Subgroups — C₂²×#11719335 #16769848

Order 3328.

14462 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719335	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88201	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88148	C₂	1	2	yes	maximal, complemented
6	C₂²×#88149	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88149	C₂	1	2	yes	maximal, complemented
8	C₂²×#88136	C₂	1	2	yes	maximal, complemented
9	C₂²×#88147	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
17	C₂²×#6131	—	2	16	no	—
18	C₂²×#6131	C₂²	1	24	yes	complemented
19	C₂³×D₅₂	—	2	16	no	—
20	C₂³×D₅₂	C₂²	1	2	yes	—
21	C₂³×D₅₂	C₂²	1	1	yes	characteristic
22	C₂³×D₅₂	C₂²	1	1	yes	characteristic
23	C₂³×D₅₂	C₂²	1	24	yes	complemented
24	C₂³×D₅₂	C₂²	1	2	yes	complemented
25	C₂³×D₅₂	C₂²	1	2	yes	complemented
26	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
27	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂×#88201	C₂²	1	24	yes	complemented
35	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
36	C₂²×#6103	C₂²	1	2	yes	complemented
37	C₂²×#6103	C₂²	1	2	yes	complemented
38	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
39	C₂²×#6103	C₂²	1	2	yes	complemented
40	C₂²×#6103	C₂²	1	2	yes	complemented
41	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	#11719335	C₂²	1	256	yes	direct product factor
44	C₂×#88149	C₂²	1	24	yes	complemented
45	C₂×#88149	C₂²	1	48	yes	complemented
46	C₂×#88148	C₂²	1	48	yes	complemented
47	C₂×#88147	C₂²	1	24	yes	complemented
48	C₂×#88136	C₂²	1	48	yes	complemented
49	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂⁴×D₁₃	—	2	16	no	—
52	C₂⁴×D₁₃	—	2	16	no	—
53	C₂⁴×D₁₃	—	4	8	no	—
54	C₂⁴×D₁₃	C₂³	1	2	yes	—
55	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
56	C₂⁴×D₁₃	C₂³	1	24	yes	—
57	C₂⁴×D₁₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃	—	2	8	no	—
59	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₂²⋊D₁₃	—	2	8	no	—
67	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
68	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
69	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
70	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂×#6131	—	2	192	no	—
72	C₂×#6131	C₂³	1	64	yes	complemented
73	C₂²×D₅₂	—	2	16	no	—
74	C₂²×D₅₂	—	2	16	no	—
75	C₂²×D₅₂	—	2	8	no	—
76	C₂²×D₅₂	—	2	192	no	—
77	C₂²×D₅₂	—	4	8	no	—
78	C₂²×D₅₂	D₄	1	16	yes	complemented
79	C₂²×D₅₂	C₂³	1	24	yes	—
80	C₂²×D₅₂	C₂³	1	12	yes	—
81	C₂²×D₅₂	C₂³	1	12	yes	—
82	C₂²×D₅₂	C₂³	1	64	yes	complemented
83	C₂²×D₅₂	C₂³	1	24	yes	complemented
84	C₂²×D₅₂	C₂³	1	24	yes	complemented
85	C₂²×C₄×D₁₃	—	2	16	no	—
86	C₂²×C₄×D₁₃	—	2	8	no	—
87	C₂²×C₄×D₁₃	—	4	8	no	—
88	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
89	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
90	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
91	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
95	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
96	#88201	C₂³	1	64	yes	complemented
97	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
98	C₂×#6103	C₂³	1	24	yes	complemented
99	C₂×#6103	C₂³	1	24	yes	complemented
100	C₂×#6103	C₂³	1	24	yes	complemented
101	C₂×#6103	C₂³	1	24	yes	complemented
102	C₂×#6103	C₂³	1	12	yes	complemented
103	C₂×#6101	C₂³	1	12	yes	complemented
104	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
105	#88149	C₂³	1	64	yes	complemented
106	#88149	C₂³	1	128	yes	complemented
107	#88148	C₂³	1	128	yes	complemented
108	#88147	C₂³	1	64	yes	complemented
109	#88136	C₂³	1	128	yes	complemented
110	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	complemented
111	C₂²×#546	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	#41	1	8	yes	complemented
115	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂³×D₁₃	—	2	8	no	—
118	C₂³×D₁₃	—	2	8	no	—
119	C₂³×D₁₃	—	2	4	no	—
120	C₂³×D₁₃	—	2	8	no	—
121	C₂³×D₁₃	—	2	4	no	—
122	C₂³×D₁₃	—	2	8	no	—
123	C₂³×D₁₃	—	2	96	no	—
124	C₂³×D₁₃	—	2	4	no	—
125	C₂³×D₁₃	—	2	8	no	—
126	C₂³×D₁₃	—	2	96	no	—
127	C₂³×D₁₃	—	4	48	no	—
128	C₂³×D₁₃	—	4	128	no	—
129	C₂³×D₁₃	C₂×D₄	1	16	yes	—
130	C₂³×D₁₃	C₂⁴	1	12	yes	—
131	C₂³×D₁₃	C₂⁴	1	6	yes	—
132	C₂³×D₁₃	C₂⁴	1	32	yes	—
133	C₂³×D₁₃	C₂⁴	1	12	yes	—
134	C₂×Q₈×C₁₃	—	2	48	no	—
135	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	48	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
146	C₂×C₂²⋊D₁₃	—	2	48	no	—
147	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
148	C₂²×Dic₁₃	—	2	4	no	—
149	C₂²×Dic₁₃	—	2	4	no	—
150	C₂²×Dic₁₃	—	2	4	no	—
151	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
152	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
153	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
154	#6131	—	2	256	no	—
155	C₂×D₅₂	—	2	96	no	—
156	C₂×D₅₂	—	2	96	no	—
157	C₂×D₅₂	—	2	48	no	—
158	C₂×D₅₂	—	2	256	no	—
159	C₂×D₅₂	—	4	48	no	—
160	C₂×D₅₂	C₂×D₄	1	96	yes	complemented
161	C₂×D₅₂	C₂⁴	1	32	yes	—
162	C₂×D₅₂	C₂⁴	1	16	yes	—
163	C₂×D₅₂	C₂⁴	1	16	yes	—
164	C₂×D₅₂	C₂⁴	1	32	yes	complemented
165	C₂×D₅₂	C₂⁴	1	32	yes	complemented
166	C₂×C₄×D₁₃	—	2	96	no	—
167	C₂×C₄×D₁₃	—	2	48	no	—
168	C₂×C₄×D₁₃	—	4	48	no	—
169	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
170	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
171	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
172	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
173	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
174	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
175	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
176	#6103	C₂⁴	1	32	yes	complemented
177	#6103	C₂⁴	1	32	yes	complemented
178	#6103	C₂⁴	1	32	yes	complemented
179	#6103	C₂⁴	1	32	yes	complemented
180	#6103	C₂⁴	1	16	yes	complemented
181	#6101	C₂⁴	1	16	yes	complemented
182	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
183	C₂³×#41	—	13	1	no	—
184	C₂⁴×D₄	—	13	1	no	—
185	C₂×#546	—	13	48	no	—
186	C₂²×#124	—	13	1	no	—
187	C₂²×#123	—	13	2	no	—
188	C₂²×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic, complemented
189	C₂²×#121	—	13	1	no	—
190	C₂²×#121	—	13	2	no	—
191	C₂²×#120	—	13	2	no	—
192	C₂²×C₄×D₄	—	13	1	no	—
193	C₂²×C₄×D₄	—	13	1	no	—
194	C₂³×C₂²⋊C₄	—	13	2	no	—
195	C₂³×C₁₃	—	2	32	no	—
196	C₂³×C₁₃	—	2	12	no	—
197	C₂³×C₁₃	—	2	12	no	—
198	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
199	C₂³×C₁₃	C₂×#41	1	4	yes	—
200	C₂³×C₁₃	C₂×#41	1	24	yes	complemented
201	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
202	C₂³×C₁₃	C₂⁵	1	4	yes	—
203	C₂³×C₁₃	C₂⁵	1	3	yes	—
204	C₂²×D₁₃	—	2	64	no	—
205	C₂²×D₁₃	—	2	24	no	—
206	C₂²×D₁₃	—	2	24	no	—
207	C₂²×D₁₃	—	2	12	no	—
208	C₂²×D₁₃	—	2	24	no	—
209	C₂²×D₁₃	—	2	12	no	—
210	C₂²×D₁₃	—	2	24	no	—
211	C₂²×D₁₃	—	2	64	no	—
212	C₂²×D₁₃	—	2	12	no	—
213	C₂²×D₁₃	—	2	24	no	—
214	C₂²×D₁₃	—	2	64	no	—
215	C₂²×D₁₃	—	4	32	no	—
216	C₂²×D₁₃	—	4	384	no	—
217	C₂²×D₁₃	—	4	16	no	—
218	C₂²×D₁₃	—	4	32	no	—
219	C₂²×D₁₃	C₂²×D₄	1	48	yes	—
220	C₂²×D₁₃	C₂⁵	1	8	yes	—
221	C₂²×D₁₃	C₂⁵	1	4	yes	—
222	C₂²×D₁₃	C₂⁵	1	8	yes	—
223	Q₈×C₁₃	—	2	32	no	—
224	C₂×C₄×C₁₃	—	2	24	no	—
225	C₂×C₄×C₁₃	—	2	12	no	—
226	C₂×C₄×C₁₃	—	2	24	no	—
227	C₂×C₄×C₁₃	—	2	32	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
229	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
233	C₂²⋊D₁₃	—	2	32	no	—
234	C₂×Dic₁₃	—	2	12	no	—
235	C₂×Dic₁₃	—	2	12	no	—
236	C₂×Dic₁₃	—	2	12	no	—
237	C₂×Dic₁₃	C₂⁵	1	4	yes	—
238	C₂×Dic₁₃	C₂⁵	1	4	yes	—
239	C₂×Dic₁₃	C₂⁵	1	4	yes	—
240	D₅₂	—	2	64	no	—
241	D₅₂	—	2	64	no	—
242	D₅₂	—	2	32	no	—
243	D₅₂	—	4	32	no	—
244	D₅₂	C₂²×D₄	1	64	yes	complemented
245	C₄×D₁₃	—	2	64	no	—
246	C₄×D₁₃	—	2	32	no	—
247	C₄×D₁₃	—	4	32	no	—
248	C₂⁶	—	13	2	no	—
249	C₂²×#41	—	13	24	no	—
250	C₂²×#41	—	26	16	no	—
251	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
252	C₂³×D₄	—	13	1	no	—
253	C₂³×D₄	—	13	1	no	—
254	C₂³×D₄	—	13	2	no	—
255	C₂³×D₄	—	13	1	no	—
256	C₂³×D₄	—	13	24	no	—
257	C₂³×D₄	—	13	2	no	—
258	C₂³×D₄	—	13	2	no	—
259	C₂³×D₄	—	26	16	no	—
260	C₂⁴×C₄	—	13	2	no	—
261	C₂⁴×C₄	—	13	1	no	—
262	C₂⁴×C₄	—	13	2	no	—
263	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
264	#546	—	13	256	no	—
265	C₂×#124	—	13	24	no	—
266	C₂×#123	—	13	48	no	—
267	C₂×C₂²⋊Q₈	C₂×D₁₃	1	24	yes	complemented
268	C₂×#121	—	13	24	no	—
269	C₂×#121	—	13	48	no	—
270	C₂×#120	—	13	48	no	—
271	C₂×C₄×D₄	—	13	24	no	—
272	C₂×C₄×D₄	—	13	24	no	—
273	C₂²×C₄⋊C₄	—	13	1	no	—
274	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
275	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
276	C₂²×C₂²⋊C₄	—	13	1	no	—
277	C₂²×C₂²⋊C₄	—	13	2	no	—
278	C₂²×C₂²⋊C₄	—	13	2	no	—
279	C₂²×C₂²⋊C₄	—	13	2	no	—
280	C₂²×C₂²⋊C₄	—	13	1	no	—
281	C₂²×C₂²⋊C₄	—	13	2	no	—
282	C₂²×C₂²⋊C₄	—	13	48	no	—
283	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
284	C₂²×C₄²	—	13	1	no	—
285	C₂²×C₁₃	—	2	4	no	—
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	48	no	—
288	C₂²×C₁₃	#546	1	16	yes	complemented
289	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
290	C₂²×C₁₃	C₂²×#41	1	6	yes	—
291	C₂²×C₁₃	C₂²×#41	1	8	yes	complemented
292	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
293	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
294	C₂×D₁₃	—	2	8	no	—
295	C₂×D₁₃	—	2	8	no	—
296	C₂×D₁₃	—	2	96	no	—
297	C₂×D₁₃	—	2	4	no	—
298	C₂×D₁₃	—	2	8	no	—
299	C₂×D₁₃	—	2	4	no	—
300	C₂×D₁₃	—	2	8	no	—
301	C₂×D₁₃	—	2	4	no	—
302	C₂×D₁₃	—	2	8	no	—
303	C₂×D₁₃	—	4	128	no	—
304	C₂×D₁₃	—	4	24	no	—
305	C₂×D₁₃	—	4	48	no	—
306	C₂×D₁₃	C₂³×D₄	1	16	yes	—
307	C₄×C₁₃	—	2	8	no	—
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	8	no	—
310	C₄×C₁₃	C₂³×D₄	1	8	yes	—
311	Dic₁₃	—	2	4	no	—
312	Dic₁₃	—	2	4	no	—
313	Dic₁₃	—	2	4	no	—
314	C₂⁵	—	13	2	no	—
315	C₂⁵	—	13	2	no	—
316	C₂⁵	—	13	1	no	—
317	C₂⁵	—	13	24	no	—
318	C₂⁵	—	26	16	no	—
319	C₂⁵	—	26	16	no	—
320	C₂⁵	—	52	8	no	—
321	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
322	C₂×#41	—	13	64	no	—
323	C₂×#41	—	26	192	no	—
324	C₂²×Q₈	—	2	8	no	—
325	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
326	C₂²×D₄	—	13	12	no	—
327	C₂²×D₄	—	13	16	no	—
328	C₂²×D₄	—	13	12	no	—
329	C₂²×D₄	—	13	24	no	—
330	C₂²×D₄	—	13	24	no	—
331	C₂²×D₄	—	13	12	no	—
332	C₂²×D₄	—	13	64	no	—
333	C₂²×D₄	—	13	24	no	—
334	C₂²×D₄	—	26	192	no	—
335	C₂²×D₄	—	26	16	no	—
336	C₂²×D₄	—	26	16	no	—
337	C₂²×D₄	—	26	8	no	—
338	C₂²×D₄	—	26	8	no	—
339	C₂²×D₄	—	52	8	no	—
340	C₂³×C₄	—	2	8	no	—
341	C₂³×C₄	—	13	1	no	—
342	C₂³×C₄	—	13	1	no	—
343	C₂³×C₄	—	13	1	no	—
344	C₂³×C₄	—	13	24	no	—
345	C₂³×C₄	—	13	12	no	—
346	C₂³×C₄	—	13	24	no	—
347	C₂³×C₄	—	26	16	no	—
348	C₂³×C₄	—	26	8	no	—
349	C₂³×C₄	—	52	8	no	—
350	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
351	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
352	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
353	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
355	#124	—	13	64	no	—
356	#123	—	13	128	no	—
357	C₂²⋊Q₈	C₂²×D₁₃	1	64	yes	complemented
358	#121	—	13	64	no	—
359	#121	—	13	128	no	—
360	#120	—	13	128	no	—
361	C₄×D₄	—	13	64	no	—
362	C₄×D₄	—	13	64	no	—
363	C₂×C₄⋊C₄	—	13	12	no	—
364	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
365	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
366	C₂×C₂²⋊C₄	—	13	12	no	—
367	C₂×C₂²⋊C₄	—	13	24	no	—
368	C₂×C₂²⋊C₄	—	13	24	no	—
369	C₂×C₂²⋊C₄	—	13	24	no	—
370	C₂×C₂²⋊C₄	—	13	12	no	—
371	C₂×C₂²⋊C₄	—	13	24	no	—
372	C₂×C₂²⋊C₄	—	13	128	no	—
373	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
374	C₂×C₄²	—	13	12	no	—
375	C₂×C₁₃	—	2	8	no	—
376	C₂×C₁₃	C₂×#546	1	12	yes	complemented
377	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
378	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
379	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
380	D₁₃	—	2	16	no	—
381	D₁₃	—	4	4	no	—
382	D₁₃	—	4	8	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	13	16	no	—
386	C₂⁴	—	13	12	no	—
387	C₂⁴	—	13	12	no	—
388	C₂⁴	—	13	6	no	—
389	C₂⁴	—	13	32	no	—
390	C₂⁴	—	26	96	no	—
391	C₂⁴	—	26	8	no	—
392	C₂⁴	—	26	8	no	—
393	C₂⁴	—	26	4	no	—
394	C₂⁴	—	26	8	no	—
395	C₂⁴	—	26	4	no	—
396	C₂⁴	—	26	8	no	—
397	C₂⁴	—	26	96	no	—
398	C₂⁴	—	26	4	no	—
399	C₂⁴	—	26	8	no	—
400	C₂⁴	—	52	48	no	—
401	C₂⁴	—	52	128	no	—
402	C₂⁴	#6131	1	8	yes	complemented
403	C₂⁴	C₂³×D₁₃	1	6	yes	—
404	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
405	#41	—	26	256	no	—
406	C₂×Q₈	—	2	48	no	—
407	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
408	C₂×D₄	—	13	16	no	—
409	C₂×D₄	—	13	96	no	—
410	C₂×D₄	—	13	16	no	—
411	C₂×D₄	—	13	32	no	—
412	C₂×D₄	—	13	32	no	—
413	C₂×D₄	—	13	16	no	—
414	C₂×D₄	—	13	32	no	—
415	C₂×D₄	—	26	256	no	—
416	C₂×D₄	—	26	96	no	—
417	C₂×D₄	—	26	96	no	—
418	C₂×D₄	—	26	48	no	—
419	C₂×D₄	—	26	48	no	—
420	C₂×D₄	—	52	48	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	48	no	—
425	C₂²×C₄	—	13	6	no	—
426	C₂²×C₄	—	13	6	no	—
427	C₂²×C₄	—	13	6	no	—
428	C₂²×C₄	—	13	32	no	—
429	C₂²×C₄	—	13	16	no	—
430	C₂²×C₄	—	13	32	no	—
431	C₂²×C₄	—	26	96	no	—
432	C₂²×C₄	—	26	4	no	—
433	C₂²×C₄	—	26	4	no	—
434	C₂²×C₄	—	26	4	no	—
435	C₂²×C₄	—	26	48	no	—
436	C₂²×C₄	—	52	48	no	—
437	C₂²×C₄	D₄×D₁₃	1	8	yes	—
438	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
439	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
440	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
441	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
442	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
443	C₄⋊C₄	—	13	16	no	—
444	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
445	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
446	C₂²⋊C₄	—	13	16	no	—
447	C₂²⋊C₄	—	13	32	no	—
448	C₂²⋊C₄	—	13	32	no	—
449	C₂²⋊C₄	—	13	32	no	—
450	C₂²⋊C₄	—	13	16	no	—
451	C₂²⋊C₄	—	13	32	no	—
452	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
453	C₄²	—	13	16	no	—
454	C₁₃	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	32	no	—
456	C₂³	—	2	12	no	—
457	C₂³	—	2	12	no	—
458	C₂³	—	13	48	no	—
459	C₂³	—	13	8	no	—
460	C₂³	—	13	8	no	—
461	C₂³	—	13	4	no	—
462	C₂³	—	26	64	no	—
463	C₂³	—	26	64	no	—
464	C₂³	—	26	24	no	—
465	C₂³	—	26	24	no	—
466	C₂³	—	26	12	no	—
467	C₂³	—	26	24	no	—
468	C₂³	—	26	12	no	—
469	C₂³	—	26	24	no	—
470	C₂³	—	26	64	no	—
471	C₂³	—	26	12	no	—
472	C₂³	—	26	24	no	—
473	C₂³	—	52	32	no	—
474	C₂³	—	52	384	no	—
475	C₂³	—	52	32	no	—
476	C₂³	—	52	16	no	—
477	C₂³	C₂×D₄×D₁₃	1	4	yes	—
478	C₂³	C₂×#6131	1	4	yes	—
479	C₂³	C₂×#6131	1	24	yes	complemented
480	C₂³	#88256	1	4	yes	—
481	C₂³	C₂⁴×D₁₃	1	4	yes	—
482	C₂³	C₂⁴×D₁₃	1	3	yes	—
483	Q₈	—	2	32	no	—
484	D₄	—	13	64	no	—
485	D₄	—	26	64	no	—
486	D₄	—	26	64	no	—
487	D₄	—	26	32	no	—
488	D₄	—	26	32	no	—
489	D₄	—	52	32	no	—
490	C₂×C₄	—	2	12	no	—
491	C₂×C₄	—	2	24	no	—
492	C₂×C₄	—	2	24	no	—
493	C₂×C₄	—	2	32	no	—
494	C₂×C₄	—	13	4	no	—
495	C₂×C₄	—	13	4	no	—
496	C₂×C₄	—	13	4	no	—
497	C₂×C₄	—	26	64	no	—
498	C₂×C₄	—	26	12	no	—
499	C₂×C₄	—	26	12	no	—
500	C₂×C₄	—	26	12	no	—
501	C₂×C₄	—	26	32	no	—
502	C₂×C₄	—	52	32	no	—
503	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
504	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
505	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
506	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
507	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
508	C₂²	—	2	48	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	13	16	no	—
512	C₂²	—	26	96	no	—
513	C₂²	—	26	8	no	—
514	C₂²	—	26	8	no	—
515	C₂²	—	26	4	no	—
516	C₂²	—	26	8	no	—
517	C₂²	—	26	4	no	—
518	C₂²	—	26	8	no	—
519	C₂²	—	26	4	no	—
520	C₂²	—	26	8	no	—
521	C₂²	—	52	128	no	—
522	C₂²	—	52	24	no	—
523	C₂²	—	52	48	no	—
524	C₂²	#11719335	1	16	yes	direct product factor
525	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
526	C₂²	C₂²×#6131	1	6	yes	—
527	C₂²	C₂²×#6131	1	8	yes	complemented
528	C₂²	C₂×#88256	1	6	yes	—
529	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	8	no	—
532	C₄	—	2	8	no	—
533	C₄	—	26	4	no	—
534	C₄	—	26	4	no	—
535	C₄	—	26	4	no	—
536	C₄	C₂²×D₄×D₁₃	1	8	yes	—
537	C₂	—	2	8	no	—
538	C₂	—	26	16	no	—
539	C₂	—	52	8	no	—
540	C₂	—	52	4	no	—
541	C₂	C₂×#11719335	1	12	yes	direct product factor
542	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
543	C₂	C₂³×#6131	1	1	yes	characteristic
544	C₂	C₂²×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×C₂²⋊Q₈	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₂²⋊Q₈	D₁₃
hypocenter	C₁₃	C₂²×#546
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×#6131	C₂	semidirect
2. C₂⁴×D₅₂	C₂	semidirect
3. C₂×#11719335	C₂	direct (N × H)
4. C₂²×#88201	C₂	semidirect
5. C₂²×#88148	C₂	semidirect
6. C₂²×#88149	C₂	semidirect
7. C₂²×#88149	C₂	semidirect
8. C₂²×#88136	C₂	semidirect
9. C₂²×#88147	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
11. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
12. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂²×#6131	C₂²	semidirect
23. C₂³×D₅₂	C₂²	semidirect
24. C₂³×D₅₂	C₂²	semidirect
25. C₂³×D₅₂	C₂²	semidirect
26. C₂³×C₄×D₁₃	C₂²	semidirect
27. C₂³×C₄×D₁₃	C₂²	semidirect
28. C₂³×C₄×D₁₃	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₂×#88201	C₂²	semidirect
35. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
36. C₂²×#6103	C₂²	semidirect
37. C₂²×#6103	C₂²	semidirect
38. C₂²×#6103	C₂²	semidirect
39. C₂²×#6103	C₂²	semidirect
40. C₂²×#6103	C₂²	semidirect
41. C₂²×#6101	C₂²	semidirect
42. C₂²×C₄×Dic₁₃	C₂²	semidirect
43. #11719335	C₂²	direct (N × H)
44. C₂×#88149	C₂²	semidirect
45. C₂×#88149	C₂²	semidirect
46. C₂×#88148	C₂²	semidirect
47. C₂×#88147	C₂²	semidirect
48. C₂×#88136	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
59. C₂²×Q₈×C₁₃	C₂³	semidirect
72. C₂×#6131	C₂³	semidirect
78. C₂²×D₅₂	D₄	semidirect
82. C₂²×D₅₂	C₂³	semidirect
83. C₂²×D₅₂	C₂³	semidirect
84. C₂²×D₅₂	C₂³	semidirect
88. C₂²×C₄×D₁₃	C₂³	semidirect
89. C₂²×C₄×D₁₃	C₂³	semidirect
90. C₂²×C₄×D₁₃	C₂³	semidirect
91. C₁₃×C₂²⋊Q₈	C₂³	semidirect
92. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
93. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
96. #88201	C₂³	semidirect
97. C₄×C₂²⋊D₁₃	C₂³	semidirect
98. C₂×#6103	C₂³	semidirect
99. C₂×#6103	C₂³	semidirect
100. C₂×#6103	C₂³	semidirect
101. C₂×#6103	C₂³	semidirect
102. C₂×#6103	C₂³	semidirect
103. C₂×#6101	C₂³	semidirect
104. C₂×C₄×Dic₁₃	C₂³	semidirect
105. #88149	C₂³	semidirect
106. #88149	C₂³	semidirect
107. #88148	C₂³	semidirect
108. #88147	C₂³	semidirect
109. #88136	C₂³	semidirect
110. C₂²⋊C₄×D₁₃	C₂³	semidirect
114. C₂⁴×C₁₃	#41	semidirect
135. C₂×Q₈×C₁₃	C₂⁴	semidirect
160. C₂×D₅₂	C₂×D₄	semidirect
164. C₂×D₅₂	C₂⁴	semidirect
165. C₂×D₅₂	C₂⁴	semidirect
169. C₂×C₄×D₁₃	C₂⁴	semidirect
170. C₂×C₄×D₁₃	C₂⁴	semidirect
171. C₂×C₄×D₁₃	C₂⁴	semidirect
172. C₁₃×C₄⋊C₄	C₂⁴	semidirect
173. C₁₃×C₄⋊C₄	C₂⁴	semidirect
176. #6103	C₂⁴	semidirect
177. #6103	C₂⁴	semidirect
178. #6103	C₂⁴	semidirect
179. #6103	C₂⁴	semidirect
180. #6103	C₂⁴	semidirect
181. #6101	C₂⁴	semidirect
182. C₄×Dic₁₃	C₂⁴	semidirect
188. C₂²×C₂²⋊Q₈	D₁₃	semidirect
200. C₂³×C₁₃	C₂×#41	semidirect
244. D₅₂	C₂²×D₄	semidirect
251. C₂³×Q₈	C₂×D₁₃	semidirect
267. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
274. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
275. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
288. C₂²×C₁₃	#546	semidirect
291. C₂²×C₁₃	C₂²×#41	semidirect
325. C₂²×Q₈	C₂²×D₁₃	semidirect
357. C₂²⋊Q₈	C₂²×D₁₃	semidirect
364. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
365. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
376. C₂×C₁₃	C₂×#546	semidirect
402. C₂⁴	#6131	semidirect
407. C₂×Q₈	C₂³×D₁₃	semidirect
444. C₄⋊C₄	C₂³×D₁₃	semidirect
445. C₄⋊C₄	C₂³×D₁₃	semidirect
454. C₁₃	C₂²×#546	semidirect
479. C₂³	C₂×#6131	semidirect
524. C₂²	#11719335	direct (N × H)
527. C₂²	C₂²×#6131	semidirect
541. C₂	C₂×#11719335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6131	2
C₂⁴×D₅₂	2
C₂×#11719335	2
C₂²×#88201	2
C₂²×#88148	2
C₂²×#88149	2
C₂²×#88136	2
C₂²×#88147	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×#546	13

Subgroups — C22×#11719335 #16769848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719335 #16769848