Subgroups — #15770804

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718116	C₂	1	2	yes	maximal
3	C₂×#11718116	C₂	1	2	yes	maximal
4	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×#1055	C₂²	1	2	yes	—
12	C₂³×#1055	C₂²	1	2	yes	—
13	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
14	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
15	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
16	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
17	C₂×C₄⋊#1055	—	2	2	no	—
18	C₂×C₄⋊#1055	—	2	4	no	—
19	#11718116	—	2	4	no	—
20	#11718116	—	2	2	no	—
21	#11718116	—	2	4	no	—
22	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	C₈	1	4	yes	complemented
35	C₂×C₄²×C₁₃	—	2	1	no	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	—	2	2	no	—
38	C₂×C₄²×C₁₃	—	2	1	no	—
39	C₂×C₄²×C₁₃	—	2	1	no	—
40	C₂×C₄²×C₁₃	—	2	2	no	—
41	C₂×C₄²×C₁₃	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	—	2	2	no	—
44	C₂×C₄²×C₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₃	D₄	1	2	yes	—
46	C₂×C₄²×C₁₃	D₄	1	2	yes	—
47	C₂×C₄²×C₁₃	D₄	1	2	yes	—
48	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
49	C₂²×#1055	—	2	2	no	—
50	C₂²×#1055	—	2	2	no	—
51	C₂²×#1055	—	2	2	no	—
52	C₂²×#1055	—	2	2	no	—
53	C₂²×#1055	—	2	2	no	—
54	C₂²×#1055	—	2	2	no	—
55	C₂²×#1055	—	2	2	no	—
56	C₂²×#1055	—	2	2	no	—
57	C₂²×#1055	—	2	2	no	—
58	C₂²×#1055	—	2	2	no	—
59	C₂²×#1055	—	2	2	no	—
60	C₂²×#1055	—	2	2	no	—
61	C₂²×#1055	D₄	1	4	yes	—
62	C₂²×#1055	Q₈	1	4	yes	—
63	C₁₃×#95	—	2	2	no	—
64	C₁₃×#95	—	2	2	no	—
65	C₄⋊#1055	—	2	8	no	—
66	#11202	—	13	1	no	maximal, Sylow
67	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	—	2	1	no	—
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
97	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
98	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
99	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	#41	1	2	yes	—
109	C₂²×C₄×C₁₃	#41	1	2	yes	—
110	C₁₃×C₄⋊C₄	—	2	8	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	4	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	4	1	no	—
120	C₄²×C₁₃	—	4	2	no	—
121	C₄²×C₁₃	—	4	1	no	—
122	C₂×#1055	—	2	4	no	—
123	C₂×#1055	—	2	4	no	—
124	C₂×#1055	—	2	4	no	—
125	C₂×#1055	—	2	4	no	—
126	C₂×#1055	—	2	4	no	—
127	C₂×#1055	—	2	4	no	—
128	C₂×#1055	—	4	2	no	—
129	C₂×#1055	—	4	2	no	—
130	C₂×#1055	—	4	2	no	—
131	C₂×#1055	—	4	2	no	—
132	C₂×#1055	—	4	2	no	—
133	C₂×#1055	—	4	2	no	—
134	C₂×#1055	—	4	2	no	—
135	C₂×#1055	—	4	2	no	—
136	C₂²×C₄⋊C₈	—	13	1	no	—
137	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
138	C₂×#336	—	13	2	no	—
139	C₂×#336	—	13	2	no	—
140	C₂×#336	—	13	1	no	—
141	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₁₃	#117	1	1	yes	characteristic
144	C₂³×C₁₃	C₄×D₄	1	2	yes	—
145	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
146	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
148	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
149	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
150	C₂³×C₁₃	#131	1	2	yes	—
151	C₂³×C₁₃	#131	1	2	yes	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
183	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	complemented
184	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₃	#121	1	2	yes	—
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#121	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#123	1	2	yes	—
195	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
196	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
197	C₂×C₄×C₁₃	#125	1	2	yes	—
198	C₂×C₄×C₁₃	#125	1	2	yes	—
199	C₂×C₄×C₁₃	#126	1	2	yes	—
200	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
202	#1055	—	4	4	no	—
203	#1055	—	4	4	no	—
204	C₂³×C₈	—	13	2	no	—
205	C₂³×C₈	—	13	2	no	—
206	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
209	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
210	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	—	26	4	no	—
212	C₂×C₄⋊C₈	—	26	2	no	—
213	C₄×C₄⋊C₄	—	2	2	no	—
214	C₄×C₄⋊C₄	—	2	2	no	—
215	C₂×#95	Dic₁₃	1	1	yes	characteristic
216	C₂×#95	Dic₁₃	1	1	yes	characteristic
217	#336	—	26	4	no	—
218	#336	—	26	4	no	—
219	#336	—	26	2	no	—
220	C₂²×C₁₃	#380	1	1	yes	characteristic
221	C₂²×C₁₃	#386	1	1	yes	characteristic
222	C₂²×C₁₃	#387	1	2	yes	—
223	C₂²×C₁₃	#389	1	2	yes	—
224	C₂²×C₁₃	#391	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₂²×C₁₃	#407	1	1	yes	characteristic
227	C₂²×C₁₃	#408	1	1	yes	characteristic
228	C₂²×C₁₃	#408	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
230	C₂²×C₁₃	#423	1	1	yes	characteristic
231	C₂²×C₁₃	#424	1	2	yes	—
232	C₂²×C₁₃	#431	1	1	yes	characteristic
233	C₂²×C₁₃	#432	1	1	yes	characteristic
234	C₂²×C₁₃	#433	1	2	yes	—
235	C₂²×C₁₃	C₈×D₄	1	2	yes	—
236	C₂²×C₁₃	#435	1	2	yes	—
237	C₂²×C₁₃	#435	1	2	yes	—
238	C₂²×C₁₃	#436	1	2	yes	—
239	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
240	C₂²×C₁₃	#446	1	2	yes	—
241	C₂²×C₁₃	#446	1	2	yes	—
242	C₂²×C₁₃	#446	1	2	yes	—
243	C₄×C₁₃	—	2	4	no	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	#394	1	1	yes	characteristic
250	C₄×C₁₃	#395	1	1	yes	characteristic
251	C₄×C₁₃	#396	1	2	yes	—
252	C₄×C₁₃	#398	1	1	yes	characteristic
253	C₄×C₁₃	#398	1	2	yes	—
254	C₄×C₁₃	#400	1	1	yes	characteristic
255	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
256	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
257	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
259	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
260	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
262	C₂²×C₈	—	13	4	no	—
263	C₂²×C₈	—	13	4	no	—
264	C₂²×C₈	—	26	2	no	—
265	C₂²×C₈	—	26	2	no	—
266	C₂²×C₈	—	26	2	no	—
267	C₂²×C₈	—	26	2	no	—
268	C₂²×C₈	—	26	2	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	—	26	2	no	—
271	C₂²×C₈	—	26	2	no	—
272	C₂²×C₈	—	26	2	no	—
273	C₂²×C₈	—	26	2	no	—
274	C₂²×C₈	—	26	2	no	—
275	C₂²×C₈	—	26	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	#1055	1	4	yes	complemented
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	Dic₂₆	1	2	yes	—
293	C₂×C₄²	D₅₂	1	2	yes	—
294	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
295	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
296	C₄⋊C₈	—	26	8	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂×C₁₃	#1441	1	1	yes	characteristic
300	C₂×C₁₃	#1797	1	1	yes	characteristic
301	C₂×C₁₃	#1798	1	1	yes	characteristic
302	C₂×C₁₃	#1869	1	1	yes	characteristic
303	C₂×C₁₃	#1870	1	1	yes	characteristic
304	C₂×C₁₃	#1916	1	2	yes	—
305	C₂×C₁₃	#1917	1	2	yes	—
306	C₂×C₁₃	#1939	1	2	yes	—
307	C₂×C₁₃	#1940	1	2	yes	—
308	C₂×C₁₃	#1984	1	1	yes	characteristic
309	C₂×C₁₃	#1985	1	1	yes	characteristic
310	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	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	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	C₂×#1055	1	2	yes	—
334	C₂²×C₄	C₂×#1055	1	2	yes	—
335	C₂²×C₄	C₂×#1055	1	2	yes	—
336	C₂²×C₄	#6099	1	2	yes	—
337	C₂²×C₄	#6099	1	2	yes	—
338	C₂²×C₄	#6099	1	2	yes	—
339	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
340	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
341	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
342	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
343	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
345	C₂²×C₄	#6127	1	1	yes	characteristic
346	C₂²×C₄	#6127	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₁₃	1	2	yes	—
348	C₂²×C₄	#6129	1	2	yes	—
349	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
350	C₂²×C₄	#6131	1	2	yes	—
351	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
353	C₂×C₈	—	26	4	no	—
354	C₂×C₈	—	26	4	no	—
355	C₂×C₈	—	26	4	no	—
356	C₂×C₈	—	26	4	no	—
357	C₂×C₈	—	26	4	no	—
358	C₂×C₈	—	26	4	no	—
359	C₂×C₈	—	52	2	no	—
360	C₂×C₈	—	52	2	no	—
361	C₂×C₈	—	52	2	no	—
362	C₂×C₈	—	52	2	no	—
363	C₂×C₈	—	52	2	no	—
364	C₂×C₈	—	52	2	no	—
365	C₂×C₈	—	52	2	no	—
366	C₂×C₈	—	52	2	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	—	4	2	no	—
379	C₁₃	#11202	1	1	yes	characteristic, complemented, Sylow
380	C₂³	C₂²×#1055	1	1	yes	characteristic
381	C₂³	C₂×#6099	1	1	yes	characteristic
382	C₂³	C₂×#6099	1	1	yes	characteristic
383	C₂³	C₂×#6099	1	1	yes	characteristic
384	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
385	C₂³	#88180	1	1	yes	characteristic
386	C₂³	D₄×Dic₁₃	1	2	yes	—
387	C₂³	Q₈×Dic₁₃	1	2	yes	—
388	C₂³	#88202	1	2	yes	—
389	C₂³	#88202	1	2	yes	—
390	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	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	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	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	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	C₄⋊#1055	1	4	yes	complemented
422	C₂×C₄	C₂²⋊#1055	1	4	yes	—
423	C₂×C₄	#88142	1	2	yes	—
424	C₂×C₄	#88143	1	2	yes	—
425	C₂×C₄	#88144	1	2	yes	—
426	C₂×C₄	#88148	1	2	yes	—
427	C₂×C₄	#88149	1	2	yes	—
428	C₂×C₄	#88150	1	2	yes	—
429	C₂×C₄	#88151	1	2	yes	—
430	C₂×C₄	#88152	1	2	yes	—
431	C₂×C₄	#88178	1	1	yes	characteristic
432	C₂×C₄	#88178	1	1	yes	characteristic
433	C₂×C₄	#88184	1	1	yes	characteristic
434	C₂×C₄	#88184	1	1	yes	characteristic
435	C₂×C₄	#88189	1	1	yes	characteristic
436	C₂×C₄	#88191	1	1	yes	characteristic
437	C₂×C₄	#88193	1	2	yes	—
438	C₂×C₄	#88198	1	1	yes	characteristic
439	C₂×C₄	#88200	1	2	yes	—
440	C₂×C₄	#88201	1	1	yes	characteristic
441	C₈	—	52	4	no	—
442	C₈	—	52	4	no	—
443	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
444	C₂²	#11718585	1	1	yes	characteristic
445	C₂²	#11718586	1	1	yes	characteristic
446	C₂²	#11718587	1	1	yes	characteristic
447	C₂²	#11718642	1	2	yes	—
448	C₂²	#11718646	1	2	yes	—
449	C₂²	#11718660	1	2	yes	—
450	C₂²	#11718661	1	2	yes	—
451	C₂²	D₄×#1055	1	2	yes	—
452	C₂²	#11718672	1	2	yes	—
453	C₂²	#11718672	1	2	yes	—
454	C₂²	#11718673	1	2	yes	—
455	C₂²	Q₈×#1055	1	2	yes	—
456	C₂²	#11718685	1	2	yes	—
457	C₂²	#11718685	1	2	yes	—
458	C₂²	#11718685	1	2	yes	—
459	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
460	C₂²	#11718868	1	1	yes	characteristic
461	C₂²	#11718873	1	1	yes	characteristic
462	C₂²	#11718881	1	1	yes	characteristic
463	C₂²	#11718891	1	1	yes	characteristic
464	C₂²	#11718895	1	1	yes	characteristic
465	C₂²	#11718895	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	#11718640	1	1	yes	characteristic
473	C₄	#11718644	1	1	yes	characteristic
474	C₄	#11718645	1	2	yes	—
475	C₄	#11718647	1	1	yes	characteristic
476	C₄	#11718652	1	1	yes	characteristic
477	C₄	#11718655	1	2	yes	—
478	C₂	#13113089	1	1	yes	characteristic
479	C₂	#13114816	1	1	yes	characteristic
480	C₂	#13114820	1	1	yes	characteristic
481	C₂	#13115129	1	1	yes	characteristic
482	C₂	#13115134	1	1	yes	characteristic
483	C₂	#13115395	1	2	yes	—
484	C₂	#13115402	1	2	yes	—
485	C₂	#13115555	1	2	yes	—
486	C₂	#13115560	1	2	yes	—
487	C₂	#13115773	1	1	yes	characteristic
488	C₂	#13115777	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₃
commutator	C₂³×C₁₃	C₂²×C₈
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	#11202
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
34. C₂×C₁₃×C₄⋊C₄	C₈	semidirect
183. C₂×C₄×C₁₃	C₄⋊C₈	semidirect
281. C₂×C₄⋊C₄	#1055	semidirect
379. C₁₃	#11202	semidirect
421. C₂×C₄	C₄⋊#1055	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#1055	2
C₂×#11718116	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#11202	13