Subgroups — #34444926

Order 20224.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#23775079	C₂	1	2	yes	maximal, complemented
3	#23765662	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765488	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765486	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765457	C₂	1	2	yes	maximal, complemented
7	#23765327	C₂	1	2	yes	maximal, complemented
8	#23765323	C₂	1	2	yes	maximal, complemented
9	D₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₆×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#508×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₇₉	C₂²	1	2	yes	—
13	#19099201	—	2	2	no	—
14	C₂×#14579104	C₂²	1	2	yes	complemented
15	C₂×D₁₂₆₄	C₂²	1	1	yes	characteristic
16	C₂×#14579102	C₂²	1	2	yes	—
17	D₁₆×D₇₉	—	2	4	no	—
18	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
19	#19098948	C₂²	1	2	yes	complemented
20	#19098801	C₂²	1	2	yes	—
21	#19098799	C₂²	1	2	yes	complemented
22	#19098780	—	2	2	no	—
23	#19098712	—	2	2	no	—
24	#19098708	—	2	2	no	—
25	D₈×Dic₇₉	C₂²	1	2	yes	complemented
26	C₈×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
27	#19098389	C₂²	1	1	yes	characteristic, complemented
28	Dic₇₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
29	#19098367	C₂²	1	2	yes	complemented
30	#19098365	C₂²	1	2	yes	complemented
31	#19098364	C₂²	1	2	yes	complemented
32	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
33	(C₂×D₇₉)⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₁₆×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₇₉	C₂²	1	2	yes	complemented
36	#508×C₇₉	—	2	4	no	—
37	C₂×Q₃₂×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×SD₃₂×C₇₉	C₂²	1	2	yes	complemented
39	C₂×D₁₆×C₇₉	C₂²	1	1	yes	characteristic
40	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₇₉	—	2	2	no	—
42	C₂×#11929611	—	2	2	no	—
43	C₂×D₆₃₂	C₂³	1	2	yes	—
44	C₂×#11929609	—	2	2	no	—
45	D₈×D₇₉	—	2	4	no	—
46	D₈×D₇₉	—	4	2	no	—
47	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
48	#14579150	—	2	2	no	—
49	#14579144	—	4	2	no	—
50	#14579137	—	2	2	no	—
51	#14579135	—	2	2	no	—
52	#14579133	—	4	2	no	—
53	#14579129	—	4	2	no	—
54	D₄×Dic₇₉	—	2	2	no	—
55	C₄×C₂²⋊D₇₉	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₇₉)⋊C₄	—	4	2	no	—
57	#14579104	—	4	2	no	—
58	D₁₂₆₄	—	2	2	no	—
59	#14579102	—	2	4	no	—
60	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
62	C₁₆×D₇₉	—	2	2	no	—
63	#14579095	C₂³	1	2	yes	—
64	Dic₇₉⋊C₈	D₄	1	1	yes	characteristic
65	#14579085	—	2	2	no	—
66	#14579083	—	2	2	no	—
67	#14579082	—	2	2	no	—
68	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
69	(C₂×D₇₉)⋊C₈	D₄	1	1	yes	characteristic
70	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
71	C₂×#41×C₇₉	—	2	2	no	—
72	#135×C₇₉	—	2	4	no	—
73	#135×C₇₉	—	4	2	no	—
74	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
75	C₂×SD₁₆×C₇₉	—	2	2	no	—
76	C₂×D₈×C₇₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	Q₃₂×C₇₉	—	2	2	no	—
79	SD₃₂×C₇₉	—	2	4	no	—
80	D₁₆×C₇₉	D₄	1	4	yes	complemented
81	C₂×C₁₆×C₇₉	—	2	2	no	—
82	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
84	C₂³×D₇₉	—	4	2	no	—
85	C₂×D₃₁₆	—	2	2	no	—
86	C₂×C₂²⋊D₇₉	—	4	2	no	—
87	C₂×C₂²⋊D₇₉	—	4	2	no	—
88	C₂×C₂²⋊D₇₉	D₈	1	1	yes	characteristic
89	D₄×D₇₉	—	4	4	no	—
90	D₄×D₇₉	—	8	2	no	—
91	C₂²×Dic₇₉	—	4	2	no	—
92	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
93	#11929611	—	8	2	no	—
94	D₆₃₂	—	2	2	no	—
95	D₆₃₂	—	2	2	no	—
96	#11929609	—	4	4	no	—
97	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
98	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
99	C₈×D₇₉	—	2	1	no	—
100	C₈×D₇₉	—	2	1	no	—
101	C₄⋊Dic₇₉	—	2	2	no	—
102	Dic₇₉⋊C₄	—	4	2	no	—
103	Dic₇₉⋊C₄	D₈	1	1	yes	characteristic
104	C₂²⋊Dic₇₉	—	4	2	no	—
105	C₂²⋊Dic₇₉	D₈	1	1	yes	characteristic
106	(C₂×D₇₉)⋊C₄	—	4	2	no	—
107	(C₂×D₇₉)⋊C₄	—	4	2	no	—
108	(C₂×D₇₉)⋊C₄	—	4	2	no	—
109	(C₂×D₇₉)⋊C₄	—	4	2	no	—
110	(C₂×D₇₉)⋊C₄	D₈	1	1	yes	characteristic
111	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
112	C₇₉⋊C₁₆	—	2	1	no	—
113	C₇₉⋊C₁₆	—	2	1	no	—
114	#41×C₇₉	—	4	4	no	—
115	#41×C₇₉	—	8	2	no	—
116	C₂×Q₈×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	4	2	no	—
119	C₂²×C₄×C₇₉	—	4	2	no	—
120	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
121	Q₁₆×C₇₉	—	2	2	no	—
122	Q₁₆×C₇₉	—	2	2	no	—
123	SD₁₆×C₇₉	—	4	4	no	—
124	D₈×C₇₉	—	2	2	no	—
125	D₈×C₇₉	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₇₉	—	2	1	no	—
127	C₂×C₈×C₇₉	—	2	1	no	—
128	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
130	C₁₆×C₇₉	—	2	1	no	—
131	C₁₆×C₇₉	C₂×D₄	1	2	yes	—
132	C₂³×C₇₉	—	4	2	no	—
133	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
134	C₂²×D₇₉	—	4	2	no	—
135	C₂²×D₇₉	—	8	4	no	—
136	C₂²×D₇₉	—	8	4	no	—
137	C₂²×D₇₉	—	16	2	no	—
138	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
139	Q₈×C₇₉	—	4	2	no	—
140	Q₈×C₇₉	—	4	2	no	—
141	D₄×C₇₉	—	2	4	no	—
142	D₄×C₇₉	—	4	2	no	—
143	D₄×C₇₉	—	8	4	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	4	2	no	—
147	C₂×C₄×C₇₉	—	8	4	no	—
148	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
150	C₂²⋊D₇₉	—	2	2	no	—
151	C₂²⋊D₇₉	—	8	4	no	—
152	C₂²⋊D₇₉	—	16	2	no	—
153	C₂×Dic₇₉	—	4	2	no	—
154	C₂×Dic₇₉	—	16	2	no	—
155	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
156	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
157	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
158	D₃₁₆	—	4	2	no	—
159	D₃₁₆	—	4	2	no	—
160	C₄×D₇₉	—	2	1	no	—
161	C₄×D₇₉	—	2	1	no	—
162	C₈×C₇₉	—	2	1	no	—
163	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₇₉⋊C₈	—	2	1	no	—
166	C₇₉⋊C₈	—	2	1	no	—
167	C₂²×C₇₉	—	2	1	no	—
168	C₂²×C₇₉	—	2	1	no	—
169	C₂²×C₇₉	—	2	1	no	—
170	C₂²×C₇₉	—	4	4	no	—
171	C₂²×C₇₉	—	8	2	no	—
172	C₂²×C₇₉	—	8	2	no	—
173	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
174	C₂×D₇₉	—	2	1	no	—
175	C₂×D₇₉	—	2	1	no	—
176	C₂×D₇₉	—	8	2	no	—
177	C₂×D₇₉	—	8	2	no	—
178	C₂×D₇₉	—	8	2	no	—
179	C₂×D₇₉	—	16	8	no	—
180	C₂×D₇₉	#508	1	2	yes	complemented
181	C₄×C₇₉	—	2	1	no	—
182	C₄×C₇₉	—	8	2	no	—
183	C₄×C₇₉	D₄²	1	1	yes	characteristic
184	C₄×C₇₉	#576	1	1	yes	characteristic
185	Dic₇₉	—	2	1	no	—
186	Dic₇₉	—	2	1	no	—
187	Dic₇₉	—	2	1	no	—
188	Dic₇₉	—	8	2	no	—
189	#33846	—	79	1	no	maximal, Sylow
190	C₂×C₇₉	—	4	1	no	—
191	C₂×C₇₉	—	8	4	no	—
192	C₂×C₇₉	D₄×D₈	1	1	yes	characteristic
193	C₂×C₇₉	C₂×#508	1	1	yes	characteristic
194	C₂×C₇₉	#3415	1	1	yes	characteristic
195	D₇₉	—	2	2	no	—
196	D₇₉	—	16	2	no	—
197	C₂×#508	D₇₉	1	1	yes	characteristic, complemented
198	C₂²×D₁₆	—	79	1	no	—
199	#3280	—	79	2	no	—
200	#2249	—	79	1	no	—
201	#2216	—	79	1	no	—
202	#2215	—	79	1	no	—
203	#2210	—	79	2	no	—
204	#2187	—	79	2	no	—
205	#2186	—	79	2	no	—
206	C₄×D₁₆	—	79	1	no	—
207	D₄×C₁₆	—	79	1	no	—
208	C₇₉	#33846	1	1	yes	characteristic, complemented, Sylow
209	C₂×#135	C₂×D₇₉	1	2	yes	complemented
210	C₂²×D₈	—	79	2	no	—
211	#546	—	158	2	no	—
212	#508	—	2	4	no	—
213	C₂×Q₃₂	C₂×D₇₉	1	1	yes	characteristic, complemented
214	C₂×SD₃₂	—	79	2	no	—
215	C₂×SD₃₂	C₂×D₇₉	1	2	yes	complemented
216	C₂×D₁₆	—	79	2	no	—
217	C₂×D₁₆	—	79	1	no	—
218	C₂×D₁₆	—	158	4	no	—
219	C₂×D₁₆	C₂×D₇₉	1	1	yes	characteristic
220	C₂²×C₁₆	—	79	1	no	—
221	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
222	#495	—	79	2	no	—
223	#467	—	79	2	no	—
224	#466	—	79	2	no	—
225	#463	—	158	2	no	—
226	#450	—	158	2	no	—
227	#449	—	158	2	no	—
228	C₄×D₈	—	79	2	no	—
229	C₈×D₄	—	79	1	no	—
230	#366	—	79	1	no	—
231	C₄⋊C₁₆	—	79	1	no	—
232	#358	—	79	2	no	—
233	#357	—	79	2	no	—
234	#357	—	79	2	no	—
235	C₂²⋊C₁₆	—	79	1	no	—
236	C₂²⋊C₁₆	—	79	1	no	—
237	C₄×C₁₆	—	79	1	no	—
238	C₂×#41	—	2	2	no	—
239	C₂²×D₄	—	158	2	no	—
240	#135	—	2	4	no	—
241	#135	—	4	2	no	—
242	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×SD₁₆	—	158	2	no	—
245	C₂×D₈	—	316	2	no	—
246	C₂×D₈	—	79	2	no	—
247	C₂×D₈	—	158	2	no	—
248	C₂×D₈	—	158	4	no	—
249	C₂×D₈	C₂²×D₇₉	1	2	yes	—
250	C₂²×C₈	—	79	1	no	—
251	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
252	#124	—	158	2	no	—
253	#123	—	316	2	no	—
254	C₂²⋊Q₈	—	158	2	no	—
255	#121	—	316	2	no	—
256	#121	—	158	2	no	—
257	#120	—	316	2	no	—
258	C₄×D₄	—	79	1	no	—
259	C₄×D₄	—	158	2	no	—
260	C₂×C₂²⋊C₄	—	316	2	no	—
261	Q₃₂	—	2	2	no	—
262	SD₃₂	—	2	4	no	—
263	SD₃₂	—	316	2	no	—
264	D₁₆	—	158	4	no	—
265	D₁₆	—	158	2	no	—
266	D₁₆	C₂²⋊D₇₉	1	4	yes	complemented
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	79	1	no	—
269	C₂×C₁₆	—	79	1	no	—
270	C₂×C₁₆	—	158	2	no	—
271	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
272	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
273	#107	—	79	2	no	—
274	C₄⋊C₈	—	79	1	no	—
275	#103	—	158	2	no	—
276	#102	—	158	2	no	—
277	#102	—	158	2	no	—
278	C₂²⋊C₈	—	79	1	no	—
279	C₂²⋊C₈	—	79	1	no	—
280	C₄×C₈	—	79	1	no	—
281	C₂⁴	—	316	2	no	—
282	#41	—	4	4	no	—
283	#41	—	8	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	316	2	no	—
288	C₂×D₄	—	316	2	no	—
289	C₂×D₄	—	316	4	no	—
290	C₂×D₄	—	79	1	no	—
291	C₂×D₄	—	632	2	no	—
292	C₂×D₄	—	158	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	316	2	no	—
295	C₂²×C₄	—	79	1	no	—
296	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	SD₁₆	—	4	4	no	—
300	SD₁₆	—	632	2	no	—
301	D₈	—	2	2	no	—
302	D₈	—	316	4	no	—
303	D₈	—	158	2	no	—
304	D₈	—	158	2	no	—
305	D₈	C₂×C₂²⋊D₇₉	1	4	yes	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	79	1	no	—
309	C₂×C₈	—	79	1	no	—
310	C₂×C₈	—	158	1	no	—
311	C₂×C₈	—	158	1	no	—
312	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
313	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
314	C₄⋊C₄	—	316	2	no	—
315	C₄⋊C₄	—	79	1	no	—
316	C₄⋊C₄	—	158	2	no	—
317	C₂²⋊C₄	—	316	2	no	—
318	C₂²⋊C₄	—	316	2	no	—
319	C₂²⋊C₄	—	316	2	no	—
320	C₂²⋊C₄	—	316	2	no	—
321	C₂²⋊C₄	—	316	2	no	—
322	C₂²⋊C₄	—	79	1	no	—
323	C₂²⋊C₄	—	79	1	no	—
324	C₄²	—	79	1	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	158	1	no	—
327	C₁₆	—	158	1	no	—
328	C₁₆	C₂×C₂²⋊D₇₉	1	2	yes	—
329	C₂³	—	4	2	no	—
330	C₂³	—	316	2	no	—
331	C₂³	—	79	1	no	—
332	C₂³	—	632	4	no	—
333	C₂³	—	632	4	no	—
334	C₂³	—	1264	2	no	—
335	C₂³	D₈×D₇₉	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	8	4	no	—
341	D₄	—	316	2	no	—
342	D₄	—	316	2	no	—
343	D₄	—	632	4	no	—
344	D₄	—	158	2	no	—
345	D₄	—	1264	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	—	316	2	no	—
351	C₂×C₄	—	79	1	no	—
352	C₂×C₄	—	79	1	no	—
353	C₂×C₄	—	79	1	no	—
354	C₂×C₄	—	158	1	no	—
355	C₂×C₄	—	158	1	no	—
356	C₂×C₄	—	1264	2	no	—
357	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
358	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	158	1	no	—
361	C₈	—	158	1	no	—
362	C₈	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
363	C₈	#14579206	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	79	2	no	—
371	C₂²	—	632	2	no	—
372	C₂²	—	632	2	no	—
373	C₂²	—	632	2	no	—
374	C₂²	—	158	1	no	—
375	C₂²	—	158	1	no	—
376	C₂²	—	1264	8	no	—
377	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	8	2	no	—
380	C₄	—	632	2	no	—
381	C₄	—	158	1	no	—
382	C₄	—	158	1	no	—
383	C₄	—	158	1	no	—
384	C₄	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
385	C₄	#19099364	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	8	4	no	—
388	C₂	—	158	2	no	—
389	C₂	—	1264	2	no	—
390	C₂	D₈×C₂²⋊D₇₉	1	1	yes	characteristic
391	C₂	#508×D₇₉	1	1	yes	characteristic
392	C₂	#23776538	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₂×#508×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₈
hypercenter	C₂×#508	D₇₉
hypocenter	C₇₉	#33846
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×D₇₉	C₂	semidirect
2. #23775079	C₂	semidirect
3. #23765662	C₂	semidirect
4. #23765488	C₂	semidirect
5. #23765486	C₂	semidirect
6. #23765457	C₂	semidirect
7. #23765327	C₂	semidirect
8. #23765323	C₂	semidirect
9. D₁₆×Dic₇₉	C₂	semidirect
10. C₁₆×C₂²⋊D₇₉	C₂	semidirect
11. C₂×#508×C₇₉	C₂	semidirect
14. C₂×#14579104	C₂²	semidirect
19. #19098948	C₂²	semidirect
21. #19098799	C₂²	semidirect
25. D₈×Dic₇₉	C₂²	semidirect
27. #19098389	C₂²	semidirect
28. Dic₇₉⋊C₁₆	C₂²	semidirect
29. #19098367	C₂²	semidirect
30. #19098365	C₂²	semidirect
31. #19098364	C₂²	semidirect
32. C₂²⋊(C₇₉⋊C₁₆)	C₂²	semidirect
34. C₁₆×Dic₇₉	C₂²	semidirect
35. C₂×#135×C₇₉	C₂²	semidirect
37. C₂×Q₃₂×C₇₉	C₂²	semidirect
38. C₂×SD₃₂×C₇₉	C₂²	semidirect
40. C₂²×C₁₆×C₇₉	C₂²	semidirect
80. D₁₆×C₇₉	D₄	semidirect
180. C₂×D₇₉	#508	semidirect
197. C₂×#508	D₇₉	semidirect
208. C₇₉	#33846	semidirect
209. C₂×#135	C₂×D₇₉	semidirect
213. C₂×Q₃₂	C₂×D₇₉	semidirect
215. C₂×SD₃₂	C₂×D₇₉	semidirect
221. C₂²×C₁₆	C₂×D₇₉	semidirect
266. D₁₆	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×D₁₆×D₇₉	2
#23775079	2
#23765662	2
#23765488	2
#23765486	2
#23765457	2
#23765327	2
#23765323	2
D₁₆×Dic₇₉	2
C₁₆×C₂²⋊D₇₉	2
C₂×#508×C₇₉	2
#33846	79