Subgroups — #35202125

Order 20224.

10836 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099399	C₂	1	2	yes	maximal, complemented
2	#23778188	C₂	1	16	yes	maximal, complemented
3	#23778181	C₂	1	16	yes	maximal, complemented
4	#23778174	C₂	1	16	yes	maximal, complemented
5	C₂×#19099363	C₂	1	12	yes	maximal, complemented
6	C₂×#568×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099399	—	2	8	no	—
8	#19099399	—	2	8	no	—
9	#19099399	C₂²	1	16	yes	complemented
10	#19099399	C₂²	1	16	yes	complemented
11	C₂×#14579209	—	2	2	no	—
12	C₂×#14579208	C₂²	1	8	yes	complemented
13	C₂×#14579207	C₂²	1	8	yes	complemented
14	C₂×#14579206	—	2	6	no	—
15	C₂²×#11929624	C₂²	1	12	yes	complemented
16	C₂×#41×D₇₉	—	2	8	no	—
17	#19099380	C₂²	1	64	yes	complemented
18	#19099375	C₂²	1	128	yes	complemented
19	#19099368	C₂²	1	64	yes	complemented
20	#19099363	C₂²	1	16	yes	complemented
21	#19099363	C₂²	1	96	yes	complemented
22	#19099363	C₂²	1	48	yes	complemented
23	C₂×#14579194	C₂²	1	48	yes	complemented
24	C₂×#14579189	C₂²	1	48	yes	complemented
25	C₂×#14579183	C₂²	1	48	yes	complemented
26	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
27	#568×C₇₉	C₂²	1	16	yes	complemented
28	C₂×#131×C₇₉	C₂²	1	8	yes	complemented
29	C₂²×M₁₆×C₇₉	C₂²	1	6	yes	complemented
30	#14579209	—	2	16	no	—
31	#14579209	—	2	16	no	—
32	#14579208	—	2	32	no	—
33	#14579208	C₂³	1	64	yes	complemented
34	#14579207	—	2	32	no	—
35	#14579207	C₂³	1	64	yes	complemented
36	#14579206	—	2	48	no	—
37	#14579206	—	2	48	no	—
38	C₂×#11929625	—	2	8	no	—
39	C₂×#11929624	—	2	12	no	—
40	C₂×#11929624	—	2	24	no	—
41	C₂×#11929624	—	2	24	no	—
42	C₂×#11929624	—	2	12	no	—
43	C₂×#11929624	C₂³	1	48	yes	—
44	C₂×#11929624	C₂³	1	8	yes	—
45	C₂×#11929624	C₂³	1	24	yes	complemented
46	C₂×#11929624	C₂³	1	48	yes	complemented
47	C₂×#11929623	—	2	24	no	—
48	#41×D₇₉	—	2	64	no	—
49	#41×D₇₉	—	2	64	no	—
50	C₂²×Dic₁₅₈	C₂³	1	12	yes	complemented
51	C₂×Q₈×D₇₉	—	2	8	no	—
52	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
53	C₂²×C₂²⋊D₇₉	—	2	12	no	—
54	C₂×D₄×D₇₉	—	2	24	no	—
55	C₂²×C₄×D₇₉	—	2	12	no	—
56	#14579194	C₂³	1	64	yes	complemented
57	#14579194	C₂³	1	192	yes	complemented
58	#14579189	C₂³	1	64	yes	complemented
59	#14579189	C₂³	1	192	yes	complemented
60	#14579183	C₂³	1	64	yes	complemented
61	#14579183	C₂³	1	192	yes	complemented
62	C₂×Dic₃₁₆	C₂³	1	48	yes	complemented
63	C₂×#11929613	C₂³	1	96	yes	complemented
64	C₂×D₆₃₂	C₂³	1	48	yes	complemented
65	C₂×#41×C₇₉	D₄	1	4	yes	—
66	C₂×#41×C₇₉	D₄	1	8	yes	—
67	C₂×#41×C₇₉	C₂³	1	8	yes	—
68	C₂×#41×C₇₉	C₂³	1	4	yes	—
69	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₇₉	D₄	1	3	yes	—
71	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
72	#131×C₇₉	C₂³	1	64	yes	complemented
73	C₂×M₁₆×C₇₉	C₂³	1	4	yes	—
74	C₂×M₁₆×C₇₉	C₂³	1	12	yes	complemented
75	C₂×M₁₆×C₇₉	C₂³	1	48	yes	complemented
76	C₂²×C₈×C₇₉	C₂³	1	12	yes	complemented
77	C₂³×D₇₉	—	2	12	no	—
78	#11929625	—	2	64	no	—
79	#11929624	—	2	48	no	—
80	#11929624	—	2	48	no	—
81	#11929624	—	2	8	no	—
82	#11929624	—	2	8	no	—
83	#11929624	—	2	48	no	—
84	#11929624	—	2	48	no	—
85	#11929624	—	2	48	no	—
86	#11929624	C₂⁴	1	16	yes	—
87	#11929624	C₂⁴	1	16	yes	—
88	#11929624	C₂⁴	1	96	yes	—
89	#11929623	—	2	192	no	—
90	C₂×Dic₁₅₈	—	2	12	no	—
91	C₂×Dic₁₅₈	—	2	24	no	—
92	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
93	C₂×Dic₁₅₈	C₂⁴	1	48	yes	—
94	Q₈×D₇₉	—	2	64	no	—
95	C₂×D₃₁₆	—	2	12	no	—
96	C₂×D₃₁₆	—	2	24	no	—
97	C₂×D₃₁₆	C₂⁴	1	8	yes	—
98	C₂×D₃₁₆	C₂⁴	1	48	yes	—
99	C₂×C₂²⋊D₇₉	—	2	24	no	—
100	C₂×C₂²⋊D₇₉	—	2	8	no	—
101	C₂×C₂²⋊D₇₉	—	2	48	no	—
102	C₂×C₂²⋊D₇₉	—	2	48	no	—
103	D₄×D₇₉	—	2	192	no	—
104	C₂²×Dic₇₉	—	2	12	no	—
105	C₂×C₄×D₇₉	—	2	24	no	—
106	C₂×C₄×D₇₉	—	2	48	no	—
107	C₂×C₄×D₇₉	—	2	48	no	—
108	C₂×C₄×D₇₉	—	2	8	no	—
109	Dic₃₁₆	C₂⁴	1	64	yes	—
110	#11929613	C₂⁴	1	128	yes	—
111	D₆₃₂	C₂⁴	1	64	yes	—
112	C₂⁴×C₇₉	C₂×D₄	1	3	yes	—
113	#41×C₇₉	C₂×D₄	1	16	yes	—
114	#41×C₇₉	C₂×D₄	1	32	yes	—
115	#41×C₇₉	C₂⁴	1	16	yes	—
116	C₂×Q₈×C₇₉	C₂×D₄	1	8	yes	—
117	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
118	C₂×D₄×C₇₉	C₂×D₄	1	24	yes	—
119	C₂×D₄×C₇₉	C₂×D₄	1	12	yes	—
120	C₂²×C₄×C₇₉	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₇₉	C₂×D₄	1	6	yes	—
122	C₂²×C₄×C₇₉	C₂×D₄	1	12	yes	—
123	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
124	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
126	M₁₆×C₇₉	C₂⁴	1	16	yes	—
127	M₁₆×C₇₉	C₂⁴	1	48	yes	—
128	C₂×C₈×C₇₉	C₂⁴	1	8	yes	—
129	C₂×C₈×C₇₉	C₂⁴	1	48	yes	—
130	C₂³×C₇₉	—	8	3	no	—
131	C₂³×C₇₉	C₂²×D₄	1	12	yes	—
132	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
133	C₂³×C₇₉	C₂²×D₄	1	6	yes	—
134	C₂²×D₇₉	—	2	8	no	—
135	C₂²×D₇₉	—	2	48	no	—
136	C₂²×D₇₉	—	8	24	no	—
137	Q₈×C₇₉	C₂²×D₄	1	16	yes	—
138	D₄×C₇₉	C₂²×D₄	1	48	yes	—
139	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₇₉	C₂²×D₄	1	12	yes	—
141	C₂×C₄×C₇₉	C₂²×D₄	1	12	yes	—
142	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
143	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₂²×D₄	1	6	yes	—
145	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
146	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
147	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
148	C₂²⋊D₇₉	—	2	96	no	—
149	C₂²⋊D₇₉	—	2	16	no	—
150	C₂²⋊D₇₉	—	2	16	no	—
151	C₂×Dic₇₉	—	2	8	no	—
152	C₂×Dic₇₉	—	2	48	no	—
153	D₃₁₆	—	2	48	no	—
154	D₃₁₆	—	2	8	no	—
155	D₃₁₆	C₂⁵	1	16	yes	—
156	C₄×D₇₉	—	2	16	no	—
157	C₄×D₇₉	—	2	16	no	—
158	C₄×D₇₉	—	2	96	no	—
159	Dic₁₅₈	—	2	48	no	—
160	Dic₁₅₈	—	2	8	no	—
161	Dic₁₅₈	C₂⁵	1	16	yes	—
162	C₈×C₇₉	C₂⁵	1	16	yes	—
163	C₂²×C₇₉	—	4	12	no	—
164	C₂²×C₇₉	—	4	1	no	—
165	C₂²×C₇₉	—	4	6	no	—
166	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
167	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
168	C₂²×C₇₉	C₂³×D₄	1	12	yes	—
169	C₂×D₇₉	—	2	16	no	—
170	C₂×D₇₉	—	4	16	no	—
171	C₂×D₇₉	—	8	48	no	—
172	C₄×C₇₉	C₂³×D₄	1	2	yes	—
173	C₄×C₇₉	C₂³×D₄	1	12	yes	—
174	C₄×C₇₉	C₂³×D₄	1	1	yes	characteristic
175	C₄×C₇₉	C₂⁶	1	1	yes	characteristic
176	Dic₇₉	—	2	16	no	—
177	#63090	—	79	1	no	maximal, Sylow
178	C₂×C₇₉	—	2	2	no	—
179	C₂×C₇₉	—	2	12	no	—
180	C₂×C₇₉	—	2	1	no	—
181	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
182	D₇₉	—	4	16	no	—
183	C₂×#585	—	79	2	no	—
184	#3586	—	79	16	no	—
185	#3585	—	79	16	no	—
186	#3584	—	79	16	no	—
187	C₂×#575	—	79	12	no	—
188	C₂×#568	D₇₉	1	1	yes	characteristic, complemented
189	C₇₉	#63090	1	1	yes	characteristic, complemented, Sylow
190	#585	—	79	16	no	—
191	#585	—	79	16	no	—
192	#585	—	158	8	no	—
193	#585	—	158	8	no	—
194	C₂×2₋¹⁺⁴	—	79	8	no	—
195	C₂×2₋¹⁺⁴	—	158	2	no	—
196	C₂×H(5,𝔽₂)	—	79	8	no	—
197	C₂×H(5,𝔽₂)	—	158	6	no	—
198	C₂²×#41	—	79	12	no	—
199	C₂²×#41	—	158	8	no	—
200	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
201	#578	—	79	64	no	—
202	#577	—	79	128	no	—
203	#576	—	79	64	no	—
204	#575	—	79	16	no	—
205	#575	—	79	48	no	—
206	#575	—	79	96	no	—
207	C₂×#137	—	79	48	no	—
208	C₂×AGL(1,ℤ/8)	—	79	48	no	—
209	C₂×#135	—	79	48	no	—
210	#568	C₂×D₇₉	1	16	yes	complemented
211	C₂×#131	C₂×D₇₉	1	8	yes	complemented
212	C₂²×M₁₆	C₂×D₇₉	1	6	yes	complemented
213	2₋¹⁺⁴	—	79	64	no	—
214	2₋¹⁺⁴	—	158	32	no	—
215	2₋¹⁺⁴	—	158	16	no	—
216	2₋¹⁺⁴	—	158	16	no	—
217	H(5,𝔽₂)	—	79	64	no	—
218	H(5,𝔽₂)	—	158	32	no	—
219	H(5,𝔽₂)	—	158	48	no	—
220	H(5,𝔽₂)	—	158	48	no	—
221	C₂×#41	—	79	48	no	—
222	C₂×#41	—	79	8	no	—
223	C₂×#41	—	79	48	no	—
224	C₂×#41	—	79	24	no	—
225	C₂×#41	—	158	64	no	—
226	C₂×#41	—	158	64	no	—
227	C₂×#41	—	158	8	no	—
228	C₂×#41	—	158	24	no	—
229	C₂×#41	—	158	12	no	—
230	C₂×#41	—	158	12	no	—
231	C₂×#41	—	158	24	no	—
232	C₂×#41	—	158	24	no	—
233	C₂×#41	D₃₁₆	1	8	yes	—
234	C₂×#41	D₃₁₆	1	4	yes	—
235	C₂×#41	C₂²×D₇₉	1	4	yes	—
236	C₂×#41	C₂²×D₇₉	1	8	yes	—
237	C₂²×Q₈	—	79	12	no	—
238	C₂²×Q₈	—	158	8	no	—
239	C₂²×Q₈	D₃₁₆	1	1	yes	characteristic
240	C₂²×D₄	—	79	12	no	—
241	C₂²×D₄	—	158	12	no	—
242	C₂²×D₄	—	158	24	no	—
243	C₂²×D₄	D₃₁₆	1	3	yes	—
244	C₂³×C₄	—	158	12	no	—
245	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
246	#137	—	79	64	no	—
247	#137	—	79	192	no	—
248	AGL(1,ℤ/8)	—	79	64	no	—
249	AGL(1,ℤ/8)	—	79	192	no	—
250	#135	—	79	64	no	—
251	#135	—	79	192	no	—
252	C₂×Q₁₆	—	79	48	no	—
253	C₂×SD₁₆	—	79	96	no	—
254	C₂×D₈	—	79	48	no	—
255	#131	C₂²×D₇₉	1	64	yes	complemented
256	C₂×M₁₆	C₂²×D₇₉	1	4	yes	—
257	C₂×M₁₆	C₂²×D₇₉	1	12	yes	complemented
258	C₂×M₁₆	C₂²×D₇₉	1	48	yes	complemented
259	C₂²×C₈	C₂²×D₇₉	1	12	yes	complemented
260	C₂⁴	—	158	12	no	—
261	C₂⁴	C₂×D₃₁₆	1	3	yes	—
262	#41	—	79	16	no	—
263	#41	—	79	96	no	—
264	#41	—	79	16	no	—
265	#41	—	158	64	no	—
266	#41	—	158	192	no	—
267	#41	—	158	48	no	—
268	#41	—	158	8	no	—
269	#41	—	158	8	no	—
270	#41	—	158	48	no	—
271	#41	—	158	48	no	—
272	#41	—	158	48	no	—
273	#41	—	158	48	no	—
274	#41	C₂×D₃₁₆	1	16	yes	—
275	#41	C₂×D₃₁₆	1	32	yes	—
276	#41	C₂³×D₇₉	1	16	yes	—
277	C₂×Q₈	—	79	48	no	—
278	C₂×Q₈	—	79	8	no	—
279	C₂×Q₈	—	158	64	no	—
280	C₂×Q₈	—	158	12	no	—
281	C₂×Q₈	—	158	24	no	—
282	C₂×Q₈	C₂×D₃₁₆	1	8	yes	—
283	C₂×Q₈	C₂×D₃₁₆	1	4	yes	—
284	C₂×D₄	—	79	48	no	—
285	C₂×D₄	—	79	8	no	—
286	C₂×D₄	—	158	24	no	—
287	C₂×D₄	—	158	8	no	—
288	C₂×D₄	—	158	48	no	—
289	C₂×D₄	—	158	48	no	—
290	C₂×D₄	—	158	192	no	—
291	C₂×D₄	—	158	12	no	—
292	C₂×D₄	—	158	24	no	—
293	C₂×D₄	C₂×D₃₁₆	1	24	yes	—
294	C₂×D₄	C₂×D₃₁₆	1	12	yes	—
295	C₂²×C₄	—	158	12	no	—
296	C₂²×C₄	—	158	8	no	—
297	C₂²×C₄	—	158	24	no	—
298	C₂²×C₄	—	158	48	no	—
299	C₂²×C₄	—	158	48	no	—
300	C₂²×C₄	C₂×D₃₁₆	1	12	yes	—
301	C₂²×C₄	C₂×D₃₁₆	1	3	yes	—
302	C₂²×C₄	C₂×D₃₁₆	1	6	yes	—
303	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
304	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
305	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
306	Q₁₆	—	79	64	no	—
307	SD₁₆	—	79	128	no	—
308	D₈	—	79	64	no	—
309	M₁₆	C₂³×D₇₉	1	16	yes	—
310	M₁₆	C₂³×D₇₉	1	48	yes	—
311	C₂×C₈	C₂³×D₇₉	1	8	yes	—
312	C₂×C₈	C₂³×D₇₉	1	48	yes	—
313	C₂³	—	8	3	no	—
314	C₂³	—	632	24	no	—
315	C₂³	—	158	8	no	—
316	C₂³	—	158	48	no	—
317	C₂³	C₂²×D₃₁₆	1	12	yes	—
318	C₂³	C₂²×D₃₁₆	1	1	yes	characteristic
319	C₂³	C₂²×D₃₁₆	1	6	yes	—
320	Q₈	—	79	16	no	—
321	Q₈	—	158	8	no	—
322	Q₈	—	158	48	no	—
323	Q₈	C₂²×D₃₁₆	1	16	yes	—
324	D₄	—	79	16	no	—
325	D₄	—	158	16	no	—
326	D₄	—	158	96	no	—
327	D₄	—	158	16	no	—
328	D₄	—	158	8	no	—
329	D₄	—	158	48	no	—
330	D₄	C₂²×D₃₁₆	1	48	yes	—
331	C₂×C₄	—	158	8	no	—
332	C₂×C₄	—	158	48	no	—
333	C₂×C₄	—	158	16	no	—
334	C₂×C₄	—	158	96	no	—
335	C₂×C₄	—	158	16	no	—
336	C₂×C₄	C₂²×D₃₁₆	1	12	yes	—
337	C₂×C₄	C₂²×D₃₁₆	1	24	yes	—
338	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₃₁₆	1	6	yes	—
340	C₂×C₄	C₂²×D₃₁₆	1	2	yes	—
341	C₂×C₄	C₂²×D₃₁₆	1	12	yes	—
342	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
343	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
344	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
345	C₈	C₂⁴×D₇₉	1	16	yes	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	12	no	—
348	C₂²	—	4	6	no	—
349	C₂²	—	316	16	no	—
350	C₂²	—	632	48	no	—
351	C₂²	—	158	16	no	—
352	C₂²	C₂³×D₃₁₆	1	2	yes	—
353	C₂²	C₂³×D₃₁₆	1	12	yes	—
354	C₂²	C₂³×D₃₁₆	1	1	yes	characteristic
355	C₄	—	158	16	no	—
356	C₄	C₂³×D₃₁₆	1	2	yes	—
357	C₄	C₂³×D₃₁₆	1	12	yes	—
358	C₄	C₂³×D₃₁₆	1	1	yes	characteristic
359	C₄	C₂⁵×D₇₉	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	12	no	—
363	C₂	—	316	16	no	—
364	C₂	C₂⁴×D₃₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×D₃₁₆
commutator, cosocle	C₄×C₇₉	C₂⁶
Frattini	C₄	C₂⁵×D₇₉
Fitting	C₂×#568×C₇₉	C₂
socle	C₂×C₇₉	C₂⁴×D₄
hypercenter	C₂×#568	D₇₉
hypocenter	C₇₉	#63090
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×#41 ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
1. C₂×#19099399	C₂	semidirect
2. #23778188	C₂	semidirect
3. #23778181	C₂	semidirect
4. #23778174	C₂	semidirect
5. C₂×#19099363	C₂	semidirect
6. C₂×#568×C₇₉	C₂	semidirect
9. #19099399	C₂²	semidirect
10. #19099399	C₂²	semidirect
12. C₂×#14579208	C₂²	semidirect
13. C₂×#14579207	C₂²	semidirect
15. C₂²×#11929624	C₂²	semidirect
17. #19099380	C₂²	semidirect
18. #19099375	C₂²	semidirect
19. #19099368	C₂²	semidirect
20. #19099363	C₂²	semidirect
21. #19099363	C₂²	semidirect
22. #19099363	C₂²	semidirect
23. C₂×#14579194	C₂²	semidirect
24. C₂×#14579189	C₂²	semidirect
25. C₂×#14579183	C₂²	semidirect
27. #568×C₇₉	C₂²	semidirect
28. C₂×#131×C₇₉	C₂²	semidirect
29. C₂²×M₁₆×C₇₉	C₂²	semidirect
33. #14579208	C₂³	semidirect
35. #14579207	C₂³	semidirect
45. C₂×#11929624	C₂³	semidirect
46. C₂×#11929624	C₂³	semidirect
50. C₂²×Dic₁₅₈	C₂³	semidirect
52. C₂²×D₃₁₆	C₂³	semidirect
56. #14579194	C₂³	semidirect
57. #14579194	C₂³	semidirect
58. #14579189	C₂³	semidirect
59. #14579189	C₂³	semidirect
60. #14579183	C₂³	semidirect
61. #14579183	C₂³	semidirect
62. C₂×Dic₃₁₆	C₂³	semidirect
63. C₂×#11929613	C₂³	semidirect
64. C₂×D₆₃₂	C₂³	semidirect
72. #131×C₇₉	C₂³	semidirect
74. C₂×M₁₆×C₇₉	C₂³	semidirect
75. C₂×M₁₆×C₇₉	C₂³	semidirect
76. C₂²×C₈×C₇₉	C₂³	semidirect
188. C₂×#568	D₇₉	semidirect
189. C₇₉	#63090	semidirect
210. #568	C₂×D₇₉	semidirect
211. C₂×#131	C₂×D₇₉	semidirect
212. C₂²×M₁₆	C₂×D₇₉	semidirect
255. #131	C₂²×D₇₉	semidirect
257. C₂×M₁₆	C₂²×D₇₉	semidirect
258. C₂×M₁₆	C₂²×D₇₉	semidirect
259. C₂²×C₈	C₂²×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19099399	2
#23778188	2
#23778181	2
#23778174	2
C₂×#19099363	2
C₂×#568×C₇₉	2
#63090	79