Subgroups — #15872378

Order 3328.

1194 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88123	C₂	1	1	yes	maximal, characteristic
2	#13123469	C₂	1	1	yes	maximal, characteristic
3	#13115825	C₂	1	4	yes	maximal, complemented
4	#13115824	C₂	1	4	yes	maximal, complemented
5	#13114914	C₂	1	4	yes	maximal
6	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₂₆	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₃	C₄	1	2	yes	—
10	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×#88123	—	2	1	no	—
12	C₂×#88123	—	2	1	no	—
13	C₂×#88123	—	2	1	no	—
14	C₂×#88123	—	2	1	no	—
15	C₂×#88123	—	2	1	no	—
16	C₂×#88123	—	2	1	no	—
17	C₂×#88123	—	2	1	no	—
18	C₂×#88123	—	2	1	no	—
19	C₂×#88123	C₄	1	2	yes	—
20	C₂×#88123	C₄	1	2	yes	—
21	C₂×#88123	C₂²	1	2	yes	—
22	C₂×#88123	C₂²	1	2	yes	—
23	C₁₃×#432	—	2	1	no	—
24	C₁₃×#432	—	2	1	no	—
25	C₁₃×#431	—	2	1	no	—
26	C₁₃×#431	—	2	1	no	—
27	C₁₃×#423	C₂²	1	2	yes	—
28	C₁₃×#407	C₂²	1	2	yes	—
29	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
30	#11718868	C₂²	1	2	yes	—
31	#11718587	—	2	1	no	—
32	#11718587	—	2	1	no	—
33	#11718586	—	2	1	no	—
34	#11718586	—	2	1	no	—
35	#11718585	C₂²	1	2	yes	—
36	C₄×#6099	C₂²	1	2	yes	—
37	#11718146	C₂²	1	16	yes	—
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×Dic₁₃	C₂×C₄	1	4	yes	—
42	C₂²×Dic₂₆	—	2	2	no	—
43	C₂²×Dic₂₆	—	2	2	no	—
44	C₂²×Dic₂₆	—	2	2	no	—
45	C₂²×Dic₂₆	—	2	2	no	—
46	C₂²×Dic₂₆	—	4	8	no	—
47	C₂²×Dic₂₆	C₂×C₄	1	4	yes	—
48	C₂²×Dic₂₆	C₂×C₄	1	4	yes	—
49	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₁₃	—	2	2	no	—
63	C₂×C₄⋊Dic₁₃	—	2	2	no	—
64	C₂×C₄⋊Dic₁₃	—	2	2	no	—
65	C₂×C₄⋊Dic₁₃	—	2	2	no	—
66	C₂×C₄⋊Dic₁₃	—	2	2	no	—
67	C₂×C₄⋊Dic₁₃	—	2	2	no	—
68	C₂×C₄⋊Dic₁₃	—	2	2	no	—
69	C₂×C₄⋊Dic₁₃	—	2	2	no	—
70	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
74	C₂×#6099	C₂³	1	4	yes	—
75	#88123	—	2	2	no	—
76	#88123	—	2	2	no	—
77	#88123	—	2	2	no	—
78	#88123	—	2	2	no	—
79	#88123	—	2	2	no	—
80	#88123	—	2	2	no	—
81	#88123	—	2	2	no	—
82	#88123	—	2	2	no	—
83	#88123	—	2	2	no	—
84	#88123	—	2	2	no	—
85	#88123	—	2	2	no	—
86	#88123	—	2	2	no	—
87	#88123	—	2	2	no	—
88	#88123	—	2	2	no	—
89	#88123	—	2	2	no	—
90	#88123	—	2	2	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	C₂²⋊#1055	—	2	2	no	—
98	C₂²⋊#1055	—	2	2	no	—
99	C₄⋊#1055	—	2	2	no	—
100	C₄⋊#1055	—	2	2	no	—
101	#88043	—	2	2	no	—
102	C₄×#1055	—	2	2	no	—
103	#21829	—	13	1	no	maximal, Sylow
104	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂²×Dic₁₃	—	2	4	no	—
127	C₂²×Dic₁₃	—	2	4	no	—
128	C₂²×Dic₁₃	—	4	8	no	—
129	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
130	C₂×Dic₂₆	—	2	4	no	—
131	C₂×Dic₂₆	—	2	4	no	—
132	C₂×Dic₂₆	—	2	4	no	—
133	C₂×Dic₂₆	—	2	4	no	—
134	C₂×Dic₂₆	—	4	8	no	—
135	C₂×Dic₂₆	—	4	8	no	—
136	C₂×Dic₂₆	—	4	8	no	—
137	C₂×Dic₂₆	—	4	8	no	—
138	C₂×Dic₂₆	—	4	8	no	—
139	C₂×Dic₂₆	—	4	8	no	—
140	C₁₃×M₁₆	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₄⋊Dic₁₃	—	2	4	no	—
159	C₄⋊Dic₁₃	—	2	4	no	—
160	C₄⋊Dic₁₃	—	2	4	no	—
161	C₄⋊Dic₁₃	—	2	4	no	—
162	C₄⋊Dic₁₃	—	2	4	no	—
163	C₄⋊Dic₁₃	—	2	4	no	—
164	C₄⋊Dic₁₃	—	2	4	no	—
165	C₄⋊Dic₁₃	—	2	4	no	—
166	#6099	—	2	8	no	—
167	C₂×#1055	—	2	4	no	—
168	C₂²×C₄⋊Q₈	—	13	1	no	—
169	#2920	—	13	1	no	—
170	#2920	D₁₃	1	1	yes	characteristic
171	#1997	—	13	4	no	—
172	#1997	—	13	4	no	—
173	#1821	—	13	4	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
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	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	#100	1	4	yes	—
196	C₂×C₄×C₁₃	#101	1	4	yes	—
197	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
210	C₂×Dic₁₃	—	2	8	no	—
211	C₂×Dic₁₃	—	4	8	no	—
212	C₂×Dic₁₃	—	4	8	no	—
213	C₂×Dic₁₃	—	4	8	no	—
214	Dic₂₆	—	4	8	no	—
215	Dic₂₆	—	4	8	no	—
216	Dic₂₆	—	4	8	no	—
217	Dic₂₆	—	4	8	no	—
218	C₈×C₁₃	—	4	4	no	—
219	#1055	—	4	4	no	—
220	C₂³×Q₈	—	13	2	no	—
221	C₂×C₄⋊Q₈	—	13	2	no	—
222	C₂×C₄⋊Q₈	—	13	2	no	—
223	C₂×C₄⋊Q₈	—	13	2	no	—
224	C₂×C₄⋊Q₈	—	13	2	no	—
225	C₂×C₄⋊Q₈	—	26	1	no	—
226	C₂×C₄⋊Q₈	—	26	1	no	—
227	C₂×C₄⋊Q₈	—	26	1	no	—
228	C₂×C₄⋊Q₈	—	26	1	no	—
229	C₂×C₄⋊Q₈	—	26	1	no	—
230	C₂×C₄⋊Q₈	—	26	1	no	—
231	C₂×C₄⋊Q₈	—	26	1	no	—
232	C₂×C₄⋊Q₈	—	26	1	no	—
233	C₂²×C₄⋊C₄	—	13	2	no	—
234	C₂²×C₄⋊C₄	—	13	2	no	—
235	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
236	#432	—	2	1	no	—
237	#432	—	2	1	no	—
238	#432	—	26	1	no	—
239	#432	—	26	1	no	—
240	#431	—	2	1	no	—
241	#431	—	2	1	no	—
242	#431	—	26	1	no	—
243	#431	—	26	1	no	—
244	#423	—	13	2	no	—
245	#423	C₂×D₁₃	1	2	yes	—
246	#407	—	13	2	no	—
247	#407	C₂×D₁₃	1	2	yes	—
248	C₄×M₁₆	—	13	2	no	—
249	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
250	#343	—	13	16	no	—
251	C₂²×C₁₃	—	2	8	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	C₂×#100	1	2	yes	—
259	C₂²×C₁₃	C₂×#101	1	2	yes	—
260	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₁₃	#519	1	2	yes	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	C₂×#100	1	2	yes	—
269	C₄×C₁₃	C₂×#100	1	2	yes	—
270	C₄×C₁₃	C₂×#101	1	2	yes	—
271	C₄×C₁₃	C₂×#101	1	2	yes	—
272	C₄×C₁₃	#536	1	2	yes	—
273	C₄×C₁₃	#536	1	2	yes	—
274	Dic₁₃	—	4	8	no	—
275	C₂²×Q₈	—	13	4	no	—
276	C₂²×Q₈	—	13	4	no	—
277	C₂²×Q₈	—	26	2	no	—
278	C₂²×Q₈	—	26	2	no	—
279	C₂²×Q₈	—	26	2	no	—
280	C₂²×Q₈	—	26	2	no	—
281	C₂²×Q₈	—	52	8	no	—
282	C₂³×C₄	—	13	4	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	—	13	4	no	—
287	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
288	C₄⋊Q₈	—	26	2	no	—
289	C₄⋊Q₈	—	26	2	no	—
290	C₄⋊Q₈	—	26	2	no	—
291	C₄⋊Q₈	—	26	2	no	—
292	C₄⋊Q₈	—	26	2	no	—
293	C₄⋊Q₈	—	26	2	no	—
294	C₄⋊Q₈	—	26	2	no	—
295	C₄⋊Q₈	—	26	2	no	—
296	C₄⋊Q₈	—	26	2	no	—
297	C₄⋊Q₈	—	26	2	no	—
298	C₄⋊Q₈	—	26	2	no	—
299	C₄⋊Q₈	—	26	2	no	—
300	C₄⋊Q₈	—	26	2	no	—
301	C₄⋊Q₈	—	26	2	no	—
302	C₄⋊Q₈	—	26	2	no	—
303	C₄⋊Q₈	—	26	2	no	—
304	C₂×C₄⋊C₄	—	13	4	no	—
305	C₂×C₄⋊C₄	—	13	4	no	—
306	C₂×C₄⋊C₄	—	13	4	no	—
307	C₂×C₄⋊C₄	—	13	4	no	—
308	C₂×C₄⋊C₄	—	26	2	no	—
309	C₂×C₄⋊C₄	—	26	2	no	—
310	C₂×C₄⋊C₄	—	26	2	no	—
311	C₂×C₄⋊C₄	—	26	2	no	—
312	C₂×C₄⋊C₄	—	26	2	no	—
313	C₂×C₄⋊C₄	—	26	2	no	—
314	C₂×C₄⋊C₄	—	26	2	no	—
315	C₂×C₄⋊C₄	—	26	2	no	—
316	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
318	C₂×C₄²	D₅₂	1	1	yes	characteristic
319	C₂×C₄²	D₅₂	1	1	yes	characteristic
320	C₂×C₄²	D₅₂	1	1	yes	characteristic
321	C₂×C₄²	D₅₂	1	1	yes	characteristic
322	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
325	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	26	2	no	—
331	C₄⋊C₈	—	26	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	26	2	no	—
335	C₂²⋊C₈	—	26	2	no	—
336	#97	—	2	2	no	—
337	#97	—	26	2	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	—	26	2	no	—
340	C₂×C₁₃	—	2	2	no	—
341	C₂×C₁₃	—	2	2	no	—
342	C₂×C₁₃	—	2	2	no	—
343	C₂×C₁₃	#2310	1	1	yes	characteristic
344	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
345	C₂×C₁₃	C₂²×#101	1	1	yes	characteristic
346	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₂×Q₈	—	26	4	no	—
348	C₂×Q₈	—	26	4	no	—
349	C₂×Q₈	—	26	4	no	—
350	C₂×Q₈	—	26	4	no	—
351	C₂×Q₈	—	52	8	no	—
352	C₂×Q₈	—	52	8	no	—
353	C₂×Q₈	—	52	8	no	—
354	C₂×Q₈	—	52	8	no	—
355	C₂×Q₈	—	52	8	no	—
356	C₂×Q₈	—	52	8	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	13	8	no	—
361	C₂²×C₄	—	26	4	no	—
362	C₂²×C₄	—	26	4	no	—
363	C₂²×C₄	—	52	8	no	—
364	C₂²×C₄	#6103	1	1	yes	characteristic
365	C₂²×C₄	#6103	1	1	yes	characteristic
366	C₂²×C₄	#6103	1	1	yes	characteristic
367	C₂²×C₄	#6103	1	1	yes	characteristic
368	C₂²×C₄	#6103	1	1	yes	characteristic
369	C₂²×C₄	#6103	1	1	yes	characteristic
370	C₂²×C₄	#6103	1	1	yes	characteristic
371	C₂²×C₄	#6103	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
382	M₁₆	—	2	8	no	—
383	M₁₆	—	26	8	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	26	4	no	—
386	C₄⋊C₄	—	26	4	no	—
387	C₄⋊C₄	—	26	4	no	—
388	C₄⋊C₄	—	26	4	no	—
389	C₄⋊C₄	—	26	4	no	—
390	C₄⋊C₄	—	26	4	no	—
391	C₄⋊C₄	—	26	4	no	—
392	C₄⋊C₄	—	26	4	no	—
393	C₄⋊C₄	—	26	4	no	—
394	C₄²	#6103	1	1	yes	characteristic
395	C₄²	#6103	1	1	yes	characteristic
396	C₄²	#6103	1	1	yes	characteristic
397	C₄²	#6103	1	1	yes	characteristic
398	C₄²	#6103	1	1	yes	characteristic
399	C₄²	#6103	1	1	yes	characteristic
400	C₄²	#6103	1	1	yes	characteristic
401	C₄²	#6103	1	1	yes	characteristic
402	C₄²	C₂×D₅₂	1	1	yes	characteristic
403	C₄²	C₂×D₅₂	1	1	yes	characteristic
404	C₄²	C₂×D₅₂	1	1	yes	characteristic
405	C₄²	C₂×D₅₂	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
407	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
409	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
410	C₁₃	#21829	1	1	yes	characteristic, complemented, Sylow
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×#6103	1	1	yes	characteristic
415	C₂³	C₂×#6103	1	1	yes	characteristic
416	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
417	Q₈	—	52	8	no	—
418	Q₈	—	52	8	no	—
419	Q₈	—	52	8	no	—
420	Q₈	—	52	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	26	8	no	—
437	C₂×C₄	—	52	8	no	—
438	C₂×C₄	—	52	8	no	—
439	C₂×C₄	—	52	8	no	—
440	C₂×C₄	#88063	1	4	yes	—
441	C₂×C₄	#88064	1	4	yes	—
442	C₂×C₄	C₂×#6103	1	1	yes	characteristic
443	C₂×C₄	C₂×#6103	1	1	yes	characteristic
444	C₂×C₄	C₂×#6103	1	1	yes	characteristic
445	C₂×C₄	C₂×#6103	1	1	yes	characteristic
446	C₂×C₄	C₂×#6103	1	1	yes	characteristic
447	C₂×C₄	C₂×#6103	1	1	yes	characteristic
448	C₂×C₄	C₂×#6103	1	1	yes	characteristic
449	C₂×C₄	C₂×#6103	1	1	yes	characteristic
450	C₂×C₄	C₂×#6103	1	1	yes	characteristic
451	C₂×C₄	C₂×#6103	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
453	C₂×C₄	#88257	1	4	yes	—
454	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
455	C₈	—	4	4	no	—
456	C₈	—	52	4	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	C₂×#88063	1	2	yes	—
465	C₂²	C₂×#88064	1	2	yes	—
466	C₂²	#11719221	1	2	yes	—
467	C₂²	C₂²×#6103	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	52	8	no	—
475	C₄	C₂×#88063	1	2	yes	—
476	C₄	C₂×#88063	1	2	yes	—
477	C₄	C₂×#88064	1	2	yes	—
478	C₄	C₂×#88064	1	2	yes	—
479	C₄	#11719231	1	2	yes	—
480	C₄	#11719530	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	2	no	—
483	C₂	—	2	2	no	—
484	C₂	#13117420	1	1	yes	characteristic
485	C₂	C₂²×#88063	1	1	yes	characteristic
486	C₂	C₂²×#88064	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6103
commutator	C₂³×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2920	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#21829
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13115825	C₂	semidirect
4. #13115824	C₂	semidirect
410. C₁₃	#21829	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88123	2
#13123469	2
#13115825	2
#13115824	2
#13114914	2
C₁₃×#2920	2
#21829	13