Subgroups — #15880717

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
2	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115402	C₂	1	2	yes	maximal, complemented
4	#13115395	C₂	1	2	yes	maximal, complemented
5	#13114820	C₂	1	2	yes	maximal
6	#13114816	C₂	1	1	yes	maximal, characteristic
7	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114602	C₂	1	2	yes	maximal
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	2	yes	—
24	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#1055	C₂²	1	2	yes	—
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	C₂×#88043	C₂²	1	2	yes	—
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	2	yes	—
34	#11718116	C₂²	1	1	yes	characteristic
35	#11718116	C₂²	1	2	yes	—
36	#11718116	C₂²	1	2	yes	—
37	#11718116	C₂²	1	2	yes	—
38	#11718116	C₂²	1	1	yes	characteristic
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₁₃×#117	—	4	2	no	—
45	C₁₃×#117	—	4	2	no	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×#1055	C₂³	1	1	yes	characteristic
65	C₂²×#1055	C₂³	1	1	yes	characteristic
66	C₂²×#1055	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	2	yes	—
68	C₂²×#1055	C₂³	1	1	yes	characteristic
69	C₂²×#1055	C₂³	1	1	yes	characteristic
70	C₁₃×#95	C₂×C₄	1	2	yes	—
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	C₂²⋊#1055	—	2	4	no	—
75	C₂²⋊#1055	—	2	2	no	—
76	C₂²⋊#1055	Q₈	1	4	yes	—
77	C₄⋊#1055	—	2	2	no	—
78	C₄⋊#1055	—	2	2	no	—
79	C₄⋊#1055	—	4	2	no	—
80	C₄⋊#1055	—	4	2	no	—
81	#88043	—	4	2	no	—
82	C₄×#1055	—	2	2	no	—
83	C₄×#1055	—	2	2	no	—
84	C₄×#1055	—	4	2	no	—
85	#22626	—	13	1	no	maximal, Sylow
86	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
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	2	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	—	4	1	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	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	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₂²⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	4	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	—	2	1	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	#41	1	2	yes	—
128	C₄²×C₁₃	#41	1	2	yes	—
129	C₂×#1055	—	2	1	no	—
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	1	no	—
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	2	1	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	C₂×Q₈	1	2	yes	—
146	C₂×#1055	C₂×Q₈	1	2	yes	—
147	#2285	D₁₃	1	1	yes	characteristic
148	#1939	—	13	1	no	—
149	#1939	—	13	1	no	—
150	#1917	—	13	2	no	—
151	#1916	—	13	2	no	—
152	#1798	—	13	2	no	—
153	#1797	—	13	1	no	—
154	#1770	—	13	1	no	—
155	C₈×C₄⋊C₄	—	13	1	no	—
156	#1750	—	13	2	no	—
157	C₄×C₂²⋊C₈	—	13	1	no	—
158	C₂³×C₁₃	—	2	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	C₄×Q₈	1	2	yes	—
165	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	—	2	1	no	—
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	2	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	1	no	—
177	C₂×C₄×C₁₃	—	2	2	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	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	#117	1	2	yes	—
194	C₂×C₄×C₁₃	#117	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃	#131	1	2	yes	—
197	C₂×C₄×C₁₃	#131	1	2	yes	—
198	C₂×C₄×C₁₃	#131	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	#1055	—	2	2	no	—
206	#1055	—	2	2	no	—
207	#1055	—	4	1	no	—
208	#1055	—	4	1	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	2	no	—
211	C₂×#117	C₂×D₁₃	1	2	yes	—
212	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	13	1	no	—
214	C₂×C₄⋊C₈	—	13	1	no	—
215	C₂×C₄⋊C₈	—	13	2	no	—
216	C₂×C₄⋊C₈	—	13	2	no	—
217	C₂×C₂²⋊C₈	—	13	1	no	—
218	C₂×C₂²⋊C₈	—	13	2	no	—
219	C₂×C₂²⋊C₈	—	13	1	no	—
220	C₂×#97	—	13	2	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	2	no	—
224	#384	Dic₁₃	1	1	yes	characteristic
225	#384	Dic₁₃	1	1	yes	characteristic
226	#382	Dic₁₃	1	2	yes	—
227	#380	Dic₁₃	1	1	yes	characteristic
228	#380	Dic₁₃	1	1	yes	characteristic
229	#380	Dic₁₃	1	2	yes	—
230	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
231	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
233	#336	—	13	2	no	—
234	#336	—	13	2	no	—
235	#336	—	13	2	no	—
236	#336	—	13	1	no	—
237	#336	—	13	2	no	—
238	#336	—	13	1	no	—
239	#336	—	13	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
249	C₂²×C₁₃	#518	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
253	C₂²×C₁₃	#568	1	1	yes	characteristic
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	#433	1	4	yes	—
263	C₄×C₁₃	#553	1	1	yes	characteristic
264	C₄×C₁₃	#553	1	1	yes	characteristic
265	C₄×C₁₃	#554	1	1	yes	characteristic
266	C₄×C₁₃	#554	1	1	yes	characteristic
267	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
268	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	2	no	—
275	C₂²×C₈	—	13	2	no	—
276	#117	—	4	2	no	—
277	#117	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
293	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
294	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
296	C₄⋊C₈	—	26	2	no	—
297	C₄⋊C₈	—	26	2	no	—
298	C₄⋊C₈	—	52	2	no	—
299	C₄⋊C₈	—	52	2	no	—
300	C₂²⋊C₈	—	13	4	no	—
301	C₂²⋊C₈	—	26	4	no	—
302	C₂²⋊C₈	—	26	2	no	—
303	#97	—	52	2	no	—
304	C₄×C₈	—	26	2	no	—
305	C₄×C₈	—	26	2	no	—
306	C₄×C₈	—	52	2	no	—
307	#95	C₂×Dic₁₃	1	2	yes	—
308	#95	C₂×Dic₁₃	1	2	yes	—
309	#95	C₂×Dic₁₃	1	2	yes	—
310	#95	C₂×Dic₁₃	1	2	yes	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2345	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
314	C₂×C₁₃	#2924	1	1	yes	characteristic
315	C₂×C₁₃	#2960	1	1	yes	characteristic
316	C₂×C₁₃	#2962	1	1	yes	characteristic
317	C₂×C₁₃	#2979	1	1	yes	characteristic
318	C₂×C₁₃	#2981	1	1	yes	characteristic
319	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
331	C₂²×C₄	#6131	1	2	yes	—
332	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
334	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
335	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
336	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	26	1	no	—
345	C₂×C₈	—	26	1	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	2	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	26	1	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	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	#6127	1	2	yes	—
379	C₄²	#6127	1	2	yes	—
380	C₁₃	#22626	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	Q₈×Dic₁₃	1	2	yes	—
388	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
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	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	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	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	#88180	1	2	yes	—
417	C₂×C₄	#88180	1	2	yes	—
418	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
419	C₂×C₄	#88202	1	2	yes	—
420	C₂×C₄	#88202	1	2	yes	—
421	C₂×C₄	#88202	1	2	yes	—
422	C₂×C₄	C₂×#6127	1	1	yes	characteristic
423	C₂×C₄	C₂×#6127	1	1	yes	characteristic
424	C₂×C₄	#88251	1	1	yes	characteristic
425	C₂×C₄	#88251	1	1	yes	characteristic
426	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×#6131	1	1	yes	characteristic
428	C₈	—	26	2	no	—
429	C₈	—	26	2	no	—
430	C₈	—	52	1	no	—
431	C₈	—	52	1	no	—
432	C₈	—	52	2	no	—
433	C₈	—	52	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×#88180	1	1	yes	characteristic
442	C₂²	#11719503	1	1	yes	characteristic
443	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
444	C₂²	C₂×#88202	1	1	yes	characteristic
445	C₂²	C₂×#88202	1	1	yes	characteristic
446	C₂²	C₂×#88202	1	1	yes	characteristic
447	C₂²	#11719524	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	1	no	—
456	C₄	#11718661	1	4	yes	—
457	C₄	#11719216	1	1	yes	characteristic
458	C₄	#11719216	1	1	yes	characteristic
459	C₄	#11719219	1	1	yes	characteristic
460	C₄	#11719219	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	#13117713	1	1	yes	characteristic
463	C₂	C₂×#11718661	1	1	yes	characteristic
464	C₂	#13123494	1	1	yes	characteristic
465	C₂	#13123771	1	1	yes	characteristic
466	C₂	#13123785	1	1	yes	characteristic
467	C₂	#13123903	1	1	yes	characteristic
468	C₂	#13123912	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	#22626
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
1. #13115555	C₂	semidirect
2. #13115555	C₂	semidirect
3. #13115402	C₂	semidirect
4. #13115395	C₂	semidirect
7. #13114705	C₂	semidirect
8. C₄⋊C₄×#1055	C₂	semidirect
380. C₁₃	#22626	semidirect

Maximal subgroups

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

subgroup	index
#13115555	2
#13115402	2
#13115395	2
#13114820	2
#13114816	2
#13114705	2
C₄⋊C₄×#1055	2
#13114602	2
C₄×C₂²⋊#1055	2
C₁₃×#2285	2
#22626	13