Subgroups — C₂²×#11719265 #16769646

Order 3328.

9566 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719265	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88130	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88148	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88183	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#88132	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88184	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#88138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#88193	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#88136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#88191	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×#6103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₂³×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂³×D₅₂	C₂²	1	1	yes	characteristic
27	C₂³×D₅₂	C₂²	1	1	yes	characteristic
28	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#88193	C₂²	1	24	yes	complemented
38	C₂×#88191	C₂²	1	24	yes	complemented
39	C₂×#88184	C₂²	1	24	yes	complemented
40	C₂×#88183	C₂²	1	24	yes	complemented
41	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
42	C₂²×#6103	C₂²	1	1	yes	characteristic
43	C₂²×#6103	C₂²	1	1	yes	characteristic
44	C₂²×#6103	C₂²	1	1	yes	characteristic
45	C₂²×#6103	C₂²	1	1	yes	characteristic
46	C₂²×#6103	C₂²	1	1	yes	characteristic
47	C₂²×#6103	C₂²	1	1	yes	characteristic
48	C₂²×#6103	C₂²	1	1	yes	characteristic
49	C₂²×#6103	C₂²	1	1	yes	characteristic
50	C₂²×#6103	C₂²	1	24	yes	complemented
51	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#6103	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
56	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#6101	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	#11719265	C₂²	1	256	yes	direct product factor
60	C₂×#88152	C₂²	1	24	yes	complemented
61	C₂×#88148	C₂²	1	24	yes	complemented
62	C₂×#88139	C₂²	1	24	yes	complemented
63	C₂×#88138	C₂²	1	24	yes	complemented
64	C₂×#88136	C₂²	1	24	yes	complemented
65	C₂×#88132	C₂²	1	24	yes	complemented
66	C₂×#88130	C₂²	1	24	yes	complemented
67	C₂×#88129	C₂²	1	24	yes	complemented
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
70	C₂⁴×D₁₃	—	2	8	no	—
71	C₂⁴×D₁₃	—	4	4	no	—
72	C₂⁴×D₁₃	—	4	4	no	—
73	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
74	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
75	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
76	C₂⁴×D₁₃	C₂³	1	12	yes	—
77	C₂²×D₄×C₁₃	—	2	8	no	—
78	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
79	C₂³×C₄×C₁₃	—	4	4	no	—
80	C₂³×C₄×C₁₃	—	4	4	no	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
88	C₂²×C₂²⋊D₁₃	—	2	8	no	—
89	C₂²×C₂²⋊D₁₃	—	4	4	no	—
90	C₂²×C₂²⋊D₁₃	—	4	4	no	—
91	C₂²×C₂²⋊D₁₃	—	4	4	no	—
92	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
93	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
94	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
95	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	complemented
96	C₂³×Dic₁₃	—	4	4	no	—
97	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
99	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
100	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
101	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
102	C₂³×Dic₁₃	C₂³	1	12	yes	—
103	C₂²×D₅₂	—	4	4	no	—
104	C₂²×D₅₂	—	4	4	no	—
105	C₂²×D₅₂	C₂³	1	12	yes	—
106	C₂²×D₅₂	C₂³	1	12	yes	—
107	C₂²×C₄×D₁₃	—	4	4	no	—
108	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
109	C₂²×Dic₂₆	—	4	4	no	—
110	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
111	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
115	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
116	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
117	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	complemented
118	#88193	C₂³	1	64	yes	complemented
119	#88191	C₂³	1	64	yes	complemented
120	#88184	C₂³	1	64	yes	complemented
121	#88183	C₂³	1	64	yes	complemented
122	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
123	C₂×#6103	C₂³	1	12	yes	—
124	C₂×#6103	C₂³	1	12	yes	—
125	C₂×#6103	C₂³	1	12	yes	—
126	C₂×#6103	C₂³	1	12	yes	—
127	C₂×#6103	C₂³	1	12	yes	—
128	C₂×#6103	C₂³	1	12	yes	—
129	C₂×#6103	C₂³	1	12	yes	—
130	C₂×#6103	C₂³	1	12	yes	—
131	C₂×#6103	C₂³	1	64	yes	complemented
132	C₂×#6103	C₂³	1	12	yes	complemented
133	C₂×#6103	C₂³	1	12	yes	complemented
134	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
135	C₂×#6101	C₂³	1	12	yes	complemented
136	C₂×#6101	C₂³	1	12	yes	complemented
137	C₂×#6101	C₂³	1	12	yes	complemented
138	C₂×#6101	C₂³	1	12	yes	complemented
139	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
140	#88152	C₂³	1	64	yes	complemented
141	#88148	C₂³	1	64	yes	complemented
142	#88139	C₂³	1	64	yes	complemented
143	#88138	C₂³	1	64	yes	complemented
144	#88136	C₂³	1	64	yes	complemented
145	#88132	C₂³	1	64	yes	complemented
146	#88130	C₂³	1	64	yes	complemented
147	#88129	C₂³	1	64	yes	complemented
148	C₂²×#538	—	13	1	no	maximal, Sylow
149	C₂⁴×C₁₃	—	2	4	no	—
150	C₂⁴×C₁₃	—	2	4	no	—
151	C₂⁴×C₁₃	—	2	4	no	—
152	C₂⁴×C₁₃	—	2	4	no	—
153	C₂⁴×C₁₃	—	2	4	no	—
154	C₂⁴×C₁₃	#41	1	8	yes	—
155	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂³×D₁₃	—	2	4	no	—
159	C₂³×D₁₃	—	2	48	no	—
160	C₂³×D₁₃	—	2	4	no	—
161	C₂³×D₁₃	—	2	4	no	—
162	C₂³×D₁₃	—	2	4	no	—
163	C₂³×D₁₃	—	2	4	no	—
164	C₂³×D₁₃	—	2	4	no	—
165	C₂³×D₁₃	—	2	4	no	—
166	C₂³×D₁₃	—	2	4	no	—
167	C₂³×D₁₃	—	2	4	no	—
168	C₂³×D₁₃	—	4	24	no	—
169	C₂³×D₁₃	—	4	24	no	—
170	C₂³×D₁₃	—	4	64	no	—
171	C₂³×D₁₃	C₂⁴	1	6	yes	—
172	C₂³×D₁₃	C₂⁴	1	6	yes	—
173	C₂³×D₁₃	C₂⁴	1	6	yes	—
174	C₂³×D₁₃	C₂⁴	1	16	yes	—
175	C₂×D₄×C₁₃	—	2	48	no	—
176	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	4	24	no	—
183	C₂²×C₄×C₁₃	—	4	24	no	—
184	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
191	C₂×C₂²⋊D₁₃	—	2	48	no	—
192	C₂×C₂²⋊D₁₃	—	4	24	no	—
193	C₂×C₂²⋊D₁₃	—	4	24	no	—
194	C₂×C₂²⋊D₁₃	—	4	24	no	—
195	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
196	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
197	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
198	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
199	C₂²×Dic₁₃	—	2	4	no	—
200	C₂²×Dic₁₃	—	2	4	no	—
201	C₂²×Dic₁₃	—	2	4	no	—
202	C₂²×Dic₁₃	—	2	4	no	—
203	C₂²×Dic₁₃	—	2	4	no	—
204	C₂²×Dic₁₃	—	4	24	no	—
205	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
206	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
207	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
208	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
209	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
210	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
211	C₂×D₅₂	—	4	24	no	—
212	C₂×D₅₂	—	4	24	no	—
213	C₂×D₅₂	C₂⁴	1	16	yes	—
214	C₂×D₅₂	C₂⁴	1	16	yes	—
215	C₂×C₄×D₁₃	—	4	24	no	—
216	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
217	C₂×Dic₂₆	—	4	24	no	—
218	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
219	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
220	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
222	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
223	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
224	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
225	#6103	C₂⁴	1	16	yes	—
226	#6103	C₂⁴	1	16	yes	—
227	#6103	C₂⁴	1	16	yes	—
228	#6103	C₂⁴	1	16	yes	—
229	#6103	C₂⁴	1	16	yes	—
230	#6103	C₂⁴	1	16	yes	—
231	#6103	C₂⁴	1	16	yes	—
232	#6103	C₂⁴	1	16	yes	—
233	#6103	C₂⁴	1	16	yes	complemented
234	#6103	C₂⁴	1	16	yes	complemented
235	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
236	#6101	C₂⁴	1	16	yes	complemented
237	#6101	C₂⁴	1	16	yes	complemented
238	#6101	C₂⁴	1	16	yes	complemented
239	#6101	C₂⁴	1	16	yes	complemented
240	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
241	C₂×#538	—	13	48	no	—
242	C₂²×#126	—	13	1	no	—
243	C₂²×#126	—	13	1	no	—
244	C₂²×#124	—	13	1	no	—
245	C₂²×#124	—	13	1	no	—
246	C₂²×#123	—	13	1	no	—
247	C₂²×#123	—	13	1	no	—
248	C₂²×C₂²⋊Q₈	—	13	1	no	—
249	C₂²×#121	—	13	1	no	—
250	C₂²×#121	—	13	1	no	—
251	C₂²×#121	—	13	1	no	—
252	C₂²×#120	—	13	1	no	—
253	C₂²×#120	—	13	1	no	—
254	C₂²×C₄×D₄	—	13	1	no	—
255	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₂²⋊C₄	—	13	1	no	—
257	C₂³×C₁₃	—	2	32	no	—
258	C₂³×C₁₃	—	2	12	no	—
259	C₂³×C₁₃	—	2	12	no	—
260	C₂³×C₁₃	—	2	12	no	—
261	C₂³×C₁₃	—	2	12	no	—
262	C₂³×C₁₃	—	2	12	no	—
263	C₂³×C₁₃	—	4	16	no	—
264	C₂³×C₁₃	C₂×#41	1	24	yes	—
265	C₂³×C₁₃	C₂×#41	1	4	yes	—
266	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
267	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
268	C₂³×C₁₃	C₂⁵	1	4	yes	—
269	C₂³×C₁₃	C₂⁵	1	4	yes	—
270	C₂³×C₁₃	C₂⁵	1	3	yes	—
271	C₂²×D₁₃	—	2	12	no	—
272	C₂²×D₁₃	—	2	32	no	—
273	C₂²×D₁₃	—	2	12	no	—
274	C₂²×D₁₃	—	2	12	no	—
275	C₂²×D₁₃	—	2	12	no	—
276	C₂²×D₁₃	—	2	12	no	—
277	C₂²×D₁₃	—	2	12	no	—
278	C₂²×D₁₃	—	2	12	no	—
279	C₂²×D₁₃	—	2	12	no	—
280	C₂²×D₁₃	—	2	12	no	—
281	C₂²×D₁₃	—	4	16	no	—
282	C₂²×D₁₃	—	4	16	no	—
283	C₂²×D₁₃	—	4	192	no	—
284	C₂²×D₁₃	—	4	16	no	—
285	C₂²×D₁₃	—	4	16	no	—
286	C₂²×D₁₃	—	4	16	no	—
287	C₂²×D₁₃	C₂⁵	1	4	yes	—
288	C₂²×D₁₃	C₂⁵	1	4	yes	—
289	C₂²×D₁₃	C₂⁵	1	4	yes	—
290	D₄×C₁₃	—	2	32	no	—
291	C₂×C₄×C₁₃	—	2	12	no	—
292	C₂×C₄×C₁₃	—	2	12	no	—
293	C₂×C₄×C₁₃	—	2	12	no	—
294	C₂×C₄×C₁₃	—	2	12	no	—
295	C₂×C₄×C₁₃	—	2	12	no	—
296	C₂×C₄×C₁₃	—	4	16	no	—
297	C₂×C₄×C₁₃	—	4	16	no	—
298	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
300	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
302	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
303	C₂²⋊D₁₃	—	2	32	no	—
304	C₂²⋊D₁₃	—	4	16	no	—
305	C₂²⋊D₁₃	—	4	16	no	—
306	C₂²⋊D₁₃	—	4	16	no	—
307	C₂×Dic₁₃	—	2	12	no	—
308	C₂×Dic₁₃	—	2	12	no	—
309	C₂×Dic₁₃	—	2	12	no	—
310	C₂×Dic₁₃	—	2	12	no	—
311	C₂×Dic₁₃	—	2	12	no	—
312	C₂×Dic₁₃	—	4	16	no	—
313	C₂×Dic₁₃	C₂⁵	1	4	yes	—
314	C₂×Dic₁₃	C₂⁵	1	4	yes	—
315	C₂×Dic₁₃	C₂⁵	1	4	yes	—
316	C₂×Dic₁₃	C₂⁵	1	4	yes	—
317	C₂×Dic₁₃	C₂⁵	1	4	yes	—
318	D₅₂	—	4	16	no	—
319	D₅₂	—	4	16	no	—
320	C₄×D₁₃	—	4	16	no	—
321	Dic₂₆	—	4	16	no	—
322	C₂⁶	—	13	1	no	—
323	C₂³×Q₈	—	13	1	no	—
324	C₂³×D₄	—	13	1	no	—
325	C₂³×D₄	—	13	1	no	—
326	C₂³×D₄	—	13	1	no	—
327	C₂³×D₄	—	13	1	no	—
328	C₂³×D₄	—	13	1	no	—
329	C₂³×D₄	—	13	1	no	—
330	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
331	C₂⁴×C₄	—	13	1	no	—
332	C₂⁴×C₄	—	13	1	no	—
333	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
334	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
335	#538	—	13	256	no	—
336	C₂×#126	—	13	24	no	—
337	C₂×#126	—	13	24	no	—
338	C₂×#124	—	13	24	no	—
339	C₂×#124	—	13	24	no	—
340	C₂×#123	—	13	24	no	—
341	C₂×#123	—	13	24	no	—
342	C₂×C₂²⋊Q₈	—	13	24	no	—
343	C₂×#121	—	13	24	no	—
344	C₂×#121	—	13	24	no	—
345	C₂×#121	—	13	24	no	—
346	C₂×#120	—	13	24	no	—
347	C₂×#120	—	13	24	no	—
348	C₂×C₄×D₄	—	13	24	no	—
349	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
350	C₂²×C₄⋊C₄	—	13	1	no	—
351	C₂²×C₄⋊C₄	—	13	1	no	—
352	C₂²×C₄⋊C₄	—	13	1	no	—
353	C₂²×C₄⋊C₄	—	13	1	no	—
354	C₂²×C₄⋊C₄	—	13	1	no	—
355	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
356	C₂²×C₂²⋊C₄	—	13	1	no	—
357	C₂²×C₂²⋊C₄	—	13	1	no	—
358	C₂²×C₂²⋊C₄	—	13	1	no	—
359	C₂²×C₂²⋊C₄	—	13	1	no	—
360	C₂²×C₂²⋊C₄	—	13	1	no	—
361	C₂²×C₂²⋊C₄	—	13	1	no	—
362	C₂²×C₂²⋊C₄	—	13	1	no	—
363	C₂²×C₂²⋊C₄	—	13	1	no	—
364	C₂²×C₂²⋊C₄	—	13	1	no	—
365	C₂²×C₂²⋊C₄	—	13	1	no	—
366	C₂²×C₂²⋊C₄	—	13	24	no	—
367	C₂²×C₂²⋊C₄	—	13	1	no	—
368	C₂²×C₂²⋊C₄	—	13	1	no	—
369	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
371	C₂²×C₄²	—	13	1	no	—
372	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
373	C₂²×C₁₃	—	2	4	no	—
374	C₂²×C₁₃	—	2	4	no	—
375	C₂²×C₁₃	—	2	48	no	—
376	C₂²×C₁₃	—	2	4	no	—
377	C₂²×C₁₃	—	2	4	no	—
378	C₂²×C₁₃	—	2	4	no	—
379	C₂²×C₁₃	—	4	24	no	—
380	C₂²×C₁₃	#538	1	16	yes	complemented
381	C₂²×C₁₃	C₂²×#41	1	8	yes	—
382	C₂²×C₁₃	C₂²×#41	1	6	yes	—
383	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
384	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
385	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
386	C₂×D₁₃	—	2	4	no	—
387	C₂×D₁₃	—	2	4	no	—
388	C₂×D₁₃	—	2	4	no	—
389	C₂×D₁₃	—	2	4	no	—
390	C₂×D₁₃	—	2	4	no	—
391	C₂×D₁₃	—	2	4	no	—
392	C₂×D₁₃	—	2	4	no	—
393	C₂×D₁₃	—	2	4	no	—
394	C₂×D₁₃	—	2	4	no	—
395	C₂×D₁₃	—	4	64	no	—
396	C₂×D₁₃	—	4	24	no	—
397	C₂×D₁₃	—	4	24	no	—
398	C₂×D₁₃	—	4	24	no	—
399	C₄×C₁₃	—	2	4	no	—
400	C₄×C₁₃	—	2	4	no	—
401	C₄×C₁₃	—	2	4	no	—
402	C₄×C₁₃	—	2	4	no	—
403	C₄×C₁₃	—	2	4	no	—
404	Dic₁₃	—	2	4	no	—
405	Dic₁₃	—	2	4	no	—
406	Dic₁₃	—	2	4	no	—
407	Dic₁₃	—	2	4	no	—
408	Dic₁₃	—	2	4	no	—
409	C₂⁵	—	13	1	no	—
410	C₂⁵	—	13	1	no	—
411	C₂⁵	—	13	1	no	—
412	C₂⁵	—	13	12	no	—
413	C₂⁵	—	26	8	no	—
414	C₂⁵	—	52	4	no	—
415	C₂⁵	—	52	4	no	—
416	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
417	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
418	C₂²×Q₈	—	13	12	no	—
419	C₂²×Q₈	—	52	4	no	—
420	C₂²×D₄	—	2	8	no	—
421	C₂²×D₄	—	13	12	no	—
422	C₂²×D₄	—	13	12	no	—
423	C₂²×D₄	—	13	12	no	—
424	C₂²×D₄	—	13	12	no	—
425	C₂²×D₄	—	13	12	no	—
426	C₂²×D₄	—	13	12	no	—
427	C₂²×D₄	—	26	8	no	—
428	C₂²×D₄	—	52	4	no	—
429	C₂²×D₄	—	52	4	no	—
430	C₂²×D₄	—	52	4	no	—
431	C₂²×D₄	—	52	4	no	—
432	C₂²×D₄	—	52	4	no	—
433	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
434	C₂³×C₄	—	4	4	no	—
435	C₂³×C₄	—	4	4	no	—
436	C₂³×C₄	—	13	1	no	—
437	C₂³×C₄	—	13	1	no	—
438	C₂³×C₄	—	13	1	no	—
439	C₂³×C₄	—	13	1	no	—
440	C₂³×C₄	—	13	1	no	—
441	C₂³×C₄	—	13	12	no	—
442	C₂³×C₄	—	13	12	no	—
443	C₂³×C₄	—	52	4	no	—
444	C₂³×C₄	—	52	4	no	—
445	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
448	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
449	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
450	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
451	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
452	#126	—	13	64	no	—
453	#126	—	13	64	no	—
454	#124	—	13	64	no	—
455	#124	—	13	64	no	—
456	#123	—	13	64	no	—
457	#123	—	13	64	no	—
458	C₂²⋊Q₈	—	13	64	no	—
459	#121	—	13	64	no	—
460	#121	—	13	64	no	—
461	#121	—	13	64	no	—
462	#120	—	13	64	no	—
463	#120	—	13	64	no	—
464	C₄×D₄	—	13	64	no	—
465	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
466	C₂×C₄⋊C₄	—	13	12	no	—
467	C₂×C₄⋊C₄	—	13	12	no	—
468	C₂×C₄⋊C₄	—	13	12	no	—
469	C₂×C₄⋊C₄	—	13	12	no	—
470	C₂×C₄⋊C₄	—	13	12	no	—
471	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
472	C₂×C₂²⋊C₄	—	13	12	no	—
473	C₂×C₂²⋊C₄	—	13	12	no	—
474	C₂×C₂²⋊C₄	—	13	12	no	—
475	C₂×C₂²⋊C₄	—	13	12	no	—
476	C₂×C₂²⋊C₄	—	13	12	no	—
477	C₂×C₂²⋊C₄	—	13	12	no	—
478	C₂×C₂²⋊C₄	—	13	64	no	—
479	C₂×C₂²⋊C₄	—	13	12	no	—
480	C₂×C₂²⋊C₄	—	13	12	no	—
481	C₂×C₂²⋊C₄	—	13	12	no	—
482	C₂×C₂²⋊C₄	—	13	12	no	—
483	C₂×C₂²⋊C₄	—	13	12	no	—
484	C₂×C₂²⋊C₄	—	13	12	no	—
485	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
486	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	complemented
487	C₂×C₄²	—	13	12	no	—
488	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
489	C₂×C₁₃	—	2	8	no	—
490	C₂×C₁₃	—	4	4	no	—
491	C₂×C₁₃	C₂×#538	1	12	yes	complemented
492	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
493	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
495	D₁₃	—	4	4	no	—
496	D₁₃	—	4	4	no	—
497	D₁₃	—	4	4	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	2	4	no	—
502	C₂⁴	—	2	4	no	—
503	C₂⁴	—	13	6	no	—
504	C₂⁴	—	13	6	no	—
505	C₂⁴	—	13	6	no	—
506	C₂⁴	—	13	16	no	—
507	C₂⁴	—	26	4	no	—
508	C₂⁴	—	26	48	no	—
509	C₂⁴	—	26	4	no	—
510	C₂⁴	—	26	4	no	—
511	C₂⁴	—	26	4	no	—
512	C₂⁴	—	26	4	no	—
513	C₂⁴	—	26	4	no	—
514	C₂⁴	—	26	4	no	—
515	C₂⁴	—	26	4	no	—
516	C₂⁴	—	26	4	no	—
517	C₂⁴	—	52	24	no	—
518	C₂⁴	—	52	24	no	—
519	C₂⁴	—	52	64	no	—
520	C₂⁴	#6127	1	8	yes	—
521	C₂⁴	C₂³×D₁₃	1	6	yes	—
522	C₂⁴	C₂³×D₁₃	1	6	yes	—
523	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
524	C₂×Q₈	—	13	16	no	—
525	C₂×Q₈	—	52	24	no	—
526	C₂×D₄	—	2	48	no	—
527	C₂×D₄	—	13	16	no	—
528	C₂×D₄	—	13	16	no	—
529	C₂×D₄	—	13	16	no	—
530	C₂×D₄	—	13	16	no	—
531	C₂×D₄	—	13	16	no	—
532	C₂×D₄	—	13	16	no	—
533	C₂×D₄	—	26	48	no	—
534	C₂×D₄	—	52	24	no	—
535	C₂×D₄	—	52	24	no	—
536	C₂×D₄	—	52	24	no	—
537	C₂×D₄	—	52	24	no	—
538	C₂×D₄	—	52	24	no	—
539	C₂×D₄	C₂³×D₁₃	1	16	yes	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	4	24	no	—
546	C₂²×C₄	—	4	24	no	—
547	C₂²×C₄	—	13	6	no	—
548	C₂²×C₄	—	13	6	no	—
549	C₂²×C₄	—	13	6	no	—
550	C₂²×C₄	—	13	6	no	—
551	C₂²×C₄	—	13	6	no	—
552	C₂²×C₄	—	13	16	no	—
553	C₂²×C₄	—	13	16	no	—
554	C₂²×C₄	—	26	4	no	—
555	C₂²×C₄	—	26	4	no	—
556	C₂²×C₄	—	26	4	no	—
557	C₂²×C₄	—	26	4	no	—
558	C₂²×C₄	—	26	4	no	—
559	C₂²×C₄	—	52	24	no	—
560	C₂²×C₄	—	52	24	no	—
561	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
562	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
563	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
564	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
565	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
566	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
567	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
568	C₄⋊C₄	—	13	16	no	—
569	C₄⋊C₄	—	13	16	no	—
570	C₄⋊C₄	—	13	16	no	—
571	C₄⋊C₄	—	13	16	no	—
572	C₄⋊C₄	—	13	16	no	—
573	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
574	C₂²⋊C₄	—	13	16	no	—
575	C₂²⋊C₄	—	13	16	no	—
576	C₂²⋊C₄	—	13	16	no	—
577	C₂²⋊C₄	—	13	16	no	—
578	C₂²⋊C₄	—	13	16	no	—
579	C₂²⋊C₄	—	13	16	no	—
580	C₂²⋊C₄	—	13	16	no	—
581	C₂²⋊C₄	—	13	16	no	—
582	C₂²⋊C₄	—	13	16	no	—
583	C₂²⋊C₄	—	13	16	no	—
584	C₂²⋊C₄	—	13	16	no	—
585	C₂²⋊C₄	—	13	16	no	—
586	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
587	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
588	C₄²	—	13	16	no	—
589	C₄²	C₂³×D₁₃	1	16	yes	complemented
590	C₁₃	C₂²×#538	1	1	yes	characteristic, complemented, Sylow
591	C₂³	—	2	32	no	—
592	C₂³	—	2	12	no	—
593	C₂³	—	2	12	no	—
594	C₂³	—	2	12	no	—
595	C₂³	—	2	12	no	—
596	C₂³	—	2	12	no	—
597	C₂³	—	4	16	no	—
598	C₂³	—	13	4	no	—
599	C₂³	—	13	4	no	—
600	C₂³	—	13	4	no	—
601	C₂³	—	26	12	no	—
602	C₂³	—	26	32	no	—
603	C₂³	—	26	12	no	—
604	C₂³	—	26	12	no	—
605	C₂³	—	26	12	no	—
606	C₂³	—	26	12	no	—
607	C₂³	—	26	12	no	—
608	C₂³	—	26	12	no	—
609	C₂³	—	26	12	no	—
610	C₂³	—	26	12	no	—
611	C₂³	—	52	16	no	—
612	C₂³	—	52	16	no	—
613	C₂³	—	52	192	no	—
614	C₂³	—	52	16	no	—
615	C₂³	—	52	16	no	—
616	C₂³	—	52	16	no	—
617	C₂³	C₂×#6127	1	24	yes	—
618	C₂³	C₂×#6127	1	4	yes	—
619	C₂³	#88251	1	4	yes	—
620	C₂³	#88256	1	4	yes	—
621	C₂³	C₂⁴×D₁₃	1	4	yes	—
622	C₂³	C₂⁴×D₁₃	1	4	yes	—
623	C₂³	C₂⁴×D₁₃	1	3	yes	—
624	Q₈	—	52	16	no	—
625	D₄	—	2	32	no	—
626	D₄	—	26	32	no	—
627	D₄	—	52	16	no	—
628	D₄	—	52	16	no	—
629	D₄	—	52	16	no	—
630	D₄	—	52	16	no	—
631	D₄	—	52	16	no	—
632	C₂×C₄	—	2	12	no	—
633	C₂×C₄	—	2	12	no	—
634	C₂×C₄	—	2	12	no	—
635	C₂×C₄	—	2	12	no	—
636	C₂×C₄	—	2	12	no	—
637	C₂×C₄	—	4	16	no	—
638	C₂×C₄	—	4	16	no	—
639	C₂×C₄	—	13	4	no	—
640	C₂×C₄	—	13	4	no	—
641	C₂×C₄	—	13	4	no	—
642	C₂×C₄	—	13	4	no	—
643	C₂×C₄	—	13	4	no	—
644	C₂×C₄	—	26	12	no	—
645	C₂×C₄	—	26	12	no	—
646	C₂×C₄	—	26	12	no	—
647	C₂×C₄	—	26	12	no	—
648	C₂×C₄	—	26	12	no	—
649	C₂×C₄	—	52	16	no	—
650	C₂×C₄	—	52	16	no	—
651	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
652	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
653	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
654	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
655	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	48	no	—
659	C₂²	—	2	4	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	4	24	no	—
663	C₂²	—	26	4	no	—
664	C₂²	—	26	4	no	—
665	C₂²	—	26	4	no	—
666	C₂²	—	26	4	no	—
667	C₂²	—	26	4	no	—
668	C₂²	—	26	4	no	—
669	C₂²	—	26	4	no	—
670	C₂²	—	26	4	no	—
671	C₂²	—	26	4	no	—
672	C₂²	—	52	64	no	—
673	C₂²	—	52	24	no	—
674	C₂²	—	52	24	no	—
675	C₂²	—	52	24	no	—
676	C₂²	#11719265	1	16	yes	direct product factor
677	C₂²	C₂²×#6127	1	8	yes	—
678	C₂²	C₂²×#6127	1	6	yes	—
679	C₂²	C₂×#88251	1	6	yes	—
680	C₂²	C₂×#88256	1	6	yes	—
681	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	4	no	—
687	C₄	—	26	4	no	—
688	C₄	—	26	4	no	—
689	C₄	—	26	4	no	—
690	C₄	—	26	4	no	—
691	C₄	—	26	4	no	—
692	C₂	—	2	8	no	—
693	C₂	—	4	4	no	—
694	C₂	—	52	4	no	—
695	C₂	—	52	4	no	—
696	C₂	—	52	4	no	—
697	C₂	C₂×#11719265	1	12	yes	direct product factor
698	C₂	C₂³×#6127	1	1	yes	characteristic
699	C₂	C₂²×#88251	1	1	yes	characteristic
700	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×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×#538
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11719265	C₂	direct (N × H)
2. C₂²×#88152	C₂	semidirect
3. C₂²×#88130	C₂	semidirect
4. C₂²×#88129	C₂	semidirect
5. C₂²×#88139	C₂	semidirect
6. C₂²×#88148	C₂	semidirect
7. C₂²×#88183	C₂	semidirect
8. C₂²×#88132	C₂	semidirect
9. C₂²×#88184	C₂	semidirect
10. C₂²×#88138	C₂	semidirect
11. C₂²×#88193	C₂	semidirect
12. C₂²×#88136	C₂	semidirect
13. C₂²×#88191	C₂	semidirect
14. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
15. C₂³×#6103	C₂	semidirect
16. C₂²×C₄×D₄×C₁₃	C₂	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
24. C₂³×C₂²⋊D₁₃	C₂²	semidirect
28. C₂³×C₄×D₁₃	C₂²	semidirect
29. C₂³×Dic₂₆	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
31. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
34. C₂²×C₄²×C₁₃	C₂²	semidirect
36. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
37. C₂×#88193	C₂²	semidirect
38. C₂×#88191	C₂²	semidirect
39. C₂×#88184	C₂²	semidirect
40. C₂×#88183	C₂²	semidirect
41. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
50. C₂²×#6103	C₂²	semidirect
51. C₂²×#6103	C₂²	semidirect
52. C₂²×#6103	C₂²	semidirect
53. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
54. C₂²×#6101	C₂²	semidirect
55. C₂²×#6101	C₂²	semidirect
56. C₂²×#6101	C₂²	semidirect
57. C₂²×#6101	C₂²	semidirect
58. C₂²×C₄×Dic₁₃	C₂²	semidirect
59. #11719265	C₂²	direct (N × H)
60. C₂×#88152	C₂²	semidirect
61. C₂×#88148	C₂²	semidirect
62. C₂×#88139	C₂²	semidirect
63. C₂×#88138	C₂²	semidirect
64. C₂×#88136	C₂²	semidirect
65. C₂×#88132	C₂²	semidirect
66. C₂×#88130	C₂²	semidirect
67. C₂×#88129	C₂²	semidirect
87. C₂³×C₄×C₁₃	C₂³	semidirect
95. C₂²×C₂²⋊D₁₃	C₂³	semidirect
108. C₂²×C₄×D₁₃	C₂³	semidirect
110. C₂²×Dic₂₆	C₂³	semidirect
111. C₄×D₄×C₁₃	C₂³	semidirect
112. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
114. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
115. C₂×C₄²×C₁₃	C₂³	semidirect
117. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
118. #88193	C₂³	semidirect
119. #88191	C₂³	semidirect
120. #88184	C₂³	semidirect
121. #88183	C₂³	semidirect
122. C₄×C₂²⋊D₁₃	C₂³	semidirect
131. C₂×#6103	C₂³	semidirect
132. C₂×#6103	C₂³	semidirect
133. C₂×#6103	C₂³	semidirect
134. C₂×C₄⋊Dic₁₃	C₂³	semidirect
135. C₂×#6101	C₂³	semidirect
136. C₂×#6101	C₂³	semidirect
137. C₂×#6101	C₂³	semidirect
138. C₂×#6101	C₂³	semidirect
139. C₂×C₄×Dic₁₃	C₂³	semidirect
140. #88152	C₂³	semidirect
141. #88148	C₂³	semidirect
142. #88139	C₂³	semidirect
143. #88138	C₂³	semidirect
144. #88136	C₂³	semidirect
145. #88132	C₂³	semidirect
146. #88130	C₂³	semidirect
147. #88129	C₂³	semidirect
190. C₂²×C₄×C₁₃	C₂⁴	semidirect
198. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
216. C₂×C₄×D₁₃	C₂⁴	semidirect
218. C₂×Dic₂₆	C₂⁴	semidirect
219. C₁₃×C₄⋊C₄	C₂⁴	semidirect
221. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
222. C₄²×C₁₃	C₂⁴	semidirect
224. C₂²⋊Dic₁₃	C₂⁴	semidirect
233. #6103	C₂⁴	semidirect
234. #6103	C₂⁴	semidirect
235. C₄⋊Dic₁₃	C₂⁴	semidirect
236. #6101	C₂⁴	semidirect
237. #6101	C₂⁴	semidirect
238. #6101	C₂⁴	semidirect
239. #6101	C₂⁴	semidirect
240. C₄×Dic₁₃	C₂⁴	semidirect
255. C₂²×C₄×D₄	D₁₃	semidirect
334. C₂⁴×C₄	C₂×D₁₃	semidirect
349. C₂×C₄×D₄	C₂×D₁₃	semidirect
355. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
370. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
372. C₂²×C₄²	C₂×D₁₃	semidirect
380. C₂²×C₁₃	#538	semidirect
451. C₂³×C₄	C₂²×D₁₃	semidirect
465. C₄×D₄	C₂²×D₁₃	semidirect
471. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
486. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
488. C₂×C₄²	C₂²×D₁₃	semidirect
491. C₂×C₁₃	C₂×#538	semidirect
567. C₂²×C₄	C₂³×D₁₃	semidirect
573. C₄⋊C₄	C₂³×D₁₃	semidirect
587. C₂²⋊C₄	C₂³×D₁₃	semidirect
589. C₄²	C₂³×D₁₃	semidirect
590. C₁₃	C₂²×#538	semidirect
676. C₂²	#11719265	direct (N × H)
697. C₂	C₂×#11719265	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719265	2
C₂²×#88152	2
C₂²×#88130	2
C₂²×#88129	2
C₂²×#88139	2
C₂²×#88148	2
C₂²×#88183	2
C₂²×#88132	2
C₂²×#88184	2
C₂²×#88138	2
C₂²×#88193	2
C₂²×#88136	2
C₂²×#88191	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂³×#6103	2
C₂²×C₄×D₄×C₁₃	2
C₂²×#538	13

Subgroups — C22×#11719265 #16769646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719265 #16769646