Subgroups — #15768885

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 550 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	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
6	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₃×#95	C₂	1	1	yes	maximal, 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	1	yes	characteristic
12	C₂³×#1055	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₂³×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#95	C₄	1	2	yes	—
16	C₂×C₁₃×#95	C₄	1	2	yes	—
17	C₂×C₄⋊#1055	—	2	2	no	—
18	C₂×C₄⋊#1055	—	2	2	no	—
19	C₂×C₄⋊#1055	C₄	1	4	yes	complemented
20	C₂×C₄×#1055	—	2	2	no	—
21	C₂×C₄×#1055	—	2	2	no	—
22	C₂×C₄×#1055	—	2	2	no	—
23	#11718116	—	2	2	no	—
24	#11718116	—	2	2	no	—
25	#11718116	—	2	2	no	—
26	#11718116	C₄	1	4	yes	complemented
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	—	2	1	no	—
33	C₂×C₄²×C₁₃	—	2	1	no	—
34	C₂×C₄²×C₁₃	—	2	1	no	—
35	C₂×C₄²×C₁₃	—	2	1	no	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	—	2	1	no	—
39	C₂×C₄²×C₁₃	—	2	1	no	—
40	C₂×C₄²×C₁₃	—	2	1	no	—
41	C₂×C₄²×C₁₃	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	—	2	1	no	—
45	C₂×C₄²×C₁₃	—	2	1	no	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	D₄	1	2	yes	—
49	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
50	C₂²×#1055	—	2	1	no	—
51	C₂²×#1055	—	2	1	no	—
52	C₂²×#1055	—	2	1	no	—
53	C₂²×#1055	—	2	1	no	—
54	C₂²×#1055	—	2	1	no	—
55	C₂²×#1055	—	2	1	no	—
56	C₂²×#1055	—	2	1	no	—
57	C₂²×#1055	—	2	1	no	—
58	C₂²×#1055	—	2	1	no	—
59	C₂²×#1055	—	2	1	no	—
60	C₂²×#1055	—	2	1	no	—
61	C₂²×#1055	—	2	1	no	—
62	C₂²×#1055	—	2	1	no	—
63	C₂²×#1055	—	2	1	no	—
64	C₂²×#1055	—	2	1	no	—
65	C₂²×#1055	—	2	1	no	—
66	C₂²×#1055	—	2	1	no	—
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	—	2	1	no	—
69	C₂²×#1055	—	2	1	no	—
70	C₂²×#1055	C₂×C₄	1	2	yes	—
71	C₂²×#1055	C₂×C₄	1	2	yes	—
72	C₂²×#1055	C₂×C₄	1	2	yes	—
73	C₂²×#1055	C₂×C₄	1	2	yes	—
74	C₂²×#1055	D₄	1	2	yes	—
75	C₂²×#1055	D₄	1	2	yes	—
76	C₂²×#1055	D₄	1	2	yes	—
77	C₂²×#1055	Q₈	1	2	yes	—
78	C₁₃×#95	—	2	4	no	—
79	C₁₃×#95	C₈	1	8	yes	complemented
80	C₄⋊#1055	—	2	8	no	—
81	C₄×#1055	—	2	8	no	—
82	#10876	—	13	1	no	maximal, Sylow
83	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	1	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	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	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	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
102	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
103	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
107	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₄²×C₁₃	—	2	2	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	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	4	1	no	—
131	C₄²×C₁₃	—	4	1	no	—
132	C₄²×C₁₃	—	4	1	no	—
133	C₄²×C₁₃	—	4	1	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	2	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	2	2	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	2	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	—	2	2	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	—	4	1	no	—
153	C₂×#1055	—	4	1	no	—
154	C₂×#1055	—	4	1	no	—
155	C₂×#1055	—	4	1	no	—
156	C₂×#1055	—	4	1	no	—
157	C₂×#1055	—	4	1	no	—
158	C₂×#1055	—	4	1	no	—
159	C₂×#1055	—	4	1	no	—
160	C₂×#1055	C₂²⋊C₄	1	4	yes	—
161	C₂×#1055	C₄⋊C₄	1	4	yes	—
162	C₂²×C₄⋊C₈	—	13	1	no	—
163	C₂²×C₄×C₈	—	13	1	no	—
164	C₂×#336	—	13	1	no	—
165	C₂×#336	—	13	1	no	—
166	C₂×#336	—	13	1	no	—
167	C₂×#336	—	13	1	no	—
168	C₄×#95	D₁₃	1	1	yes	characteristic
169	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₃	#117	1	1	yes	characteristic
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
176	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
177	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
178	C₂³×C₁₃	#131	1	2	yes	—
179	C₂³×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	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	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	complemented
203	C₂×C₄×C₁₃	C₄⋊C₈	1	8	yes	complemented
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
232	#1055	—	2	4	no	—
233	#1055	—	2	4	no	—
234	#1055	—	4	2	no	—
235	#1055	—	4	2	no	—
236	C₂³×C₈	—	13	1	no	—
237	C₂³×C₈	—	13	1	no	—
238	C₂³×C₈	—	13	1	no	—
239	C₂³×C₈	—	13	1	no	—
240	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
241	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	13	4	no	—
244	C₂×C₄⋊C₈	—	26	2	no	—
245	C₂×C₄⋊C₈	—	26	2	no	—
246	C₂×C₄×C₈	—	26	2	no	—
247	C₂×C₄×C₈	—	26	2	no	—
248	C₂×C₄×C₈	—	26	2	no	—
249	C₂×#95	Dic₁₃	1	2	yes	—
250	C₂×#95	Dic₁₃	1	2	yes	—
251	#336	—	13	4	no	—
252	#336	—	26	2	no	—
253	#336	—	26	2	no	—
254	#336	—	26	2	no	—
255	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₃	#385	1	1	yes	characteristic
259	C₂²×C₁₃	#387	1	1	yes	characteristic
260	C₂²×C₁₃	#388	1	1	yes	characteristic
261	C₂²×C₁₃	#389	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
263	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
264	C₂²×C₁₃	#405	1	1	yes	characteristic
265	C₂²×C₁₃	#405	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
267	C₂²×C₁₃	#424	1	2	yes	—
268	C₂²×C₁₃	#431	1	2	yes	—
269	C₂²×C₁₃	#433	1	2	yes	—
270	C₂²×C₁₃	C₈×D₄	1	2	yes	—
271	C₂²×C₁₃	C₈×D₄	1	2	yes	—
272	C₂²×C₁₃	C₈×D₄	1	2	yes	—
273	C₂²×C₁₃	#435	1	2	yes	—
274	C₂²×C₁₃	#435	1	2	yes	—
275	C₂²×C₁₃	#436	1	2	yes	—
276	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
277	C₂²×C₁₃	#446	1	2	yes	—
278	C₄×C₁₃	—	2	8	no	—
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	#385	1	1	yes	characteristic
283	C₄×C₁₃	#386	1	1	yes	characteristic
284	C₄×C₁₃	#387	1	1	yes	characteristic
285	C₄×C₁₃	#387	1	1	yes	characteristic
286	C₄×C₁₃	#387	1	1	yes	characteristic
287	C₄×C₁₃	#388	1	1	yes	characteristic
288	C₄×C₁₃	#389	1	1	yes	characteristic
289	C₄×C₁₃	#391	1	1	yes	characteristic
290	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
291	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
294	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
295	C₂²×C₈	—	13	2	no	—
296	C₂²×C₈	—	13	2	no	—
297	C₂²×C₈	—	13	2	no	—
298	C₂²×C₈	—	13	2	no	—
299	C₂²×C₈	—	13	2	no	—
300	C₂²×C₈	—	13	2	no	—
301	C₂²×C₈	—	13	2	no	—
302	C₂²×C₈	—	13	2	no	—
303	C₂²×C₈	—	26	1	no	—
304	C₂²×C₈	—	26	1	no	—
305	C₂²×C₈	—	26	1	no	—
306	C₂²×C₈	—	26	1	no	—
307	C₂²×C₈	—	26	1	no	—
308	C₂²×C₈	—	26	1	no	—
309	C₂²×C₈	—	26	1	no	—
310	C₂²×C₈	—	26	1	no	—
311	C₂²×C₈	—	26	1	no	—
312	C₂²×C₈	—	26	1	no	—
313	C₂²×C₈	—	26	1	no	—
314	C₂²×C₈	—	26	1	no	—
315	C₂²×C₈	—	26	1	no	—
316	C₂²×C₈	—	26	1	no	—
317	C₂²×C₈	—	26	1	no	—
318	C₂²×C₈	—	26	1	no	—
319	C₂²×C₈	—	26	1	no	—
320	C₂²×C₈	—	26	1	no	—
321	C₂²×C₈	—	26	1	no	—
322	C₂²×C₈	—	26	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	Dic₂₆	1	2	yes	—
338	C₂×C₄²	C₄×D₁₃	1	2	yes	—
339	C₂×C₄²	C₄×D₁₃	1	2	yes	—
340	C₂×C₄²	D₅₂	1	2	yes	—
341	C₄⋊C₈	—	26	8	no	—
342	C₄×C₈	—	26	8	no	—
343	#95	—	2	4	no	—
344	#95	#1055	1	8	yes	complemented
345	C₂×C₁₃	#1436	1	1	yes	characteristic
346	C₂×C₁₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₁₃	#1753	1	1	yes	characteristic
348	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
349	C₂×C₁₃	#1768	1	1	yes	characteristic
350	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₁₃	#1771	1	1	yes	characteristic
352	C₂×C₁₃	#1850	1	2	yes	—
353	C₂×C₁₃	#1916	1	2	yes	—
354	C₂×C₁₃	#1923	1	2	yes	—
355	C₂×C₁₃	#1939	1	2	yes	—
356	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₂×#1055	1	4	yes	—
375	C₂²×C₄	C₂×#1055	1	4	yes	—
376	C₂²×C₄	C₂×#1055	1	4	yes	—
377	C₂²×C₄	#6099	1	4	yes	—
378	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
379	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
380	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
381	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
385	C₂²×C₄	#6127	1	1	yes	characteristic
386	C₂²×C₄	#6127	1	1	yes	characteristic
387	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
388	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
389	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
390	C₂²×C₄	#6129	1	1	yes	characteristic
391	C₂²×C₄	#6129	1	1	yes	characteristic
392	C₂²×C₄	#6129	1	1	yes	characteristic
393	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
394	C₂²×C₄	#6131	1	1	yes	characteristic
395	C₂×C₈	—	13	4	no	—
396	C₂×C₈	—	13	4	no	—
397	C₂×C₈	—	26	2	no	—
398	C₂×C₈	—	26	2	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	—	26	2	no	—
401	C₂×C₈	—	26	2	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	2	no	—
404	C₂×C₈	—	26	2	no	—
405	C₂×C₈	—	26	2	no	—
406	C₂×C₈	—	26	2	no	—
407	C₂×C₈	—	26	2	no	—
408	C₂×C₈	—	26	2	no	—
409	C₂×C₈	—	26	2	no	—
410	C₂×C₈	—	26	2	no	—
411	C₂×C₈	—	26	2	no	—
412	C₂×C₈	—	26	2	no	—
413	C₂×C₈	—	26	2	no	—
414	C₂×C₈	—	26	2	no	—
415	C₂×C₈	—	52	1	no	—
416	C₂×C₈	—	52	1	no	—
417	C₂×C₈	—	52	1	no	—
418	C₂×C₈	—	52	1	no	—
419	C₂×C₈	—	52	1	no	—
420	C₂×C₈	—	52	1	no	—
421	C₂×C₈	—	52	1	no	—
422	C₂×C₈	—	52	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	4	1	no	—
433	C₄²	—	4	1	no	—
434	C₄²	—	4	1	no	—
435	C₁₃	#10876	1	1	yes	characteristic, complemented, Sylow
436	C₂³	C₂²×#1055	1	2	yes	—
437	C₂³	C₂×#6099	1	2	yes	—
438	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
439	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
440	C₂³	#88180	1	1	yes	characteristic
441	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
442	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
443	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
444	C₂³	Q₈×Dic₁₃	1	1	yes	characteristic
445	C₂³	#88202	1	2	yes	—
446	C₂³	#88202	1	2	yes	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	C₄×#1055	1	4	yes	complemented
470	C₂×C₄	C₄⋊#1055	1	8	yes	complemented
471	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
472	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
473	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
474	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
475	C₂×C₄	#88131	1	1	yes	characteristic
476	C₂×C₄	#88132	1	1	yes	characteristic
477	C₂×C₄	#88132	1	1	yes	characteristic
478	C₂×C₄	#88133	1	1	yes	characteristic
479	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
480	C₂×C₄	#88135	1	1	yes	characteristic
481	C₂×C₄	#88135	1	1	yes	characteristic
482	C₂×C₄	#88136	1	1	yes	characteristic
483	C₂×C₄	#88137	1	1	yes	characteristic
484	C₂×C₄	#88138	1	1	yes	characteristic
485	C₂×C₄	#88139	1	1	yes	characteristic
486	C₂×C₄	#88140	1	1	yes	characteristic
487	C₂×C₄	#88141	1	1	yes	characteristic
488	C₂×C₄	#88142	1	1	yes	characteristic
489	C₂×C₄	#88143	1	1	yes	characteristic
490	C₂×C₄	#88144	1	1	yes	characteristic
491	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
492	C₂×C₄	#88146	1	1	yes	characteristic
493	C₂×C₄	#88147	1	1	yes	characteristic
494	C₂×C₄	#88148	1	1	yes	characteristic
495	C₂×C₄	#88149	1	1	yes	characteristic
496	C₂×C₄	#88150	1	1	yes	characteristic
497	C₂×C₄	#88151	1	1	yes	characteristic
498	C₂×C₄	#88152	1	1	yes	characteristic
499	C₈	—	26	4	no	—
500	C₈	—	26	4	no	—
501	C₈	—	52	2	no	—
502	C₈	—	52	2	no	—
503	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
504	C₂²	C₄×#6099	1	1	yes	characteristic
505	C₂²	C₂×C₄⋊#1055	1	2	yes	—
506	C₂²	#11718586	1	2	yes	—
507	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
508	C₂²	C₂²⋊C₄×Dic₁₃	1	1	yes	characteristic
509	C₂²	#11718611	1	1	yes	characteristic
510	C₂²	#11718612	1	1	yes	characteristic
511	C₂²	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
512	C₂²	#11718642	1	1	yes	characteristic
513	C₂²	#11718646	1	1	yes	characteristic
514	C₂²	#11718658	1	1	yes	characteristic
515	C₂²	#11718658	1	1	yes	characteristic
516	C₂²	#11718660	1	2	yes	—
517	C₂²	#11718661	1	2	yes	—
518	C₂²	D₄×#1055	1	2	yes	—
519	C₂²	D₄×#1055	1	2	yes	—
520	C₂²	D₄×#1055	1	2	yes	—
521	C₂²	#11718672	1	2	yes	—
522	C₂²	#11718672	1	2	yes	—
523	C₂²	#11718673	1	2	yes	—
524	C₂²	Q₈×#1055	1	2	yes	—
525	C₂²	#11718685	1	2	yes	—
526	C₄	—	2	8	no	—
527	C₄	—	2	4	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	2	no	—
530	C₄	#11718307	1	1	yes	characteristic
531	C₄	#11718308	1	1	yes	characteristic
532	C₄	#11718314	1	1	yes	characteristic
533	C₄	#11718315	1	1	yes	characteristic
534	C₄	#11718316	1	1	yes	characteristic
535	C₄	#11718326	1	1	yes	characteristic
536	C₄	#11718329	1	1	yes	characteristic
537	C₄	#11718331	1	1	yes	characteristic
538	C₂	#13113070	1	1	yes	characteristic
539	C₂	C₂²⋊C₄×#1055	1	1	yes	characteristic
540	C₂	#13114620	1	1	yes	characteristic
541	C₂	C₄×C₄⋊#1055	1	1	yes	characteristic
542	C₂	#13114693	1	1	yes	characteristic
543	C₂	C₄⋊C₄×#1055	1	1	yes	characteristic
544	C₂	#13114711	1	1	yes	characteristic
545	C₂	#13115016	1	2	yes	—
546	C₂	#13115395	1	2	yes	—
547	C₂	#13115444	1	2	yes	—
548	C₂	#13115555	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₄×C₁₃×#95	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₄×#95	D₁₃
hypocenter	C₁₃	#10876
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₄×#95

Complements

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

N	H ≅ G/N	type
19. C₂×C₄⋊#1055	C₄	semidirect
26. #11718116	C₄	semidirect
79. C₁₃×#95	C₈	semidirect
202. C₂×C₄×C₁₃	C₄×C₈	semidirect
203. C₂×C₄×C₁₃	C₄⋊C₈	semidirect
344. #95	#1055	semidirect
435. C₁₃	#10876	semidirect
469. C₂×C₄	C₄×#1055	semidirect
470. 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
C₂²×C₄×#1055	2
C₂×#11718116	2
C₄×C₁₃×#95	2
#10876	13