Subgroups — C₂×#13128637 #16770818

Order 3328.

7738 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128637	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719435	C₂	1	2	yes	maximal, complemented
3	C₂×#11719284	C₂	1	4	yes	maximal, complemented
4	C₂×#11719284	C₂	1	2	yes	maximal, complemented
5	C₂×#11719395	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×D₅₂	C₂	1	2	yes	maximal, complemented
7	C₂×#11719432	C₂	1	2	yes	maximal, complemented
8	C₂×#11719224	C₂	1	2	yes	maximal, complemented
9	C₂×#11719339	C₂	1	4	yes	maximal, complemented
10	C₂×#11719175	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
12	C₂×#11719226	C₂	1	2	yes	maximal
13	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×Q₈×D₁₃	C₂²	1	4	yes	complemented
16	C₂³×D₅₂	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
18	C₁₃×#533	C₂²	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×#88200	C₂²	1	8	yes	complemented
29	C₂×#88200	C₂²	1	4	yes	complemented
30	C₂²×#6103	C₂²	1	2	yes	—
31	C₂×#88180	C₂²	1	2	yes	—
32	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂×#88178	C₂²	1	2	yes	—
34	C₂×#88178	C₂²	1	2	yes	—
35	#11719435	C₂²	1	32	yes	complemented
36	#11719432	C₂²	1	32	yes	complemented
37	#11719395	C₂²	1	64	yes	complemented
38	#11719339	C₂²	1	64	yes	complemented
39	D₁₃×C₂²⋊Q₈	C₂²	1	64	yes	complemented
40	#11719284	C₂²	1	32	yes	complemented
41	#11719284	C₂²	1	64	yes	complemented
42	Q₈×D₅₂	C₂²	1	32	yes	complemented
43	#11719226	C₂²	1	32	yes	—
44	#11719224	C₂²	1	32	yes	complemented
45	C₂×#88151	C₂²	1	8	yes	complemented
46	C₂×#88151	C₂²	1	4	yes	complemented
47	C₂×#88150	C₂²	1	8	yes	complemented
48	C₂×#88150	C₂²	1	8	yes	complemented
49	C₂×#88150	C₂²	1	8	yes	complemented
50	C₂×#88147	C₂²	1	4	yes	—
51	C₂×#88147	C₂²	1	4	yes	—
52	C₂×C₄⋊C₄×D₁₃	C₂²	1	8	yes	complemented
53	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
54	C₂×#88144	C₂²	1	4	yes	complemented
55	C₂×#88142	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	—
57	C₂×#88132	C₂²	1	8	yes	—
58	C₂×C₄×D₅₂	C₂²	1	2	yes	—
59	C₂×C₄×D₅₂	C₂²	1	2	yes	—
60	C₂×C₄×D₅₂	C₂²	1	2	yes	—
61	C₂×C₄×D₅₂	C₂²	1	2	yes	—
62	C₂×C₄×D₅₂	C₂²	1	16	yes	—
63	C₂×C₄×D₅₂	C₂²	1	4	yes	—
64	C₂×C₄×D₅₂	C₂²	1	4	yes	—
65	#11719175	C₂²	1	16	yes	complemented
66	C₂×#88124	C₂²	1	4	yes	complemented
67	C₂×#88124	C₂²	1	2	yes	complemented
68	C₂×#88123	C₂²	1	4	yes	complemented
69	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
70	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
72	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
73	C₂⁴×D₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×Dic₁₃	C₂³	1	2	yes	—
80	C₂×Q₈×D₁₃	—	4	16	no	—
81	C₂×Q₈×D₁₃	C₂³	1	32	yes	complemented
82	C₂²×D₅₂	Q₈	1	16	yes	complemented
83	C₂²×D₅₂	C₂³	1	2	yes	—
84	C₂²×D₅₂	C₂³	1	2	yes	—
85	C₂²×D₅₂	C₂³	1	8	yes	—
86	C₂²×C₄×D₁₃	—	4	8	no	—
87	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
88	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
89	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
90	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
91	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
92	C₂²×Dic₂₆	C₂³	1	2	yes	—
93	C₂²×Dic₂₆	C₂³	1	2	yes	—
94	C₂²×Dic₂₆	C₂³	1	8	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
96	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
97	C₁₃×#125	C₂³	1	16	yes	complemented
98	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
100	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
101	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
102	C₁₃×#117	C₂³	1	16	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
116	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
117	#88200	C₂³	1	32	yes	complemented
118	#88200	C₂³	1	64	yes	complemented
119	C₂×#6103	C₂³	1	4	yes	—
120	C₂×#6103	C₂³	1	4	yes	—
121	C₂×#6103	C₂³	1	16	yes	—
122	C₂×#6103	C₂³	1	8	yes	—
123	C₂×#6103	C₂³	1	8	yes	—
124	#88180	C₂³	1	16	yes	—
125	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
126	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
127	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
128	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
129	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
130	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
131	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
132	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
133	#88178	C₂³	1	16	yes	—
134	#88178	C₂³	1	16	yes	—
135	C₂×#6101	C₂³	1	4	yes	—
136	C₂×#6101	C₂³	1	4	yes	—
137	C₂×#6101	C₂³	1	8	yes	—
138	C₂×#6101	C₂³	1	8	yes	—
139	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
140	#88151	C₂³	1	32	yes	complemented
141	#88151	C₂³	1	64	yes	complemented
142	#88150	C₂³	1	64	yes	complemented
143	#88150	C₂³	1	64	yes	complemented
144	#88150	C₂³	1	64	yes	complemented
145	#88147	C₂³	1	32	yes	—
146	#88147	C₂³	1	32	yes	—
147	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
148	C₄⋊C₄×D₁₃	C₂³	1	64	yes	complemented
149	#88144	C₂³	1	32	yes	complemented
150	#88142	C₂³	1	32	yes	complemented
151	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	—
152	#88132	C₂³	1	64	yes	—
153	C₄×D₅₂	C₂³	1	16	yes	—
154	C₄×D₅₂	C₂³	1	16	yes	—
155	C₄×D₅₂	C₂³	1	16	yes	—
156	C₄×D₅₂	C₂³	1	16	yes	—
157	C₄×D₅₂	C₂³	1	32	yes	—
158	C₄×D₅₂	C₂³	1	32	yes	—
159	#88124	C₂³	1	16	yes	complemented
160	#88124	C₂³	1	32	yes	complemented
161	#88123	C₂³	1	8	yes	complemented
162	#88123	C₂³	1	8	yes	complemented
163	#88123	C₂³	1	32	yes	complemented
164	C₄×Dic₂₆	C₂³	1	16	yes	complemented
165	C₄×Dic₂₆	C₂³	1	16	yes	complemented
166	C₂×#3501	—	13	1	no	maximal, Sylow
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂³×D₁₃	—	4	4	no	—
169	C₂³×D₁₃	—	4	4	no	—
170	C₂³×D₁₃	C₂×Q₈	1	16	yes	complemented
171	C₂³×D₁₃	C₂⁴	1	4	yes	—
172	C₂³×D₁₃	C₂⁴	1	8	yes	—
173	C₂×Q₈×C₁₃	—	2	8	no	—
174	C₂×Q₈×C₁₃	—	4	4	no	—
175	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	complemented
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×Dic₁₃	—	4	4	no	—
192	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
193	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
194	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
195	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
196	Q₈×D₁₃	—	4	64	no	—
197	C₂×D₅₂	C₂×Q₈	1	16	yes	complemented
198	C₂×D₅₂	C₂×Q₈	1	16	yes	complemented
199	C₂×D₅₂	C₂×Q₈	1	64	yes	complemented
200	C₂×D₅₂	C₂⁴	1	8	yes	—
201	C₂×D₅₂	C₂⁴	1	8	yes	—
202	C₂×C₄×D₁₃	—	2	16	no	—
203	C₂×C₄×D₁₃	—	4	32	no	—
204	C₂×C₄×D₁₃	—	4	8	no	—
205	C₂×C₄×D₁₃	—	4	16	no	—
206	C₂×C₄×D₁₃	—	4	16	no	—
207	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
208	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
209	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
210	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
211	C₂×Dic₂₆	—	2	8	no	—
212	C₂×Dic₂₆	—	4	4	no	—
213	C₂×Dic₂₆	—	4	16	no	—
214	C₂×Dic₂₆	C₂⁴	1	8	yes	—
215	C₂×Dic₂₆	C₂⁴	1	8	yes	—
216	C₂×Dic₂₆	C₂⁴	1	32	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
223	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
224	C₄²×C₁₃	C₂⁴	1	4	yes	—
225	C₄²×C₁₃	C₂⁴	1	4	yes	—
226	C₄²×C₁₃	C₂⁴	1	4	yes	—
227	C₄²×C₁₃	C₂⁴	1	16	yes	—
228	C₄²×C₁₃	C₂⁴	1	4	yes	—
229	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
230	#6103	C₂⁴	1	16	yes	—
231	#6103	C₂⁴	1	16	yes	—
232	#6103	C₂⁴	1	32	yes	—
233	#6103	C₂⁴	1	32	yes	—
234	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
235	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
236	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
237	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
238	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
239	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
240	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
241	#6101	C₂⁴	1	16	yes	—
242	#6101	C₂⁴	1	16	yes	—
243	#6101	C₂⁴	1	32	yes	—
244	#6101	C₂⁴	1	32	yes	—
245	C₄×Dic₁₃	C₂⁴	1	16	yes	—
246	#3501	—	13	32	no	—
247	C₂×#554	—	13	2	no	—
248	C₂×#554	—	13	4	no	—
249	C₂×#554	—	13	2	no	—
250	C₂×#554	—	13	4	no	—
251	C₂×D₄×Q₈	—	13	2	no	—
252	C₂×D₄×Q₈	—	13	2	no	—
253	C₂×#544	—	13	2	no	—
254	C₂×#543	—	13	4	no	—
255	C₂×#533	—	13	1	no	—
256	C₂×#533	D₁₃	1	1	yes	characteristic, complemented
257	C₂²×C₂²⋊Q₈	—	13	4	no	—
258	C₂×#518	—	13	2	no	—
259	C₂²×C₄×D₄	—	13	1	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
263	C₂³×C₁₃	C₂⁵	1	2	yes	—
264	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
265	C₂²×D₁₃	—	2	8	no	—
266	C₂²×D₁₃	—	2	8	no	—
267	C₂²×D₁₃	—	4	8	no	—
268	C₂²×D₁₃	—	4	32	no	—
269	C₂²×D₁₃	—	4	8	no	—
270	C₂²×D₁₃	C₂²×Q₈	1	16	yes	—
271	C₂²×D₁₃	C₂²×Q₈	1	32	yes	complemented
272	C₂²×D₁₃	C₂⁵	1	8	yes	—
273	Q₈×C₁₃	—	2	16	no	—
274	Q₈×C₁₃	—	4	8	no	—
275	C₂×C₄×C₁₃	—	2	8	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	8	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	8	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
283	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
284	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	complemented
285	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
287	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
288	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
289	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
290	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
291	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
293	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
294	C₂×Dic₁₃	—	2	8	no	—
295	C₂×Dic₁₃	—	2	8	no	—
296	C₂×Dic₁₃	—	2	8	no	—
297	C₂×Dic₁₃	—	4	8	no	—
298	C₂×Dic₁₃	C₂⁵	1	8	yes	—
299	C₂×Dic₁₃	C₂⁵	1	8	yes	—
300	C₂×Dic₁₃	C₂⁵	1	8	yes	—
301	D₅₂	C₂²×Q₈	1	32	yes	complemented
302	D₅₂	C₂²×Q₈	1	32	yes	complemented
303	C₄×D₁₃	—	2	32	no	—
304	C₄×D₁₃	—	4	16	no	—
305	C₄×D₁₃	—	4	32	no	—
306	C₄×D₁₃	—	4	32	no	—
307	Dic₂₆	—	2	16	no	—
308	Dic₂₆	—	4	8	no	—
309	Dic₂₆	—	4	32	no	—
310	C₂³×Q₈	—	13	4	no	—
311	C₂³×D₄	—	13	1	no	—
312	C₂⁴×C₄	—	13	2	no	—
313	#554	—	13	32	no	—
314	#554	—	13	64	no	—
315	#554	—	13	32	no	—
316	#554	—	13	64	no	—
317	D₄×Q₈	—	13	32	no	—
318	D₄×Q₈	—	13	32	no	—
319	#544	—	13	32	no	—
320	#543	—	13	64	no	—
321	#533	—	13	16	no	—
322	#533	C₂×D₁₃	1	16	yes	complemented
323	C₂×C₄⋊Q₈	—	13	4	no	—
324	C₂×C₄⋊Q₈	—	13	1	no	—
325	C₂×C₄⋊Q₈	—	13	1	no	—
326	C₂×C₄⋊Q₈	—	13	4	no	—
327	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
328	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
329	C₂×#125	—	13	4	no	—
330	C₂×#125	—	13	2	no	—
331	C₂×#125	—	13	4	no	—
332	C₂×#125	C₂×D₁₃	1	2	yes	complemented
333	C₂×C₂²⋊Q₈	—	13	4	no	—
334	C₂×C₂²⋊Q₈	—	13	8	no	—
335	C₂×C₂²⋊Q₈	—	13	2	no	—
336	C₂×C₂²⋊Q₈	—	13	2	no	—
337	C₂×C₂²⋊Q₈	—	13	64	no	—
338	C₂×C₂²⋊Q₈	—	13	8	no	—
339	C₂×C₂²⋊Q₈	—	13	8	no	—
340	C₂×C₂²⋊Q₈	—	13	8	no	—
341	C₂×C₂²⋊Q₈	—	13	4	no	—
342	C₂×C₂²⋊Q₈	—	13	8	no	—
343	C₂×C₂²⋊Q₈	—	13	8	no	—
344	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
345	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
346	#518	—	13	32	no	—
347	C₂×C₄×Q₈	—	13	2	no	—
348	C₂×C₄×Q₈	—	13	2	no	—
349	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
350	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
351	C₂×C₄×D₄	—	13	4	no	—
352	C₂×C₄×D₄	—	13	4	no	—
353	C₂×C₄×D₄	—	13	2	no	—
354	C₂×C₄×D₄	—	13	2	no	—
355	C₂×C₄×D₄	—	13	2	no	—
356	C₂×C₄×D₄	—	13	2	no	—
357	C₂×C₄×D₄	—	13	16	no	—
358	C₂×C₄×D₄	—	13	4	no	—
359	C₂×C₄×D₄	—	13	4	no	—
360	C₂×#117	—	13	2	no	—
361	C₂×#117	C₂×D₁₃	1	2	yes	—
362	C₂²×C₄⋊C₄	—	13	1	no	—
363	C₂²×C₄⋊C₄	—	13	8	no	—
364	C₂²×C₄⋊C₄	—	13	4	no	—
365	C₂²×C₂²⋊C₄	—	13	2	no	—
366	C₂²×C₂²⋊C₄	—	13	8	no	—
367	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
368	C₂²×C₁₃	—	2	2	no	—
369	C₂²×C₁₃	—	2	2	no	—
370	C₂²×C₁₃	—	2	8	no	—
371	C₂²×C₁₃	C₂³×Q₈	1	4	yes	—
372	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
373	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₂²×C₁₃	#585	1	2	yes	—
375	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
376	C₂×D₁₃	—	2	8	no	—
377	C₂×D₁₃	—	2	8	no	—
378	C₂×D₁₃	—	2	32	no	—
379	C₂×D₁₃	—	4	32	no	—
380	C₂×D₁₃	C₂³×Q₈	1	16	yes	—
381	C₄×C₁₃	—	2	8	no	—
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	2	8	no	—
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	C₂³×Q₈	1	4	yes	—
387	C₄×C₁₃	C₂³×Q₈	1	4	yes	—
388	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
389	Dic₁₃	—	2	8	no	—
390	Dic₁₃	—	2	8	no	—
391	Dic₁₃	—	2	8	no	—
392	C₂⁵	—	13	2	no	—
393	C₂²×Q₈	—	13	32	no	—
394	C₂²×Q₈	—	13	2	no	—
395	C₂²×Q₈	—	13	2	no	—
396	C₂²×Q₈	—	13	8	no	—
397	C₂²×Q₈	—	52	16	no	—
398	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
399	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
400	C₂²×D₄	—	13	16	no	—
401	C₂²×D₄	—	13	2	no	—
402	C₂²×D₄	—	13	2	no	—
403	C₂²×D₄	—	13	8	no	—
404	C₂³×C₄	—	13	2	no	—
405	C₂³×C₄	—	13	4	no	—
406	C₂³×C₄	—	13	8	no	—
407	C₂³×C₄	—	13	8	no	—
408	C₂³×C₄	—	13	4	no	—
409	C₂³×C₄	—	13	16	no	—
410	C₂³×C₄	—	52	8	no	—
411	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
412	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
413	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
414	C₄⋊Q₈	—	13	32	no	—
415	C₄⋊Q₈	—	13	8	no	—
416	C₄⋊Q₈	—	13	8	no	—
417	C₄⋊Q₈	—	13	32	no	—
418	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
419	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
420	#125	—	13	32	no	—
421	#125	—	13	16	no	—
422	#125	—	13	32	no	—
423	#125	C₂²×D₁₃	1	16	yes	complemented
424	C₂²⋊Q₈	—	13	32	no	—
425	C₂²⋊Q₈	—	13	64	no	—
426	C₂²⋊Q₈	—	13	16	no	—
427	C₂²⋊Q₈	—	13	16	no	—
428	C₂²⋊Q₈	—	13	32	no	—
429	C₂²⋊Q₈	—	13	64	no	—
430	C₂²⋊Q₈	—	13	64	no	—
431	C₂²⋊Q₈	—	13	64	no	—
432	C₂²⋊Q₈	—	13	64	no	—
433	C₂²⋊Q₈	—	13	64	no	—
434	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	—
435	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	—
436	C₄×Q₈	—	13	16	no	—
437	C₄×Q₈	—	13	16	no	—
438	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
439	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
440	C₄×D₄	—	13	32	no	—
441	C₄×D₄	—	13	32	no	—
442	C₄×D₄	—	13	16	no	—
443	C₄×D₄	—	13	16	no	—
444	C₄×D₄	—	13	16	no	—
445	C₄×D₄	—	13	16	no	—
446	C₄×D₄	—	13	32	no	—
447	C₄×D₄	—	13	32	no	—
448	#117	—	13	16	no	—
449	#117	C₂²×D₁₃	1	16	yes	—
450	C₂×C₄⋊C₄	—	13	4	no	—
451	C₂×C₄⋊C₄	—	13	2	no	—
452	C₂×C₄⋊C₄	—	13	2	no	—
453	C₂×C₄⋊C₄	—	13	2	no	—
454	C₂×C₄⋊C₄	—	13	8	no	—
455	C₂×C₄⋊C₄	—	13	8	no	—
456	C₂×C₄⋊C₄	—	13	8	no	—
457	C₂×C₄⋊C₄	—	13	8	no	—
458	C₂×C₄⋊C₄	—	13	2	no	—
459	C₂×C₄⋊C₄	—	13	2	no	—
460	C₂×C₄⋊C₄	—	13	4	no	—
461	C₂×C₄⋊C₄	—	13	2	no	—
462	C₂×C₄⋊C₄	—	13	64	no	—
463	C₂×C₄⋊C₄	—	13	32	no	—
464	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
465	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
470	C₂×C₂²⋊C₄	—	13	4	no	—
471	C₂×C₂²⋊C₄	—	13	8	no	—
472	C₂×C₂²⋊C₄	—	13	8	no	—
473	C₂×C₂²⋊C₄	—	13	4	no	—
474	C₂×C₂²⋊C₄	—	13	4	no	—
475	C₂×C₂²⋊C₄	—	13	16	no	—
476	C₂×C₂²⋊C₄	—	13	64	no	—
477	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
478	C₂×C₄²	—	13	4	no	—
479	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
480	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
481	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
484	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
485	C₂×C₁₃	—	2	4	no	—
486	C₂×C₁₃	#3501	1	4	yes	complemented
487	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
488	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
490	D₁₃	—	2	16	no	—
491	C₂⁴	—	13	4	no	—
492	C₂⁴	—	13	16	no	—
493	C₂⁴	—	13	8	no	—
494	C₂⁴	—	52	4	no	—
495	C₂⁴	—	52	4	no	—
496	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
497	C₂×Q₈	—	2	8	no	—
498	C₂×Q₈	—	4	4	no	—
499	C₂×Q₈	—	13	8	no	—
500	C₂×Q₈	—	13	8	no	—
501	C₂×Q₈	—	13	32	no	—
502	C₂×Q₈	—	26	8	no	—
503	C₂×Q₈	—	52	16	no	—
504	C₂×Q₈	—	52	4	no	—
505	C₂×Q₈	—	52	64	no	—
506	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
507	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
508	C₂×D₄	—	13	16	no	—
509	C₂×D₄	—	13	16	no	—
510	C₂×D₄	—	13	64	no	—
511	C₂×D₄	—	13	8	no	—
512	C₂×D₄	—	13	8	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	13	4	no	—
516	C₂²×C₄	—	13	4	no	—
517	C₂²×C₄	—	13	4	no	—
518	C₂²×C₄	—	13	8	no	—
519	C₂²×C₄	—	13	16	no	—
520	C₂²×C₄	—	13	32	no	—
521	C₂²×C₄	—	13	32	no	—
522	C₂²×C₄	—	13	16	no	—
523	C₂²×C₄	—	26	16	no	—
524	C₂²×C₄	—	52	32	no	—
525	C₂²×C₄	—	52	8	no	—
526	C₂²×C₄	—	52	16	no	—
527	C₂²×C₄	—	52	16	no	—
528	C₂²×C₄	—	52	4	no	—
529	C₂²×C₄	Q₈×D₁₃	1	8	yes	complemented
530	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
531	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
535	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
536	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
537	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
538	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
540	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	—	13	16	no	—
542	C₄⋊C₄	—	13	8	no	—
543	C₄⋊C₄	—	13	8	no	—
544	C₄⋊C₄	—	13	8	no	—
545	C₄⋊C₄	—	13	32	no	—
546	C₄⋊C₄	—	13	32	no	—
547	C₄⋊C₄	—	13	32	no	—
548	C₄⋊C₄	—	13	8	no	—
549	C₄⋊C₄	—	13	8	no	—
550	C₄⋊C₄	—	13	16	no	—
551	C₄⋊C₄	—	13	8	no	—
552	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
553	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
554	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
555	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
556	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
557	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
558	C₂²⋊C₄	—	13	16	no	—
559	C₂²⋊C₄	—	13	32	no	—
560	C₂²⋊C₄	—	13	32	no	—
561	C₂²⋊C₄	—	13	16	no	—
562	C₂²⋊C₄	—	13	16	no	—
563	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
564	C₄²	—	13	16	no	—
565	C₄²	C₂³×D₁₃	1	4	yes	—
566	C₄²	C₂³×D₁₃	1	4	yes	—
567	C₄²	C₂³×D₁₃	1	4	yes	—
568	C₄²	C₂³×D₁₃	1	4	yes	—
569	C₄²	C₂³×D₁₃	1	16	yes	—
570	C₁₃	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	13	16	no	—
574	C₂³	—	13	8	no	—
575	C₂³	—	13	32	no	—
576	C₂³	—	26	8	no	—
577	C₂³	—	26	8	no	—
578	C₂³	—	52	8	no	—
579	C₂³	—	52	8	no	—
580	C₂³	—	52	32	no	—
581	C₂³	C₂×Q₈×D₁₃	1	4	yes	—
582	C₂³	C₂⁴×D₁₃	1	2	yes	—
583	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
584	Q₈	—	2	16	no	—
585	Q₈	—	4	8	no	—
586	Q₈	—	26	16	no	—
587	Q₈	—	52	8	no	—
588	Q₈	—	52	32	no	—
589	D₄	—	13	32	no	—
590	D₄	—	13	32	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	13	8	no	—
599	C₂×C₄	—	13	8	no	—
600	C₂×C₄	—	13	8	no	—
601	C₂×C₄	—	26	8	no	—
602	C₂×C₄	—	26	8	no	—
603	C₂×C₄	—	26	8	no	—
604	C₂×C₄	—	26	32	no	—
605	C₂×C₄	—	52	32	no	—
606	C₂×C₄	—	52	16	no	—
607	C₂×C₄	—	52	32	no	—
608	C₂×C₄	—	52	8	no	—
609	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	—
610	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	—
611	C₂×C₄	C₂×Q₈×D₁₃	1	16	yes	complemented
612	C₂×C₄	#88256	1	4	yes	—
613	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
614	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
615	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
616	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
617	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
618	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
619	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
620	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	13	16	no	—
625	C₂²	—	26	8	no	—
626	C₂²	—	26	8	no	—
627	C₂²	—	26	32	no	—
628	C₂²	—	52	32	no	—
629	C₂²	C₂²×Q₈×D₁₃	1	4	yes	—
630	C₂²	C₂²×Q₈×D₁₃	1	2	yes	—
631	C₂²	C₂×#88256	1	2	yes	—
632	C₂²	#11719648	1	2	yes	—
633	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	8	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	8	no	—
639	C₄	—	26	8	no	—
640	C₄	—	26	8	no	—
641	C₄	—	26	8	no	—
642	C₄	C₂²×Q₈×D₁₃	1	4	yes	—
643	C₄	C₂²×Q₈×D₁₃	1	4	yes	—
644	C₄	C₂×#88256	1	4	yes	—
645	C₂	—	2	4	no	—
646	C₂	—	26	16	no	—
647	C₂	#13128637	1	4	yes	direct product factor
648	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
649	C₂	C₂²×#88256	1	1	yes	characteristic
650	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#533	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₂×#533	D₁₃
hypocenter	C₁₃	C₂×#3501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #13128637	C₂	direct (N × H)
2. C₂×#11719435	C₂	semidirect
3. C₂×#11719284	C₂	semidirect
4. C₂×#11719284	C₂	semidirect
5. C₂×#11719395	C₂	semidirect
6. C₂×Q₈×D₅₂	C₂	semidirect
7. C₂×#11719432	C₂	semidirect
8. C₂×#11719224	C₂	semidirect
9. C₂×#11719339	C₂	semidirect
10. C₂×#11719175	C₂	semidirect
11. C₂×D₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₂×C₁₃×#533	C₂	semidirect
15. C₂²×Q₈×D₁₃	C₂²	semidirect
18. C₁₃×#533	C₂²	semidirect
19. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×#88200	C₂²	semidirect
29. C₂×#88200	C₂²	semidirect
35. #11719435	C₂²	semidirect
36. #11719432	C₂²	semidirect
37. #11719395	C₂²	semidirect
38. #11719339	C₂²	semidirect
39. D₁₃×C₂²⋊Q₈	C₂²	semidirect
40. #11719284	C₂²	semidirect
41. #11719284	C₂²	semidirect
42. Q₈×D₅₂	C₂²	semidirect
44. #11719224	C₂²	semidirect
45. C₂×#88151	C₂²	semidirect
46. C₂×#88151	C₂²	semidirect
47. C₂×#88150	C₂²	semidirect
48. C₂×#88150	C₂²	semidirect
49. C₂×#88150	C₂²	semidirect
52. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
53. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
54. C₂×#88144	C₂²	semidirect
55. C₂×#88142	C₂²	semidirect
65. #11719175	C₂²	semidirect
66. C₂×#88124	C₂²	semidirect
67. C₂×#88124	C₂²	semidirect
68. C₂×#88123	C₂²	semidirect
69. C₂×#88123	C₂²	semidirect
70. C₂×#88123	C₂²	semidirect
71. C₂×C₄×Dic₂₆	C₂²	semidirect
72. C₂×C₄×Dic₂₆	C₂²	semidirect
81. C₂×Q₈×D₁₃	C₂³	semidirect
82. C₂²×D₅₂	Q₈	semidirect
95. C₁₃×C₄⋊Q₈	C₂³	semidirect
96. C₁₃×C₄⋊Q₈	C₂³	semidirect
97. C₁₃×#125	C₂³	semidirect
100. C₄×Q₈×C₁₃	C₂³	semidirect
101. C₄×Q₈×C₁₃	C₂³	semidirect
117. #88200	C₂³	semidirect
118. #88200	C₂³	semidirect
140. #88151	C₂³	semidirect
141. #88151	C₂³	semidirect
142. #88150	C₂³	semidirect
143. #88150	C₂³	semidirect
144. #88150	C₂³	semidirect
147. C₄⋊C₄×D₁₃	C₂³	semidirect
148. C₄⋊C₄×D₁₃	C₂³	semidirect
149. #88144	C₂³	semidirect
150. #88142	C₂³	semidirect
159. #88124	C₂³	semidirect
160. #88124	C₂³	semidirect
161. #88123	C₂³	semidirect
162. #88123	C₂³	semidirect
163. #88123	C₂³	semidirect
164. C₄×Dic₂₆	C₂³	semidirect
165. C₄×Dic₂₆	C₂³	semidirect
170. C₂³×D₁₃	C₂×Q₈	semidirect
179. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
197. C₂×D₅₂	C₂×Q₈	semidirect
198. C₂×D₅₂	C₂×Q₈	semidirect
199. C₂×D₅₂	C₂×Q₈	semidirect
256. C₂×#533	D₁₃	semidirect
271. C₂²×D₁₃	C₂²×Q₈	semidirect
284. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
301. D₅₂	C₂²×Q₈	semidirect
302. D₅₂	C₂²×Q₈	semidirect
322. #533	C₂×D₁₃	semidirect
327. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
328. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
332. C₂×#125	C₂×D₁₃	semidirect
349. C₂×C₄×Q₈	C₂×D₁₃	semidirect
350. C₂×C₄×Q₈	C₂×D₁₃	semidirect
418. C₄⋊Q₈	C₂²×D₁₃	semidirect
419. C₄⋊Q₈	C₂²×D₁₃	semidirect
423. #125	C₂²×D₁₃	semidirect
438. C₄×Q₈	C₂²×D₁₃	semidirect
439. C₄×Q₈	C₂²×D₁₃	semidirect
486. C₂×C₁₃	#3501	semidirect
529. C₂²×C₄	Q₈×D₁₃	semidirect
570. C₁₃	C₂×#3501	semidirect
611. C₂×C₄	C₂×Q₈×D₁₃	semidirect
647. C₂	#13128637	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128637	2
C₂×#11719435	2
C₂×#11719284	2
C₂×#11719395	2
C₂×Q₈×D₅₂	2
C₂×#11719432	2
C₂×#11719224	2
C₂×#11719339	2
C₂×#11719175	2
C₂×D₁₃×C₂²⋊Q₈	2
C₂×#11719226	2
C₂²×C₄×D₅₂	2
C₂×C₁₃×#533	2
C₂×#3501	13

Subgroups — C2×#13128637 #16770818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128637 #16770818