Subgroups — #15870356

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
3	#13115773	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115555	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115395	C₂	1	2	yes	maximal, complemented
6	#13115016	C₂	1	2	yes	maximal
7	#13114816	C₂	1	1	yes	maximal, characteristic
8	#13114711	C₂	1	2	yes	maximal, complemented
9	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114614	C₂	1	2	yes	maximal
11	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₂³×#1055	C₂²	1	1	yes	characteristic
17	C₁₃×#391	C₄	1	1	yes	characteristic
18	C₁₃×#389	C₄	1	1	yes	characteristic
19	C₁₃×#387	C₄	1	2	yes	—
20	C₁₃×#385	C₄	1	2	yes	—
21	C₁₃×#380	C₄	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
26	#11718685	—	2	4	no	—
27	C₂×C₄⋊#1055	C₂²	1	2	yes	—
28	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
31	C₂×#88043	C₂²	1	2	yes	—
32	C₂×#88043	C₂²	1	2	yes	—
33	C₂×C₄×#1055	—	2	4	no	—
34	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×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	C₂³	1	1	yes	characteristic
47	C₁₃×C₂²⋊Q₈	—	2	4	no	—
48	C₄×Q₈×C₁₃	—	2	2	no	—
49	C₄×Q₈×C₁₃	—	2	2	no	—
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	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂×C₄	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	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×#1055	—	2	2	no	—
67	C₂²×#1055	—	2	2	no	—
68	C₂²×#1055	—	2	2	no	—
69	C₂²×#1055	—	2	2	no	—
70	C₂²×#1055	—	2	2	no	—
71	C₂²×#1055	Q₈	1	4	yes	complemented
72	C₂²×#1055	C₂³	1	2	yes	—
73	C₂²×#1055	C₂³	1	2	yes	—
74	C₂²×#1055	C₂³	1	1	yes	characteristic
75	C₂²×#1055	C₂³	1	1	yes	characteristic
76	C₂²×#1055	C₂³	1	1	yes	characteristic
77	C₂²×#1055	C₂³	1	1	yes	characteristic
78	C₁₃×#95	C₂×C₄	1	2	yes	—
79	C₁₃×#95	C₂×C₄	1	2	yes	—
80	C₁₃×#95	C₂×C₄	1	2	yes	—
81	C₁₃×#95	C₂×C₄	1	2	yes	—
82	C₁₃×#95	C₂×C₄	1	2	yes	—
83	C₂²⋊#1055	—	2	4	no	—
84	C₄⋊#1055	—	2	2	no	—
85	C₄⋊#1055	—	2	2	no	—
86	C₄⋊#1055	—	2	4	no	—
87	C₄⋊#1055	—	2	4	no	—
88	#88043	—	2	4	no	—
89	#88043	—	2	4	no	—
90	C₄×#1055	—	2	2	no	—
91	C₄×#1055	—	2	2	no	—
92	C₄×#1055	—	2	2	no	—
93	C₄×#1055	D₄	1	4	yes	—
94	#21597	—	13	1	no	maximal, Sylow
95	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
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	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	1	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	C₂×#1055	—	2	8	no	—
140	C₂×#1055	—	2	1	no	—
141	C₂×#1055	—	2	1	no	—
142	C₂×#1055	—	2	1	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	8	no	—
147	C₂×#1055	—	2	2	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	C₂×D₄	1	2	yes	—
154	C₂×#1055	C₂×D₄	1	2	yes	—
155	C₂×#1055	C₂×Q₈	1	2	yes	—
156	C₂×#1055	C₂×Q₈	1	2	yes	—
157	C₂×#1055	#41	1	2	yes	—
158	C₂×#1055	#41	1	2	yes	—
159	C₂×#446	—	13	1	no	—
160	C₂²×C₄×C₈	—	13	1	no	—
161	C₄×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic
162	#1984	—	13	1	no	—
163	#1939	—	13	1	no	—
164	#1916	—	13	2	no	—
165	#1850	—	13	2	no	—
166	#1797	—	13	1	no	—
167	#1771	—	13	2	no	—
168	#1770	—	13	1	no	—
169	#1752	—	13	2	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
175	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
176	C₂³×C₁₃	#131	1	2	yes	—
177	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	Q₈×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	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	8	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
208	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
209	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
210	C₂×C₄×C₁₃	#131	1	2	yes	—
211	C₂×C₄×C₁₃	#131	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	#1055	—	2	2	no	—
219	#1055	—	2	2	no	—
220	#1055	—	2	2	no	—
221	#1055	—	4	2	no	—
222	#1055	—	4	2	no	—
223	#1055	C₂²⋊Q₈	1	4	yes	complemented
224	C₂³×C₈	—	13	1	no	—
225	C₂³×C₈	—	13	1	no	—
226	C₂×C₂²⋊Q₈	Dic₁₃	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
228	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
229	#446	—	26	4	no	—
230	C₂×C₄⋊C₈	—	13	1	no	—
231	C₂×C₄⋊C₈	—	13	1	no	—
232	C₂×C₄⋊C₈	—	13	2	no	—
233	C₂×C₄⋊C₈	—	13	2	no	—
234	C₂×C₂²⋊C₈	—	13	2	no	—
235	C₂×#97	—	13	2	no	—
236	C₂×#97	—	13	2	no	—
237	C₂×C₄×C₈	—	13	1	no	—
238	C₂×C₄×C₈	—	13	1	no	—
239	C₂×C₄×C₈	—	13	1	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	26	4	no	—
242	#391	Dic₁₃	1	1	yes	characteristic
243	#389	Dic₁₃	1	1	yes	characteristic
244	#387	Dic₁₃	1	2	yes	—
245	#385	Dic₁₃	1	2	yes	—
246	#380	Dic₁₃	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
248	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
250	#336	—	13	2	no	—
251	#336	—	13	2	no	—
252	#336	—	13	2	no	—
253	#336	—	13	2	no	—
254	#336	—	13	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	2	2	no	—
259	C₂²×C₁₃	—	2	2	no	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	#446	1	4	yes	complemented
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
264	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
265	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
267	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	#435	1	4	yes	—
278	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
279	C₄×C₁₃	#525	1	1	yes	characteristic
280	C₄×C₁₃	#529	1	1	yes	characteristic
281	C₄×C₁₃	#533	1	1	yes	characteristic
282	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	4	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	2	no	—
292	C₂²×C₈	—	13	2	no	—
293	C₂²×C₈	—	26	2	no	—
294	C₂²×C₈	—	26	2	no	—
295	C₂²×C₈	—	26	2	no	—
296	C₂²×C₈	—	26	2	no	—
297	C₂²×C₈	—	26	2	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
313	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
314	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
315	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
317	C₄⋊C₈	—	26	4	no	—
318	C₄⋊C₈	—	26	4	no	—
319	C₄⋊C₈	—	26	2	no	—
320	C₄⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	—	26	4	no	—
322	#97	—	26	4	no	—
323	#97	—	26	4	no	—
324	C₄×C₈	—	13	4	no	—
325	C₄×C₈	—	26	2	no	—
326	C₄×C₈	—	26	2	no	—
327	C₄×C₈	—	26	2	no	—
328	#95	C₂×Dic₁₃	1	2	yes	—
329	#95	C₂×Dic₁₃	1	2	yes	—
330	#95	C₂×Dic₁₃	1	2	yes	—
331	#95	C₂×Dic₁₃	1	2	yes	—
332	#95	C₂×Dic₁₃	1	2	yes	—
333	C₂×C₁₃	—	2	4	no	—
334	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
335	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
336	C₂×C₁₃	#2929	1	1	yes	characteristic
337	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
338	C₂×C₁₃	#2960	1	1	yes	characteristic
339	C₂×C₁₃	#2965	1	1	yes	characteristic
340	C₂×C₁₃	#2966	1	1	yes	characteristic
341	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	#6099	1	4	yes	—
355	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
356	C₂²×C₄	#6131	1	2	yes	—
357	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
358	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
359	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
360	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
361	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
367	C₂×C₈	—	13	2	no	—
368	C₂×C₈	—	13	2	no	—
369	C₂×C₈	—	13	2	no	—
370	C₂×C₈	—	13	2	no	—
371	C₂×C₈	—	13	2	no	—
372	C₂×C₈	—	13	2	no	—
373	C₂×C₈	—	26	8	no	—
374	C₂×C₈	—	26	8	no	—
375	C₂×C₈	—	26	1	no	—
376	C₂×C₈	—	26	1	no	—
377	C₂×C₈	—	26	1	no	—
378	C₂×C₈	—	26	1	no	—
379	C₂×C₈	—	26	1	no	—
380	C₂×C₈	—	26	1	no	—
381	C₂×C₈	—	26	2	no	—
382	C₂×C₈	—	26	2	no	—
383	C₂×C₈	—	26	2	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	D₄×D₁₃	1	2	yes	—
404	C₄²	#6129	1	2	yes	—
405	C₁₃	#21597	1	1	yes	characteristic, complemented, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	C₂×#6099	1	2	yes	—
411	C₂³	Q₈×Dic₁₃	1	2	yes	—
412	C₂³	#88202	1	2	yes	—
413	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
414	Q₈	—	4	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	8	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	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	C₂×#6099	1	2	yes	—
442	C₂×C₄	C₂×#6099	1	2	yes	—
443	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
444	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
445	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
446	C₂×C₄	#88202	1	2	yes	—
447	C₂×C₄	#88202	1	2	yes	—
448	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
449	C₂×C₄	C₂×#6129	1	1	yes	characteristic
450	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂×#6131	1	1	yes	characteristic
452	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
453	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
454	C₈	—	13	4	no	—
455	C₈	—	26	2	no	—
456	C₈	—	26	2	no	—
457	C₈	—	26	2	no	—
458	C₈	—	52	2	no	—
459	C₈	—	52	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	#11718685	1	4	yes	complemented
467	C₂²	C₂²×#6099	1	1	yes	characteristic
468	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
469	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
470	C₂²	C₂×#88202	1	1	yes	characteristic
471	C₂²	C₂×#88202	1	1	yes	characteristic
472	C₂²	C₂×#88202	1	1	yes	characteristic
473	C₂²	#41×Dic₁₃	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	#11718672	1	4	yes	—
483	C₄	#11719327	1	1	yes	characteristic
484	C₄	#11719329	1	1	yes	characteristic
485	C₄	D₁₃×C₂²⋊Q₈	1	1	yes	characteristic
486	C₄	#11719332	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₂²⋊Q₈×Dic₁₃	1	1	yes	characteristic
489	C₂	C₂×#11718672	1	1	yes	characteristic
490	C₂	#13123531	1	1	yes	characteristic
491	C₂	C₂×#11718685	1	1	yes	characteristic
492	C₂	#13123771	1	1	yes	characteristic
493	C₂	#13123803	1	1	yes	characteristic
494	C₂	#13123812	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×C₂²⋊Q₈	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₁₃
hypocenter	C₁₃	#21597
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11718685	C₂	semidirect
3. #13115773	C₂	semidirect
4. #13115555	C₂	semidirect
5. #13115395	C₂	semidirect
8. #13114711	C₂	semidirect
9. #13114705	C₂	semidirect
71. C₂²×#1055	Q₈	semidirect
223. #1055	C₂²⋊Q₈	semidirect
261. C₂²×C₁₃	#446	semidirect
405. C₁₃	#21597	semidirect
466. C₂²	#11718685	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718685	2
C₂²×C₄×#1055	2
#13115773	2
#13115555	2
#13115395	2
#13115016	2
#13114816	2
#13114711	2
#13114705	2
#13114614	2
C₄×C₁₃×C₂²⋊Q₈	2
#21597	13