6099	1	2	yes	—
438	C₂³	Q₈×Dic₁₃	1	2	yes	—
439	C₂³	#88202	1	2	yes	—
440	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	C₂×#6099	1	2	yes	—
481	C₂×C₄	C₂×#6099	1	2	yes	—
482	C₂×C₄	C₂×#6099	1	2	yes	—
483	C₂×C₄	C₂×#6099	1	2	yes	—
484	C₂×C₄	C₂×#6099	1	2	yes	—
485	C₂×C₄	#88180	1	2	yes	—
486	C₂×C₄	#88180	1	2	yes	—
487	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
488	C₂×C₄	C₂×#6127	1	2	yes	—
489	C₂×C₄	#88251	1	2	yes	—
490	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂×#6131	1	1	yes	characteristic
492	C₈	—	26	4	no	—
493	C₈	—	52	2	no	—
494	C₈	—	52	2	no	—
495	C₈	—	52	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	#11718685	1	4	yes	—
503	C₂²	C₂²×#6099	1	1	yes	characteristic
504	C₂²	C₂²×#6099	1	1	yes	characteristic
505	C₂²	C₂×#88180	1	1	yes	characteristic
506	C₂²	#11719503	1	1	yes	characteristic
507	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
508	C₂²	C₂×#88202	1	1	yes	characteristic
509	C₂²	#11719524	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	#11719216	1	2	yes	—
524	C₄	#11719219	1	2	yes	—
525	C₂	—	2	4	no	—
526	C₂	#13117713	1	1	yes	characteristic
527	C₂	#13123469	1	1	yes	characteristic
528	C₂	#13123494	1	1	yes	characteristic
529	C₂	C₂×#11718685	1	1	yes	characteristic
530	C₂	Q₈×#6099	1	1	yes	characteristic
531	C₂	#13123865	1	1	yes	characteristic
532	C₂	#13123871	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	#22627
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #13115560	C₂	semidirect
2. #13115402	C₂	semidirect
3. #13115395	C₂	semidirect
7. #13114711	C₂	semidirect
432. C₁₃	#22627	semidirect

Maximal subgroups

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

subgroup	index
#13115560	2
#13115402	2
#13115395	2
#13114816	2
#13114711	2
#13114598	2
C₄×C₂²⋊#1055	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#22627	13