Subgroups — C₂×#13128598 #16770808

Order 3328.

12378 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88256	C₂	1	2	yes	maximal, complemented
2	#13128598	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719256	C₂	1	2	yes	maximal, complemented
4	C₂×#11719431	C₂	1	2	yes	maximal, complemented
5	C₂×#11719255	C₂	1	4	yes	maximal, complemented
6	C₂×#11719381	C₂	1	4	yes	maximal, complemented
7	C₂×D₄×D₅₂	C₂	1	2	yes	maximal, complemented
8	C₂×#11719422	C₂	1	2	yes	maximal, complemented
9	C₂×#11719538	C₂	1	2	yes	maximal, complemented
10	C₂×#11719310	C₂	1	4	yes	maximal, complemented
11	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₁₃×#121	C₂	1	4	yes	maximal, complemented
13	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
16	C₂×#88256	—	2	32	no	—
17	C₂×#88256	C₂²	1	32	yes	complemented
18	C₂²×#6131	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
21	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
22	C₂²×#6127	C₂²	1	4	yes	complemented
23	C₂²×#6127	C₂²	1	2	yes	complemented
24	C₂³×D₅₂	C₂²	1	1	yes	characteristic
25	C₂³×D₅₂	C₂²	1	4	yes	complemented
26	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#532	C₂²	1	16	yes	complemented
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	#11719538	C₂²	1	32	yes	complemented
37	C₂×#88200	C₂²	1	4	yes	complemented
38	C₂×#88193	C₂²	1	8	yes	complemented
39	C₂×#88192	C₂²	1	4	yes	complemented
40	C₂×#88192	C₂²	1	4	yes	complemented
41	C₂×#88191	C₂²	1	8	yes	complemented
42	C₂×#88184	C₂²	1	4	yes	complemented
43	C₂×#88184	C₂²	1	2	yes	complemented
44	C₂×#88184	C₂²	1	2	yes	complemented
45	C₂²×#6103	C₂²	1	2	yes	complemented
46	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×#88178	C₂²	1	4	yes	complemented
48	#11719431	C₂²	1	32	yes	complemented
49	#11719422	C₂²	1	32	yes	complemented
50	#11719381	C₂²	1	64	yes	complemented
51	#11719310	C₂²	1	64	yes	complemented
52	D₁₃×#121	C₂²	1	64	yes	complemented
53	#11719256	C₂²	1	32	yes	complemented
54	#11719255	C₂²	1	64	yes	complemented
55	D₄×D₅₂	C₂²	1	32	yes	complemented
56	C₂×#88149	C₂²	1	4	yes	complemented
57	C₂×#88148	C₂²	1	8	yes	complemented
58	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
59	C₂×#88138	C₂²	1	8	yes	complemented
60	C₂×#88137	C₂²	1	8	yes	complemented
61	C₂×#88136	C₂²	1	8	yes	complemented
62	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
63	#11719182	C₂²	1	16	yes	complemented
64	C₂×#88129	C₂²	1	2	yes	complemented
65	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
67	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
68	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
69	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
70	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
71	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
72	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
73	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
74	C₂⁴×D₁₃	C₂³	1	8	yes	—
75	C₂⁴×D₁₃	C₂³	1	2	yes	—
76	C₂×C₁₃×#41	—	2	16	no	—
77	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
78	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
88	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
89	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
90	C₂³×Dic₁₃	C₂³	1	2	yes	—
91	#88256	—	2	256	no	—
92	C₂×#6131	—	2	32	no	—
93	C₂×#6131	C₂³	1	32	yes	complemented
94	C₂×D₄×D₁₃	—	2	64	no	—
95	C₂×D₄×D₁₃	—	2	32	no	—
96	C₂×D₄×D₁₃	—	4	16	no	—
97	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
98	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
99	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
100	C₂×#6127	—	2	16	no	—
101	C₂×#6127	—	2	32	no	—
102	C₂×#6127	C₂³	1	16	yes	complemented
103	C₂×#6127	C₂³	1	32	yes	complemented
104	C₂²×D₅₂	—	2	32	no	—
105	C₂²×D₅₂	D₄	1	16	yes	complemented
106	C₂²×D₅₂	C₂³	1	2	yes	—
107	C₂²×D₅₂	C₂³	1	2	yes	—
108	C₂²×D₅₂	C₂³	1	8	yes	—
109	C₂²×D₅₂	C₂³	1	2	yes	—
110	C₂²×D₅₂	C₂³	1	2	yes	—
111	C₂²×D₅₂	C₂³	1	2	yes	—
112	C₂²×D₅₂	C₂³	1	8	yes	—
113	C₂²×D₅₂	C₂³	1	32	yes	complemented
114	C₂²×C₄×D₁₃	—	4	8	no	—
115	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
116	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
117	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
118	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
119	C₂²×C₄×D₁₃	C₂³	1	16	yes	complemented
120	C₂²×Dic₂₆	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
122	C₁₃×#127	C₂³	1	8	yes	complemented
123	C₁₃×#124	C₂³	1	16	yes	complemented
124	C₁₃×#121	C₂³	1	16	yes	complemented
125	C₁₃×#121	C₂³	1	16	yes	complemented
126	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
127	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
137	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
138	#88200	C₂³	1	32	yes	complemented
139	#88193	C₂³	1	64	yes	complemented
140	#88192	C₂³	1	32	yes	complemented
141	#88192	C₂³	1	32	yes	complemented
142	#88191	C₂³	1	64	yes	complemented
143	#88184	C₂³	1	16	yes	complemented
144	#88184	C₂³	1	16	yes	complemented
145	#88184	C₂³	1	32	yes	complemented
146	C₂×#6103	C₂³	1	4	yes	—
147	C₂×#6103	C₂³	1	4	yes	—
148	C₂×#6103	C₂³	1	4	yes	—
149	C₂×#6103	C₂³	1	4	yes	—
150	C₂×#6103	C₂³	1	8	yes	—
151	C₂×#6103	C₂³	1	16	yes	complemented
152	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
153	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
154	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
155	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	complemented
157	#88178	C₂³	1	32	yes	complemented
158	C₂×#6101	C₂³	1	8	yes	—
159	#88149	C₂³	1	32	yes	complemented
160	#88148	C₂³	1	64	yes	complemented
161	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
162	#88138	C₂³	1	64	yes	complemented
163	#88137	C₂³	1	64	yes	complemented
164	#88136	C₂³	1	64	yes	complemented
165	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
166	#88129	C₂³	1	16	yes	complemented
167	#88128	C₂³	1	8	yes	complemented
168	C₄×D₅₂	C₂³	1	16	yes	complemented
169	C₄×D₅₂	C₂³	1	16	yes	complemented
170	C₄×D₅₂	C₂³	1	16	yes	complemented
171	C₄×D₅₂	C₂³	1	16	yes	complemented
172	C₄×D₅₂	C₂³	1	16	yes	complemented
173	C₄×D₅₂	C₂³	1	16	yes	complemented
174	#88123	C₂³	1	8	yes	complemented
175	C₂×#3496	—	13	1	no	maximal, Sylow
176	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
177	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂³×D₁₃	—	2	32	no	—
179	C₂³×D₁₃	—	4	4	no	—
180	C₂³×D₁₃	—	4	4	no	—
181	C₂³×D₁₃	—	4	16	no	—
182	C₂³×D₁₃	—	4	16	no	—
183	C₂³×D₁₃	C₂×D₄	1	16	yes	complemented
184	C₂³×D₁₃	C₂⁴	1	4	yes	—
185	C₂³×D₁₃	C₂⁴	1	4	yes	—
186	C₂³×D₁₃	C₂⁴	1	32	yes	—
187	C₂³×D₁₃	C₂⁴	1	8	yes	—
188	C₁₃×#41	—	2	64	no	—
189	C₂×Q₈×C₁₃	—	2	8	no	—
190	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
191	C₂×D₄×C₁₃	—	2	16	no	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	2	8	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
196	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
197	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
198	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₁₃	—	2	16	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
203	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₃	—	2	16	no	—
215	C₂×C₂²⋊D₁₃	—	2	32	no	—
216	C₂×C₂²⋊D₁₃	—	4	16	no	—
217	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
218	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
219	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
220	C₂²×Dic₁₃	—	4	4	no	—
221	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
222	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
223	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
224	#6131	—	2	128	no	—
225	D₄×D₁₃	—	2	256	no	—
226	D₄×D₁₃	—	2	128	no	—
227	D₄×D₁₃	—	4	64	no	—
228	#6127	—	2	64	no	—
229	#6127	—	2	128	no	—
230	C₂×D₅₂	—	2	32	no	—
231	C₂×D₅₂	—	2	8	no	—
232	C₂×D₅₂	—	2	8	no	—
233	C₂×D₅₂	—	2	128	no	—
234	C₂×D₅₂	—	4	4	no	—
235	C₂×D₅₂	C₂×D₄	1	16	yes	complemented
236	C₂×D₅₂	C₂×D₄	1	16	yes	complemented
237	C₂×D₅₂	C₂×D₄	1	64	yes	complemented
238	C₂×D₅₂	C₂⁴	1	8	yes	—
239	C₂×D₅₂	C₂⁴	1	8	yes	—
240	C₂×D₅₂	C₂⁴	1	32	yes	—
241	C₂×D₅₂	C₂⁴	1	8	yes	—
242	C₂×D₅₂	C₂⁴	1	8	yes	—
243	C₂×D₅₂	C₂⁴	1	8	yes	—
244	C₂×C₄×D₁₃	—	2	32	no	—
245	C₂×C₄×D₁₃	—	2	16	no	—
246	C₂×C₄×D₁₃	—	2	16	no	—
247	C₂×C₄×D₁₃	—	4	32	no	—
248	C₂×C₄×D₁₃	—	4	8	no	—
249	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
250	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
251	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
252	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
253	C₂×Dic₂₆	—	2	8	no	—
254	C₂×Dic₂₆	C₂⁴	1	8	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
257	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
258	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
259	C₄²×C₁₃	C₂⁴	1	4	yes	—
260	C₄²×C₁₃	C₂⁴	1	4	yes	—
261	C₄²×C₁₃	C₂⁴	1	4	yes	—
262	C₄²×C₁₃	C₂⁴	1	4	yes	—
263	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
264	#6103	C₂⁴	1	16	yes	—
265	#6103	C₂⁴	1	16	yes	—
266	#6103	C₂⁴	1	16	yes	—
267	#6103	C₂⁴	1	16	yes	—
268	#6103	C₂⁴	1	32	yes	—
269	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
270	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
271	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
272	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
273	#6101	C₂⁴	1	32	yes	—
274	C₂²×H(5,𝔽₂)	—	13	2	no	—
275	#3496	—	13	32	no	—
276	C₂×#547	—	13	2	no	—
277	C₂×#547	—	13	2	no	—
278	C₂×#546	—	13	4	no	—
279	C₂×#546	—	13	4	no	—
280	C₂×D₄²	—	13	2	no	—
281	C₂×D₄²	—	13	2	no	—
282	C₂×#537	—	13	2	no	—
283	C₂×#534	—	13	4	no	—
284	C₂×#532	—	13	1	no	—
285	C₂×#532	D₁₃	1	1	yes	characteristic, complemented
286	C₂²×#121	—	13	4	no	—
287	C₂²×C₄×D₄	—	13	1	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	8	no	—
291	C₂³×C₁₃	—	2	8	no	—
292	C₂³×C₁₃	—	2	8	no	—
293	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
294	C₂³×C₁₃	C₂⁵	1	8	yes	—
295	C₂³×C₁₃	C₂⁵	1	2	yes	—
296	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
297	C₂²×D₁₃	—	2	8	no	—
298	C₂²×D₁₃	—	2	8	no	—
299	C₂²×D₁₃	—	2	8	no	—
300	C₂²×D₁₃	—	2	8	no	—
301	C₂²×D₁₃	—	2	8	no	—
302	C₂²×D₁₃	—	2	64	no	—
303	C₂²×D₁₃	—	4	8	no	—
304	C₂²×D₁₃	—	4	32	no	—
305	C₂²×D₁₃	—	4	8	no	—
306	C₂²×D₁₃	—	4	32	no	—
307	C₂²×D₁₃	—	4	32	no	—
308	C₂²×D₁₃	—	8	64	no	—
309	C₂²×D₁₃	C₂²×D₄	1	16	yes	—
310	C₂²×D₁₃	C₂²×D₄	1	32	yes	complemented
311	C₂²×D₁₃	C₂⁵	1	8	yes	—
312	C₂²×D₁₃	C₂⁵	1	8	yes	—
313	Q₈×C₁₃	—	2	16	no	—
314	D₄×C₁₃	—	2	32	no	—
315	D₄×C₁₃	—	2	16	no	—
316	D₄×C₁₃	—	2	16	no	—
317	D₄×C₁₃	—	4	8	no	—
318	C₂×C₄×C₁₃	—	2	8	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	32	no	—
323	C₂×C₄×C₁₃	—	2	8	no	—
324	C₂×C₄×C₁₃	—	4	4	no	—
325	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	complemented
328	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
329	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
330	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
331	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
332	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
333	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
334	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
335	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
336	C₂²⋊D₁₃	—	2	32	no	—
337	C₂²⋊D₁₃	—	2	64	no	—
338	C₂²⋊D₁₃	—	4	32	no	—
339	C₂×Dic₁₃	—	2	8	no	—
340	C₂×Dic₁₃	—	2	8	no	—
341	C₂×Dic₁₃	—	4	8	no	—
342	C₂×Dic₁₃	C₂⁵	1	8	yes	—
343	C₂×Dic₁₃	C₂⁵	1	8	yes	—
344	D₅₂	—	2	64	no	—
345	D₅₂	—	2	16	no	—
346	D₅₂	—	2	16	no	—
347	D₅₂	—	4	8	no	—
348	D₅₂	C₂²×D₄	1	32	yes	complemented
349	D₅₂	C₂²×D₄	1	32	yes	complemented
350	C₄×D₁₃	—	2	64	no	—
351	C₄×D₁₃	—	2	32	no	—
352	C₄×D₁₃	—	2	32	no	—
353	C₄×D₁₃	—	4	16	no	—
354	Dic₂₆	—	2	16	no	—
355	C₂×H(5,𝔽₂)	—	13	32	no	—
356	C₂×H(5,𝔽₂)	—	26	32	no	—
357	C₂²×#41	—	13	4	no	—
358	C₂²×#41	—	13	2	no	—
359	C₂²×#41	—	13	4	no	—
360	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
361	C₂³×D₄	—	13	8	no	—
362	C₂³×D₄	—	13	4	no	—
363	C₂³×D₄	—	13	4	no	—
364	C₂³×D₄	—	13	1	no	—
365	C₂³×D₄	—	13	4	no	—
366	C₂⁴×C₄	—	13	2	no	—
367	#547	—	13	32	no	—
368	#547	—	13	32	no	—
369	#546	—	13	64	no	—
370	#546	—	13	64	no	—
371	D₄²	—	13	32	no	—
372	D₄²	—	13	32	no	—
373	#537	—	13	32	no	—
374	#534	—	13	64	no	—
375	#532	—	13	16	no	—
376	#532	C₂×D₁₃	1	16	yes	complemented
377	C₂×C₄⋊Q₈	—	13	1	no	—
378	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
379	C₂×#127	—	13	1	no	—
380	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
381	C₂×#124	—	13	2	no	—
382	C₂×#124	C₂×D₁₃	1	2	yes	complemented
383	C₂×#123	—	13	8	no	—
384	C₂×#123	—	13	8	no	—
385	C₂×C₂²⋊Q₈	—	13	4	no	—
386	C₂×C₂²⋊Q₈	—	13	4	no	—
387	C₂×#121	—	13	4	no	—
388	C₂×#121	—	13	4	no	—
389	C₂×#121	—	13	8	no	—
390	C₂×#121	—	13	2	no	—
391	C₂×#121	—	13	2	no	—
392	C₂×#121	—	13	4	no	—
393	C₂×#121	—	13	64	no	—
394	C₂×#121	—	13	4	no	—
395	C₂×#121	—	13	8	no	—
396	C₂×#121	C₂×D₁₃	1	2	yes	complemented
397	C₂×#121	C₂×D₁₃	1	2	yes	complemented
398	C₂×#120	—	13	8	no	—
399	C₂×#120	—	13	8	no	—
400	C₂×C₄×D₄	—	13	2	no	—
401	C₂×C₄×D₄	—	13	2	no	—
402	C₂×C₄×D₄	—	13	2	no	—
403	C₂×C₄×D₄	—	13	2	no	—
404	C₂×C₄×D₄	—	13	2	no	—
405	C₂×C₄×D₄	—	13	2	no	—
406	C₂×C₄×D₄	—	13	16	no	—
407	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
408	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
409	C₂²×C₄⋊C₄	—	13	1	no	—
410	C₂²×C₄⋊C₄	—	13	4	no	—
411	C₂²×C₂²⋊C₄	—	13	2	no	—
412	C₂²×C₂²⋊C₄	—	13	8	no	—
413	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	8	no	—
417	C₂²×C₁₃	—	2	8	no	—
418	C₂²×C₁₃	—	2	8	no	—
419	C₂²×C₁₃	—	2	8	no	—
420	C₂²×C₁₃	—	4	16	no	—
421	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
422	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
423	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
424	C₂²×C₁₃	#585	1	2	yes	—
425	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
426	C₂×D₁₃	—	2	8	no	—
427	C₂×D₁₃	—	2	8	no	—
428	C₂×D₁₃	—	2	32	no	—
429	C₂×D₁₃	—	2	8	no	—
430	C₂×D₁₃	—	2	8	no	—
431	C₂×D₁₃	—	2	8	no	—
432	C₂×D₁₃	—	4	32	no	—
433	C₂×D₁₃	—	4	16	no	—
434	C₂×D₁₃	—	8	64	no	—
435	C₂×D₁₃	C₂³×D₄	1	16	yes	—
436	C₄×C₁₃	—	2	8	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	2	no	—
440	C₄×C₁₃	C₂³×D₄	1	4	yes	—
441	C₄×C₁₃	C₂³×D₄	1	4	yes	—
442	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
443	Dic₁₃	—	2	8	no	—
444	Dic₁₃	—	2	8	no	—
445	C₂⁵	—	13	2	no	—
446	C₂⁵	—	13	8	no	—
447	H(5,𝔽₂)	—	26	256	no	—
448	C₂×#41	—	2	16	no	—
449	C₂×#41	—	13	32	no	—
450	C₂×#41	—	13	16	no	—
451	C₂×#41	—	13	32	no	—
452	C₂×#41	—	26	32	no	—
453	C₂×#41	—	26	32	no	—
454	C₂×#41	—	26	16	no	—
455	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
456	C₂²×Q₈	—	13	2	no	—
457	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
458	C₂²×D₄	—	13	8	no	—
459	C₂²×D₄	—	13	4	no	—
460	C₂²×D₄	—	13	8	no	—
461	C₂²×D₄	—	13	64	no	—
462	C₂²×D₄	—	13	32	no	—
463	C₂²×D₄	—	13	32	no	—
464	C₂²×D₄	—	13	16	no	—
465	C₂²×D₄	—	13	2	no	—
466	C₂²×D₄	—	13	2	no	—
467	C₂²×D₄	—	13	8	no	—
468	C₂²×D₄	—	13	2	no	—
469	C₂²×D₄	—	13	8	no	—
470	C₂²×D₄	—	13	2	no	—
471	C₂²×D₄	—	13	32	no	—
472	C₂²×D₄	—	13	2	no	—
473	C₂²×D₄	—	26	32	no	—
474	C₂²×D₄	—	26	32	no	—
475	C₂²×D₄	—	26	64	no	—
476	C₂²×D₄	—	52	16	no	—
477	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
478	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
479	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
480	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
481	C₂³×C₄	—	13	2	no	—
482	C₂³×C₄	—	13	8	no	—
483	C₂³×C₄	—	13	4	no	—
484	C₂³×C₄	—	13	4	no	—
485	C₂³×C₄	—	13	4	no	—
486	C₂³×C₄	—	13	16	no	—
487	C₂³×C₄	—	52	8	no	—
488	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
489	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
490	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
491	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
492	C₄⋊Q₈	—	13	8	no	—
493	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
494	#127	—	13	8	no	—
495	#127	C₂²×D₁₃	1	8	yes	complemented
496	#124	—	13	16	no	—
497	#124	C₂²×D₁₃	1	16	yes	complemented
498	#123	—	13	64	no	—
499	#123	—	13	64	no	—
500	C₂²⋊Q₈	—	13	32	no	—
501	C₂²⋊Q₈	—	13	32	no	—
502	#121	—	13	64	no	—
503	#121	—	13	32	no	—
504	#121	—	13	32	no	—
505	#121	—	13	16	no	—
506	#121	—	13	16	no	—
507	#121	—	13	32	no	—
508	#121	—	13	32	no	—
509	#121	—	13	64	no	—
510	#121	C₂²×D₁₃	1	16	yes	complemented
511	#121	C₂²×D₁₃	1	16	yes	complemented
512	#120	—	13	64	no	—
513	#120	—	13	64	no	—
514	C₄×D₄	—	13	16	no	—
515	C₄×D₄	—	13	16	no	—
516	C₄×D₄	—	13	16	no	—
517	C₄×D₄	—	13	16	no	—
518	C₄×D₄	—	13	16	no	—
519	C₄×D₄	—	13	16	no	—
520	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
521	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
522	C₂×C₄⋊C₄	—	13	2	no	—
523	C₂×C₄⋊C₄	—	13	2	no	—
524	C₂×C₄⋊C₄	—	13	2	no	—
525	C₂×C₄⋊C₄	—	13	8	no	—
526	C₂×C₄⋊C₄	—	13	8	no	—
527	C₂×C₄⋊C₄	—	13	2	no	—
528	C₂×C₄⋊C₄	—	13	32	no	—
529	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
531	C₂×C₂²⋊C₄	—	13	8	no	—
532	C₂×C₂²⋊C₄	—	13	4	no	—
533	C₂×C₂²⋊C₄	—	13	4	no	—
534	C₂×C₂²⋊C₄	—	13	4	no	—
535	C₂×C₂²⋊C₄	—	13	16	no	—
536	C₂×C₂²⋊C₄	—	13	8	no	—
537	C₂×C₂²⋊C₄	—	13	4	no	—
538	C₂×C₂²⋊C₄	—	13	64	no	—
539	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
541	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
542	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
543	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
544	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
545	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
546	C₂×C₁₃	—	2	4	no	—
547	C₂×C₁₃	—	4	8	no	—
548	C₂×C₁₃	#3496	1	4	yes	complemented
549	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
550	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
552	D₁₃	—	2	16	no	—
553	D₁₃	—	4	8	no	—
554	C₂⁴	—	13	4	no	—
555	C₂⁴	—	13	16	no	—
556	C₂⁴	—	13	8	no	—
557	C₂⁴	—	13	4	no	—
558	C₂⁴	—	13	32	no	—
559	C₂⁴	—	26	32	no	—
560	C₂⁴	—	52	4	no	—
561	C₂⁴	—	52	4	no	—
562	C₂⁴	—	52	16	no	—
563	C₂⁴	—	52	16	no	—
564	C₂⁴	C₂³×D₁₃	1	4	yes	—
565	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
566	#41	—	2	64	no	—
567	#41	—	26	128	no	—
568	#41	—	26	128	no	—
569	#41	—	26	64	no	—
570	C₂×Q₈	—	2	8	no	—
571	C₂×Q₈	—	13	8	no	—
572	C₂×Q₈	—	26	8	no	—
573	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
574	C₂×D₄	—	2	16	no	—
575	C₂×D₄	—	2	8	no	—
576	C₂×D₄	—	2	8	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	13	32	no	—
579	C₂×D₄	—	13	16	no	—
580	C₂×D₄	—	13	32	no	—
581	C₂×D₄	—	13	16	no	—
582	C₂×D₄	—	13	16	no	—
583	C₂×D₄	—	13	64	no	—
584	C₂×D₄	—	13	8	no	—
585	C₂×D₄	—	13	8	no	—
586	C₂×D₄	—	13	8	no	—
587	C₂×D₄	—	13	32	no	—
588	C₂×D₄	—	13	8	no	—
589	C₂×D₄	—	13	8	no	—
590	C₂×D₄	—	26	128	no	—
591	C₂×D₄	—	26	32	no	—
592	C₂×D₄	—	26	128	no	—
593	C₂×D₄	—	26	256	no	—
594	C₂×D₄	—	26	32	no	—
595	C₂×D₄	—	26	16	no	—
596	C₂×D₄	—	26	8	no	—
597	C₂×D₄	—	26	8	no	—
598	C₂×D₄	—	52	4	no	—
599	C₂×D₄	—	52	64	no	—
600	C₂×D₄	—	52	16	no	—
601	C₂×D₄	C₂³×D₁₃	1	8	yes	—
602	C₂×D₄	C₂³×D₁₃	1	16	yes	—
603	C₂×D₄	C₂³×D₁₃	1	8	yes	—
604	C₂×D₄	C₂³×D₁₃	1	8	yes	—
605	C₂²×C₄	—	2	16	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	13	4	no	—
609	C₂²×C₄	—	13	4	no	—
610	C₂²×C₄	—	13	8	no	—
611	C₂²×C₄	—	13	32	no	—
612	C₂²×C₄	—	13	16	no	—
613	C₂²×C₄	—	13	16	no	—
614	C₂²×C₄	—	13	16	no	—
615	C₂²×C₄	—	26	32	no	—
616	C₂²×C₄	—	26	16	no	—
617	C₂²×C₄	—	26	16	no	—
618	C₂²×C₄	—	52	32	no	—
619	C₂²×C₄	—	52	8	no	—
620	C₂²×C₄	—	52	4	no	—
621	C₂²×C₄	D₄×D₁₃	1	8	yes	complemented
622	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
623	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
624	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
627	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
628	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
629	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
631	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
632	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
633	C₄⋊C₄	—	13	8	no	—
634	C₄⋊C₄	—	13	8	no	—
635	C₄⋊C₄	—	13	8	no	—
636	C₄⋊C₄	—	13	32	no	—
637	C₄⋊C₄	—	13	8	no	—
638	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
639	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
640	C₂²⋊C₄	—	13	32	no	—
641	C₂²⋊C₄	—	13	16	no	—
642	C₂²⋊C₄	—	13	16	no	—
643	C₂²⋊C₄	—	13	16	no	—
644	C₂²⋊C₄	—	13	32	no	—
645	C₂²⋊C₄	—	13	16	no	—
646	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
647	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
648	C₄²	C₂³×D₁₃	1	4	yes	—
649	C₄²	C₂³×D₁₃	1	4	yes	—
650	C₄²	C₂³×D₁₃	1	4	yes	—
651	C₄²	C₂³×D₁₃	1	4	yes	—
652	C₁₃	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	8	no	—
656	C₂³	—	2	8	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	13	16	no	—
659	C₂³	—	13	8	no	—
660	C₂³	—	13	32	no	—
661	C₂³	—	13	8	no	—
662	C₂³	—	26	64	no	—
663	C₂³	—	26	8	no	—
664	C₂³	—	26	8	no	—
665	C₂³	—	26	8	no	—
666	C₂³	—	26	8	no	—
667	C₂³	—	26	8	no	—
668	C₂³	—	52	8	no	—
669	C₂³	—	52	32	no	—
670	C₂³	—	52	8	no	—
671	C₂³	—	52	32	no	—
672	C₂³	—	52	32	no	—
673	C₂³	—	104	64	no	—
674	C₂³	C₂×D₄×D₁₃	1	4	yes	—
675	C₂³	C₂⁴×D₁₃	1	8	yes	—
676	C₂³	C₂⁴×D₁₃	1	2	yes	—
677	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
678	Q₈	—	2	16	no	—
679	Q₈	—	26	16	no	—
680	D₄	—	2	32	no	—
681	D₄	—	2	16	no	—
682	D₄	—	2	16	no	—
683	D₄	—	4	8	no	—
684	D₄	—	13	32	no	—
685	D₄	—	13	32	no	—
686	D₄	—	26	64	no	—
687	D₄	—	26	64	no	—
688	D₄	—	26	32	no	—
689	D₄	—	26	16	no	—
690	D₄	—	26	16	no	—
691	D₄	—	52	8	no	—
692	D₄	—	52	32	no	—
693	C₂×C₄	—	2	8	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	32	no	—
698	C₂×C₄	—	2	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	13	8	no	—
701	C₂×C₄	—	13	8	no	—
702	C₂×C₄	—	26	64	no	—
703	C₂×C₄	—	26	8	no	—
704	C₂×C₄	—	26	8	no	—
705	C₂×C₄	—	26	32	no	—
706	C₂×C₄	—	26	32	no	—
707	C₂×C₄	—	52	16	no	—
708	C₂×C₄	—	52	8	no	—
709	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
710	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
711	C₂×C₄	C₂×D₄×D₁₃	1	16	yes	complemented
712	C₂×C₄	#88256	1	4	yes	complemented
713	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
714	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
715	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
716	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
717	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
718	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
719	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	8	no	—
726	C₂²	—	4	16	no	—
727	C₂²	—	13	16	no	—
728	C₂²	—	26	32	no	—
729	C₂²	—	26	8	no	—
730	C₂²	—	26	8	no	—
731	C₂²	—	26	8	no	—
732	C₂²	—	26	8	no	—
733	C₂²	—	26	8	no	—
734	C₂²	—	52	32	no	—
735	C₂²	—	52	16	no	—
736	C₂²	—	104	64	no	—
737	C₂²	C₂²×D₄×D₁₃	1	4	yes	—
738	C₂²	C₂²×D₄×D₁₃	1	2	yes	—
739	C₂²	C₂×#88256	1	2	yes	—
740	C₂²	#11719648	1	2	yes	—
741	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
742	C₄	—	2	8	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	26	8	no	—
747	C₄	—	26	8	no	—
748	C₄	C₂²×D₄×D₁₃	1	4	yes	—
749	C₄	C₂²×D₄×D₁₃	1	4	yes	—
750	C₄	C₂×#88256	1	4	yes	complemented
751	C₂	—	2	4	no	—
752	C₂	—	4	8	no	—
753	C₂	—	26	16	no	—
754	C₂	—	52	8	no	—
755	C₂	#13128598	1	4	yes	direct product factor
756	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
757	C₂	C₂²×#88256	1	1	yes	characteristic
758	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×#532	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#532	D₁₃
hypocenter	C₁₃	C₂×#3496
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#88256	C₂	semidirect
2. #13128598	C₂	direct (N × H)
3. C₂×#11719256	C₂	semidirect
4. C₂×#11719431	C₂	semidirect
5. C₂×#11719255	C₂	semidirect
6. C₂×#11719381	C₂	semidirect
7. C₂×D₄×D₅₂	C₂	semidirect
8. C₂×#11719422	C₂	semidirect
9. C₂×#11719538	C₂	semidirect
10. C₂×#11719310	C₂	semidirect
11. C₂×#11719182	C₂	semidirect
12. C₂×D₁₃×#121	C₂	semidirect
13. C₂²×C₄×D₅₂	C₂	semidirect
14. C₂×C₁₃×#532	C₂	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂×#88256	C₂²	semidirect
18. C₂²×#6131	C₂²	semidirect
19. C₂²×D₄×D₁₃	C₂²	semidirect
20. C₂²×D₄×D₁₃	C₂²	semidirect
21. C₂²×D₄×D₁₃	C₂²	semidirect
22. C₂²×#6127	C₂²	semidirect
23. C₂²×#6127	C₂²	semidirect
25. C₂³×D₅₂	C₂²	semidirect
26. C₂³×C₄×D₁₃	C₂²	semidirect
27. C₁₃×#532	C₂²	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#127	C₂²	semidirect
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂²×C₄²×C₁₃	C₂²	semidirect
36. #11719538	C₂²	semidirect
37. C₂×#88200	C₂²	semidirect
38. C₂×#88193	C₂²	semidirect
39. C₂×#88192	C₂²	semidirect
40. C₂×#88192	C₂²	semidirect
41. C₂×#88191	C₂²	semidirect
42. C₂×#88184	C₂²	semidirect
43. C₂×#88184	C₂²	semidirect
44. C₂×#88184	C₂²	semidirect
45. C₂²×#6103	C₂²	semidirect
46. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
47. C₂×#88178	C₂²	semidirect
48. #11719431	C₂²	semidirect
49. #11719422	C₂²	semidirect
50. #11719381	C₂²	semidirect
51. #11719310	C₂²	semidirect
52. D₁₃×#121	C₂²	semidirect
53. #11719256	C₂²	semidirect
54. #11719255	C₂²	semidirect
55. D₄×D₅₂	C₂²	semidirect
56. C₂×#88149	C₂²	semidirect
57. C₂×#88148	C₂²	semidirect
58. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
59. C₂×#88138	C₂²	semidirect
60. C₂×#88137	C₂²	semidirect
61. C₂×#88136	C₂²	semidirect
62. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
63. #11719182	C₂²	semidirect
64. C₂×#88129	C₂²	semidirect
65. C₂×#88128	C₂²	semidirect
66. C₂×C₄×D₅₂	C₂²	semidirect
67. C₂×C₄×D₅₂	C₂²	semidirect
68. C₂×C₄×D₅₂	C₂²	semidirect
69. C₂×C₄×D₅₂	C₂²	semidirect
70. C₂×C₄×D₅₂	C₂²	semidirect
71. C₂×C₄×D₅₂	C₂²	semidirect
72. C₂×C₄×D₅₂	C₂²	semidirect
73. C₂×#88123	C₂²	semidirect
77. C₂×C₁₃×#41	C₂³	semidirect
93. C₂×#6131	C₂³	semidirect
97. C₂×D₄×D₁₃	C₂³	semidirect
98. C₂×D₄×D₁₃	C₂³	semidirect
99. C₂×D₄×D₁₃	C₂³	semidirect
102. C₂×#6127	C₂³	semidirect
103. C₂×#6127	C₂³	semidirect
105. C₂²×D₅₂	D₄	semidirect
113. C₂²×D₅₂	C₂³	semidirect
119. C₂²×C₄×D₁₃	C₂³	semidirect
121. C₁₃×C₄⋊Q₈	C₂³	semidirect
122. C₁₃×#127	C₂³	semidirect
123. C₁₃×#124	C₂³	semidirect
124. C₁₃×#121	C₂³	semidirect
125. C₁₃×#121	C₂³	semidirect
126. C₄×D₄×C₁₃	C₂³	semidirect
127. C₄×D₄×C₁₃	C₂³	semidirect
136. C₂×C₄²×C₁₃	C₂³	semidirect
138. #88200	C₂³	semidirect
139. #88193	C₂³	semidirect
140. #88192	C₂³	semidirect
141. #88192	C₂³	semidirect
142. #88191	C₂³	semidirect
143. #88184	C₂³	semidirect
144. #88184	C₂³	semidirect
145. #88184	C₂³	semidirect
151. C₂×#6103	C₂³	semidirect
156. C₂×C₄⋊Dic₁₃	C₂³	semidirect
157. #88178	C₂³	semidirect
159. #88149	C₂³	semidirect
160. #88148	C₂³	semidirect
161. C₄⋊C₄×D₁₃	C₂³	semidirect
162. #88138	C₂³	semidirect
163. #88137	C₂³	semidirect
164. #88136	C₂³	semidirect
165. C₂²⋊C₄×D₁₃	C₂³	semidirect
166. #88129	C₂³	semidirect
167. #88128	C₂³	semidirect
168. C₄×D₅₂	C₂³	semidirect
169. C₄×D₅₂	C₂³	semidirect
170. C₄×D₅₂	C₂³	semidirect
171. C₄×D₅₂	C₂³	semidirect
172. C₄×D₅₂	C₂³	semidirect
173. C₄×D₅₂	C₂³	semidirect
174. #88123	C₂³	semidirect
183. C₂³×D₁₃	C₂×D₄	semidirect
202. C₂²×C₄×C₁₃	C₂×D₄	semidirect
235. C₂×D₅₂	C₂×D₄	semidirect
236. C₂×D₅₂	C₂×D₄	semidirect
237. C₂×D₅₂	C₂×D₄	semidirect
285. C₂×#532	D₁₃	semidirect
310. C₂²×D₁₃	C₂²×D₄	semidirect
327. C₂×C₄×C₁₃	C₂²×D₄	semidirect
328. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
348. D₅₂	C₂²×D₄	semidirect
349. D₅₂	C₂²×D₄	semidirect
360. C₂²×#41	C₂×D₁₃	semidirect
376. #532	C₂×D₁₃	semidirect
378. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
380. C₂×#127	C₂×D₁₃	semidirect
382. C₂×#124	C₂×D₁₃	semidirect
396. C₂×#121	C₂×D₁₃	semidirect
397. C₂×#121	C₂×D₁₃	semidirect
407. C₂×C₄×D₄	C₂×D₁₃	semidirect
408. C₂×C₄×D₄	C₂×D₁₃	semidirect
413. C₂²×C₄²	C₂×D₁₃	semidirect
442. C₄×C₁₃	C₂×H(5,𝔽₂)	semidirect
455. C₂×#41	C₂²×D₁₃	semidirect
493. C₄⋊Q₈	C₂²×D₁₃	semidirect
495. #127	C₂²×D₁₃	semidirect
497. #124	C₂²×D₁₃	semidirect
510. #121	C₂²×D₁₃	semidirect
511. #121	C₂²×D₁₃	semidirect
520. C₄×D₄	C₂²×D₁₃	semidirect
521. C₄×D₄	C₂²×D₁₃	semidirect
545. C₂×C₄²	C₂²×D₁₃	semidirect
548. C₂×C₁₃	#3496	semidirect
621. C₂²×C₄	D₄×D₁₃	semidirect
652. C₁₃	C₂×#3496	semidirect
711. C₂×C₄	C₂×D₄×D₁₃	semidirect
712. C₂×C₄	#88256	semidirect
750. C₄	C₂×#88256	semidirect
755. C₂	#13128598	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88256	2
#13128598	2
C₂×#11719256	2
C₂×#11719431	2
C₂×#11719255	2
C₂×#11719381	2
C₂×D₄×D₅₂	2
C₂×#11719422	2
C₂×#11719538	2
C₂×#11719310	2
C₂×#11719182	2
C₂×D₁₃×#121	2
C₂²×C₄×D₅₂	2
C₂×C₁₃×#532	2
C₂×#3496	13

Subgroups — C2×#13128598 #16770808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128598 #16770808