Subgroups — #15879838

Order 3328.

1280 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic
3	#13115444	C₂	1	2	yes	maximal, complemented
4	#13115444	C₂	1	2	yes	maximal, complemented
5	#13115016	C₂	1	2	yes	maximal, complemented
6	#13114904	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114816	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114746	C₂	1	1	yes	maximal, characteristic
9	C₂²⋊C₄×#1055	C₂	1	2	yes	maximal, complemented
10	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×#1055	C₂²	1	2	yes	—
18	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
27	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
28	C₂×C₂²⋊#1055	—	2	4	no	—
29	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
32	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
34	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
35	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
36	#11718586	—	2	4	no	—
37	C₂×C₄⋊#1055	C₂²	1	2	yes	complemented
38	C₂×C₄⋊#1055	C₂²	1	2	yes	complemented
39	C₂×C₄×#1055	C₂²	1	2	yes	complemented
40	C₂×C₄×#1055	C₂²	1	2	yes	complemented
41	#11718116	C₂²	1	2	yes	complemented
42	#11718116	C₂²	1	2	yes	complemented
43	#11718116	C₂²	1	2	yes	complemented
44	#11718116	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₃	—	2	2	no	—
49	C₂³×C₄×C₁₃	—	4	2	no	—
50	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₂²⋊C₄	C₈	1	8	yes	complemented
62	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	4	2	no	—
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×#1055	—	2	4	no	—
82	C₂²×#1055	—	2	4	no	—
83	C₂²×#1055	—	4	2	no	—
84	C₂²×#1055	C₂³	1	2	yes	—
85	C₂²×#1055	C₂³	1	2	yes	—
86	C₂²×#1055	C₂³	1	2	yes	—
87	C₂²×#1055	C₂³	1	2	yes	—
88	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊#1055	—	2	2	no	—
97	C₂²⋊#1055	—	2	2	no	—
98	C₂²⋊#1055	—	2	4	no	—
99	C₂²⋊#1055	—	2	2	no	—
100	C₂²⋊#1055	—	2	4	no	—
101	C₂²⋊#1055	—	4	2	no	—
102	C₂²⋊#1055	D₄	1	4	yes	—
103	C₄⋊#1055	—	2	4	no	—
104	C₄⋊#1055	—	4	2	no	—
105	C₄×#1055	—	2	4	no	—
106	C₄×#1055	—	4	2	no	—
107	#22552	—	13	1	no	maximal, Sylow
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	—	4	1	no	—
113	C₂⁴×C₁₃	—	4	1	no	—
114	C₂⁴×C₁₃	C₂×C₈	1	4	yes	—
115	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	—	4	1	no	—
141	C₂²×C₄×C₁₃	—	4	1	no	—
142	C₂²×C₄×C₁₃	—	4	1	no	—
143	C₂²×C₄×C₁₃	—	4	1	no	—
144	C₂²×C₄×C₁₃	—	4	1	no	—
145	C₂²×C₄×C₁₃	—	4	1	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	8	no	—
148	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	complemented
149	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	complemented
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	#41	1	4	yes	—
163	C₂²×C₄×C₁₃	#41	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
169	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
170	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
171	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	complemented
172	C₁₃×C₂²⋊C₄	M₁₆	1	4	yes	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	4	1	no	—
182	C₄²×C₁₃	—	4	1	no	—
183	C₂×#1055	—	2	2	no	—
184	C₂×#1055	—	2	2	no	—
185	C₂×#1055	—	2	2	no	—
186	C₂×#1055	—	2	2	no	—
187	C₂×#1055	—	2	2	no	—
188	C₂×#1055	—	2	2	no	—
189	C₂×#1055	—	2	2	no	—
190	C₂×#1055	—	2	2	no	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	2	2	no	—
193	C₂×#1055	—	2	2	no	—
194	C₂×#1055	—	4	8	no	—
195	C₂×#1055	C₂×D₄	1	4	yes	—
196	C₂×#431	—	13	1	no	—
197	C₂²×C₂²⋊C₈	—	13	1	no	—
198	C₂×C₄×C₂²⋊C₄	D₁₃	1	1	yes	characteristic
199	#1923	—	13	2	no	—
200	#1923	—	13	2	no	—
201	#1850	—	13	2	no	—
202	#1817	—	13	1	no	—
203	#1797	—	13	1	no	—
204	#1779	—	13	1	no	—
205	C₈×C₂²⋊C₄	—	13	2	no	—
206	C₄×C₂²⋊C₈	—	13	1	no	—
207	C₂³×C₁₃	—	2	1	no	—
208	C₂³×C₁₃	—	2	1	no	—
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	1	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	8	no	—
222	C₂³×C₁₃	—	2	8	no	—
223	C₂³×C₁₃	—	4	4	no	—
224	C₂³×C₁₃	—	4	4	no	—
225	C₂³×C₁₃	—	4	4	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	#117	1	2	yes	—
229	C₂³×C₁₃	C₄×D₄	1	2	yes	—
230	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
231	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
232	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
233	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
234	C₂³×C₁₃	#131	1	2	yes	—
235	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	4	4	no	—
270	C₂×C₄×C₁₃	—	4	4	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	#117	1	2	yes	—
275	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
278	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
279	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
281	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
286	#1055	—	2	4	no	—
287	#1055	—	4	2	no	—
288	#1055	—	4	2	no	—
289	#1055	—	4	2	no	—
290	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
291	C₂³×C₈	—	13	2	no	—
292	C₂²×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
294	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
295	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
296	#431	—	26	4	no	—
297	C₂×C₄⋊C₈	—	13	2	no	—
298	C₂×C₄⋊C₈	—	13	2	no	—
299	C₂×C₂²⋊C₈	—	13	1	no	—
300	C₂×C₂²⋊C₈	—	13	1	no	—
301	C₂×C₂²⋊C₈	—	13	1	no	—
302	C₂×C₂²⋊C₈	—	13	1	no	—
303	C₂×C₂²⋊C₈	—	13	2	no	—
304	C₂×C₂²⋊C₈	—	13	2	no	—
305	C₂×C₂²⋊C₈	—	13	2	no	—
306	C₂×C₂²⋊C₈	—	26	4	no	—
307	C₂×C₄×C₈	—	13	2	no	—
308	C₂×C₄×C₈	—	13	2	no	—
309	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
310	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
311	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
313	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
316	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
317	C₂×#95	Dic₁₃	1	1	yes	characteristic
318	C₂×#95	Dic₁₃	1	1	yes	characteristic
319	#336	—	13	2	no	—
320	#336	—	13	2	no	—
321	#336	—	13	2	no	—
322	#336	—	13	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	4	16	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	#431	1	4	yes	complemented
344	C₂²×C₁₃	C₈×D₄	1	4	yes	—
345	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₁₃	#518	1	1	yes	characteristic
348	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
349	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
351	C₂²×C₁₃	#568	1	1	yes	characteristic
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	#546	1	2	yes	—
364	C₄×C₁₃	#551	1	2	yes	—
365	C₂⁵	C₂×Dic₁₃	1	1	yes	characteristic
366	C₂³×C₄	—	2	4	no	—
367	C₂³×C₄	—	2	2	no	—
368	C₂³×C₄	—	2	2	no	—
369	C₂³×C₄	—	4	2	no	—
370	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
372	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
373	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
378	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
379	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
380	C₂²×C₈	—	13	2	no	—
381	C₂²×C₈	—	13	2	no	—
382	C₂²×C₈	—	13	2	no	—
383	C₂²×C₈	—	13	2	no	—
384	C₂²×C₈	—	26	4	no	—
385	C₂²×C₈	—	26	4	no	—
386	C₂²×C₈	—	52	2	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	#1055	1	8	yes	complemented
389	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	—	2	2	no	—
399	C₂×C₄²	—	4	2	no	—
400	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
403	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
407	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
408	C₄⋊C₈	—	26	4	no	—
409	C₄⋊C₈	—	52	2	no	—
410	C₂²⋊C₈	—	13	4	no	—
411	C₂²⋊C₈	—	26	4	no	—
412	C₂²⋊C₈	—	26	4	no	—
413	C₂²⋊C₈	—	26	2	no	—
414	C₂²⋊C₈	—	26	2	no	—
415	C₂²⋊C₈	—	26	2	no	—
416	C₂²⋊C₈	—	52	2	no	—
417	C₄×C₈	—	26	4	no	—
418	C₄×C₈	—	52	2	no	—
419	#95	C₂×Dic₁₃	1	1	yes	characteristic
420	#95	C₂×Dic₁₃	1	1	yes	characteristic
421	#95	C₂×Dic₁₃	1	1	yes	characteristic
422	#95	C₂×Dic₁₃	1	1	yes	characteristic
423	#95	C₂×Dic₁₃	1	1	yes	characteristic
424	#95	C₂×Dic₁₃	1	1	yes	characteristic
425	#95	C₂×Dic₁₃	1	1	yes	characteristic
426	#95	C₂×Dic₁₃	1	1	yes	characteristic
427	C₂×C₁₃	—	2	4	no	—
428	C₂×C₁₃	—	2	4	no	—
429	C₂×C₁₃	—	4	2	no	—
430	C₂×C₁₃	#2342	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
432	C₂×C₁₃	#2924	1	1	yes	characteristic
433	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
434	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
435	C₂×C₁₃	#2972	1	1	yes	characteristic
436	C₂×C₁₃	#2974	1	1	yes	characteristic
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	4	1	no	—
442	C₂⁴	—	4	1	no	—
443	C₂⁴	C₂×#1055	1	4	yes	—
444	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
445	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
446	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	8	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	C₂×#1055	1	4	yes	complemented
478	C₂²×C₄	C₂×#1055	1	4	yes	complemented
479	C₂²×C₄	#6127	1	4	yes	—
480	C₂²×C₄	D₄×D₁₃	1	2	yes	—
481	C₂²×C₄	#6129	1	2	yes	—
482	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
494	C₂×C₈	—	13	4	no	—
495	C₂×C₈	—	26	2	no	—
496	C₂×C₈	—	26	2	no	—
497	C₂×C₈	—	26	2	no	—
498	C₂×C₈	—	26	2	no	—
499	C₂×C₈	—	26	2	no	—
500	C₂×C₈	—	26	2	no	—
501	C₂×C₈	—	26	2	no	—
502	C₂×C₈	—	26	2	no	—
503	C₂×C₈	—	26	2	no	—
504	C₂×C₈	—	26	2	no	—
505	C₂×C₈	—	26	2	no	—
506	C₂×C₈	—	52	8	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	C₂×#1055	1	4	yes	—
511	C₂²⋊C₄	C₂×#1055	1	4	yes	—
512	C₂²⋊C₄	C₂×#1055	1	4	yes	complemented
513	C₂²⋊C₄	C₂×#1055	1	4	yes	complemented
514	C₂²⋊C₄	#6099	1	4	yes	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	4	1	no	—
524	C₄²	—	4	1	no	—
525	C₁₃	#22552	1	1	yes	characteristic, complemented, Sylow
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	8	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	4	no	—
547	C₂³	C₂²×#1055	1	2	yes	—
548	C₂³	C₂²×#1055	1	2	yes	—
549	C₂³	C₂²×#1055	1	2	yes	—
550	C₂³	C₂×#6099	1	2	yes	—
551	C₂³	#88180	1	2	yes	—
552	C₂³	D₄×Dic₁₃	1	2	yes	—
553	C₂³	#88202	1	2	yes	—
554	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	C₂²×#1055	1	2	yes	—
594	C₂×C₄	C₂²×#1055	1	2	yes	—
595	C₂×C₄	C₂²×#1055	1	2	yes	—
596	C₂×C₄	C₂²×#1055	1	2	yes	—
597	C₂×C₄	C₂×#6099	1	2	yes	—
598	C₂×C₄	C₂×#6099	1	2	yes	—
599	C₂×C₄	#88180	1	2	yes	—
600	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
601	C₂×C₄	C₂×#6127	1	2	yes	—
602	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
603	C₂×C₄	C₂×#6129	1	1	yes	characteristic
604	C₂×C₄	#88251	1	2	yes	—
605	C₈	—	26	4	no	—
606	C₈	—	52	2	no	—
607	C₈	—	52	2	no	—
608	C₈	—	52	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	16	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	#11718586	1	4	yes	complemented
630	C₂²	D₄×#1055	1	4	yes	—
631	C₂²	C₂³×#1055	1	1	yes	characteristic
632	C₂²	C₂²×#6099	1	1	yes	characteristic
633	C₂²	C₂×#88180	1	1	yes	characteristic
634	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
635	C₂²	#11719503	1	1	yes	characteristic
636	C₂²	C₂×#88202	1	1	yes	characteristic
637	C₂²	#11719524	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	#11719195	1	2	yes	—
650	C₄	#11719200	1	2	yes	—
651	C₂	—	2	4	no	—
652	C₂	—	2	4	no	—
653	C₂	—	4	2	no	—
654	C₂	#13117685	1	1	yes	characteristic
655	C₂	C₂×#11718586	1	1	yes	characteristic
656	C₂	#13123494	1	1	yes	characteristic
657	C₂	C₂×D₄×#1055	1	1	yes	characteristic
658	C₂	D₄×#6099	1	1	yes	characteristic
659	C₂	#13123860	1	1	yes	characteristic
660	C₂	#13123871	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Fitting	C₂×C₄×C₁₃×C₂²⋊C₄	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁵×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×C₂²⋊C₄	D₁₃
hypocenter	C₁₃	#22552
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11718586	C₂	semidirect
3. #13115444	C₂	semidirect
4. #13115444	C₂	semidirect
5. #13115016	C₂	semidirect
6. #13114904	C₂	semidirect
7. #13114816	C₂	semidirect
9. C₂²⋊C₄×#1055	C₂	semidirect
10. C₄×C₂²⋊#1055	C₂	semidirect
37. C₂×C₄⋊#1055	C₂²	semidirect
38. C₂×C₄⋊#1055	C₂²	semidirect
39. C₂×C₄×#1055	C₂²	semidirect
40. C₂×C₄×#1055	C₂²	semidirect
41. #11718116	C₂²	semidirect
42. #11718116	C₂²	semidirect
43. #11718116	C₂²	semidirect
44. #11718116	C₂²	semidirect
61. C₂×C₁₃×C₂²⋊C₄	C₈	semidirect
148. C₂²×C₄×C₁₃	C₂×C₈	semidirect
149. C₂²×C₄×C₁₃	C₂×C₈	semidirect
170. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
171. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
343. C₂²×C₁₃	#431	semidirect
388. C₂×C₂²⋊C₄	#1055	semidirect
477. C₂²×C₄	C₂×#1055	semidirect
478. C₂²×C₄	C₂×#1055	semidirect
512. C₂²⋊C₄	C₂×#1055	semidirect
513. C₂²⋊C₄	C₂×#1055	semidirect
525. C₁₃	#22552	semidirect
629. C₂²	#11718586	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
C₂²×C₂²⋊#1055	2
#13115444	2
#13115016	2
#13114904	2
#13114816	2
#13114746	2
C₂²⋊C₄×#1055	2
C₄×C₂²⋊#1055	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#22552	13