Subgroups — #15880445

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718661	C₂	1	2	yes	maximal
2	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115402	C₂	1	2	yes	maximal, complemented
5	#13115395	C₂	1	2	yes	maximal, complemented
6	#13114907	C₂	1	2	yes	maximal
7	#13114816	C₂	1	1	yes	maximal, characteristic
8	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#117	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#384	C₄	1	1	yes	characteristic
15	C₁₃×#384	C₄	1	1	yes	characteristic
16	C₁₃×#382	C₄	1	2	yes	—
17	C₁₃×#380	C₄	1	1	yes	characteristic
18	C₁₃×#380	C₄	1	1	yes	characteristic
19	C₁₃×#380	C₄	1	2	yes	—
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
25	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
26	#11718661	—	2	8	no	—
27	C₂×C₄⋊#1055	C₂²	1	2	yes	—
28	C₂×C₄⋊#1055	C₂²	1	2	yes	—
29	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
31	C₂×#88043	C₂²	1	2	yes	—
32	C₂×C₄×#1055	C₂²	1	2	yes	—
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
35	#11718116	C₂²	1	1	yes	characteristic
36	#11718116	C₂²	1	2	yes	—
37	#11718116	C₂²	1	2	yes	—
38	#11718116	C₂²	1	2	yes	—
39	#11718116	C₂²	1	1	yes	characteristic
40	#11718116	C₂²	1	2	yes	—
41	#11718116	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×#117	—	2	4	no	—
46	C₁₃×#117	—	2	4	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×#1055	C₂³	1	2	yes	—
66	C₂²×#1055	C₂³	1	1	yes	characteristic
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	C₂²×#1055	C₂³	1	2	yes	—
69	C₂²×#1055	C₂³	1	1	yes	characteristic
70	C₂²×#1055	C₂³	1	1	yes	characteristic
71	C₁₃×#95	C₂×C₄	1	2	yes	—
72	C₁₃×#95	C₂×C₄	1	2	yes	—
73	C₁₃×#95	C₂×C₄	1	2	yes	—
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	C₂²⋊#1055	—	2	4	no	—
76	C₂²⋊#1055	—	2	2	no	—
77	C₂²⋊#1055	D₄	1	4	yes	—
78	C₄⋊#1055	—	2	2	no	—
79	C₄⋊#1055	—	2	2	no	—
80	C₄⋊#1055	—	2	4	no	—
81	C₄⋊#1055	—	2	4	no	—
82	#88043	—	2	4	no	—
83	C₄×#1055	—	2	2	no	—
84	C₄×#1055	—	2	2	no	—
85	C₄×#1055	—	2	4	no	—
86	#22600	—	13	1	no	maximal, Sylow
87	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	#41	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	#41	1	2	yes	—
129	C₄²×C₁₃	#41	1	2	yes	—
130	C₂×#1055	—	2	1	no	—
131	C₂×#1055	—	2	1	no	—
132	C₂×#1055	—	2	1	no	—
133	C₂×#1055	—	2	1	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	—	2	1	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	1	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	C₂×D₄	1	2	yes	—
147	C₂×#1055	C₂×D₄	1	2	yes	—
148	C₂×#433	—	13	2	no	—
149	#2285	D₁₃	1	1	yes	characteristic
150	#1939	—	13	1	no	—
151	#1939	—	13	1	no	—
152	#1917	—	13	2	no	—
153	#1916	—	13	2	no	—
154	#1818	—	13	2	no	—
155	#1797	—	13	1	no	—
156	#1770	—	13	1	no	—
157	C₈×C₄⋊C₄	—	13	1	no	—
158	C₄×C₂²⋊C₈	—	13	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	C₄×D₄	1	2	yes	—
166	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	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	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	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	#117	1	2	yes	—
195	C₂×C₄×C₁₃	#117	1	2	yes	—
196	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	#131	1	2	yes	—
198	C₂×C₄×C₁₃	#131	1	2	yes	—
199	C₂×C₄×C₁₃	#131	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	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	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
206	#1055	—	2	2	no	—
207	#1055	—	2	2	no	—
208	#1055	—	4	2	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	1	no	—
211	#1055	—	4	1	no	—
212	C₂×#117	C₂×D₁₃	1	2	yes	—
213	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
214	#433	—	26	8	no	—
215	C₂×C₄⋊C₈	—	13	1	no	—
216	C₂×C₄⋊C₈	—	13	1	no	—
217	C₂×C₄⋊C₈	—	13	2	no	—
218	C₂×C₄⋊C₈	—	13	2	no	—
219	C₂×C₂²⋊C₈	—	13	1	no	—
220	C₂×C₂²⋊C₈	—	13	2	no	—
221	C₂×C₂²⋊C₈	—	13	1	no	—
222	C₂×#97	—	13	2	no	—
223	C₂×C₄×C₈	—	13	2	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	13	1	no	—
226	#384	Dic₁₃	1	1	yes	characteristic
227	#384	Dic₁₃	1	1	yes	characteristic
228	#382	Dic₁₃	1	2	yes	—
229	#380	Dic₁₃	1	1	yes	characteristic
230	#380	Dic₁₃	1	1	yes	characteristic
231	#380	Dic₁₃	1	2	yes	—
232	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
233	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
234	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
235	#336	—	13	2	no	—
236	#336	—	13	2	no	—
237	#336	—	13	2	no	—
238	#336	—	13	2	no	—
239	#336	—	13	2	no	—
240	#336	—	13	1	no	—
241	#336	—	13	1	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₁₃	#519	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
255	C₂²×C₁₃	#568	1	1	yes	characteristic
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	4	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	#433	1	4	yes	complemented
265	C₄×C₁₃	#547	1	1	yes	characteristic
266	C₄×C₁₃	#547	1	1	yes	characteristic
267	C₄×C₁₃	#552	1	1	yes	characteristic
268	C₄×C₁₃	#552	1	1	yes	characteristic
269	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
270	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
271	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	2	no	—
277	C₂²×C₈	—	13	2	no	—
278	#117	—	2	4	no	—
279	#117	—	2	4	no	—
280	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
295	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
298	C₄⋊C₈	—	26	4	no	—
299	C₄⋊C₈	—	26	4	no	—
300	C₄⋊C₈	—	26	2	no	—
301	C₄⋊C₈	—	26	2	no	—
302	C₂²⋊C₈	—	13	4	no	—
303	C₂²⋊C₈	—	26	4	no	—
304	C₂²⋊C₈	—	26	2	no	—
305	#97	—	26	4	no	—
306	C₄×C₈	—	26	4	no	—
307	C₄×C₈	—	26	2	no	—
308	C₄×C₈	—	26	2	no	—
309	#95	C₂×Dic₁₃	1	2	yes	—
310	#95	C₂×Dic₁₃	1	2	yes	—
311	#95	C₂×Dic₁₃	1	2	yes	—
312	#95	C₂×Dic₁₃	1	2	yes	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	#2344	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
316	C₂×C₁₃	#2924	1	1	yes	characteristic
317	C₂×C₁₃	#2931	1	1	yes	characteristic
318	C₂×C₁₃	#2935	1	1	yes	characteristic
319	C₂×C₁₃	#2985	1	1	yes	characteristic
320	C₂×C₁₃	#2986	1	1	yes	characteristic
321	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	D₄×D₁₃	1	2	yes	—
333	C₂²×C₄	#6129	1	2	yes	—
334	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
336	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
338	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
339	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	13	2	no	—
346	C₂×C₈	—	26	1	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	26	1	no	—
349	C₂×C₈	—	26	1	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	26	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	1	no	—
357	C₂×C₈	—	26	1	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	1	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	#6127	1	2	yes	—
381	C₄²	#6127	1	2	yes	—
382	C₁₃	#22600	1	1	yes	characteristic, complemented, Sylow
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	D₄×Dic₁₃	1	2	yes	—
390	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	#88180	1	2	yes	—
419	C₂×C₄	#88180	1	2	yes	—
420	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
421	C₂×C₄	#88202	1	2	yes	—
422	C₂×C₄	#88202	1	2	yes	—
423	C₂×C₄	#88202	1	2	yes	—
424	C₂×C₄	C₂×#6127	1	1	yes	characteristic
425	C₂×C₄	C₂×#6127	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×#6129	1	1	yes	characteristic
428	C₂×C₄	#88254	1	1	yes	characteristic
429	C₂×C₄	#88254	1	1	yes	characteristic
430	C₈	—	26	2	no	—
431	C₈	—	26	2	no	—
432	C₈	—	52	2	no	—
433	C₈	—	52	2	no	—
434	C₈	—	52	1	no	—
435	C₈	—	52	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₂×#88180	1	1	yes	characteristic
444	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
445	C₂²	#11719517	1	1	yes	characteristic
446	C₂²	C₂×#88202	1	1	yes	characteristic
447	C₂²	C₂×#88202	1	1	yes	characteristic
448	C₂²	C₂×#88202	1	1	yes	characteristic
449	C₂²	#11719524	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	#11718661	1	4	yes	complemented
459	C₄	#11719212	1	1	yes	characteristic
460	C₄	#11719212	1	1	yes	characteristic
461	C₄	#11719218	1	1	yes	characteristic
462	C₄	#11719218	1	1	yes	characteristic
463	C₂	—	4	2	no	—
464	C₂	#13117705	1	1	yes	characteristic
465	C₂	C₂×#11718661	1	1	yes	characteristic
466	C₂	#13123494	1	1	yes	characteristic
467	C₂	#13123548	1	1	yes	characteristic
468	C₂	#13123580	1	1	yes	characteristic
469	C₂	#13123931	1	1	yes	characteristic
470	C₂	#13123938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2285	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2285	D₁₃
hypocenter	C₁₃	#22600
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2285

Complements

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

N	H ≅ G/N	type
2. #13115555	C₂	semidirect
3. #13115555	C₂	semidirect
4. #13115402	C₂	semidirect
5. #13115395	C₂	semidirect
8. #13114705	C₂	semidirect
9. C₄⋊C₄×#1055	C₂	semidirect
264. C₄×C₁₃	#433	semidirect
382. C₁₃	#22600	semidirect
458. C₄	#11718661	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718661	2
#13115555	2
#13115402	2
#13115395	2
#13114907	2
#13114816	2
#13114705	2
C₄⋊C₄×#1055	2
C₄×C₂²⋊#1055	2
C₁₃×#2285	2
#22600	13