Subgroups — #34286829

Order 20224.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098686	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098679	C₂	1	1	yes	maximal, characteristic
3	#23772200	C₂	1	1	yes	maximal, characteristic
4	#23771822	C₂	1	2	yes	maximal, complemented
5	#23763308	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763281	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763246	C₂	1	2	yes	maximal, complemented
8	#23763234	C₂	1	2	yes	maximal, complemented
9	#23763209	C₂	1	2	yes	maximal, complemented
10	#23763088	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579183	C₂²	1	1	yes	characteristic
13	C₂×#14579169	C₂²	1	2	yes	—
14	C₂×#14579167	C₂²	1	2	yes	—
15	#19099031	C₂²	1	2	yes	—
16	#19098686	C₄	1	8	yes	complemented
17	#19098679	C₄	1	8	yes	complemented
18	#19098674	C₄	1	2	yes	complemented
19	#19098669	C₄	1	2	yes	complemented
20	#19098662	C₄	1	4	yes	complemented
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	C₂×#14579089	C₂²	1	2	yes	—
23	C₂×#14579087	C₂²	1	2	yes	—
24	#19098557	C₂²	1	2	yes	—
25	#19098520	—	2	2	no	—
26	#19098519	C₂²	1	2	yes	—
27	#19098517	—	2	2	no	—
28	#19098515	—	2	2	no	—
29	M₁₆×Dic₇₉	C₂²	1	2	yes	—
30	C₂×#14579071	C₂²	1	1	yes	characteristic
31	C₂×#14579071	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₇₉	—	2	2	no	—
36	#19098409	C₂²	1	1	yes	characteristic
37	#19098327	C₂²	1	2	yes	—
38	#19098322	C₂²	1	2	yes	—
39	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
40	#427×C₇₉	C₂²	1	1	yes	characteristic
41	#405×C₇₉	C₂²	1	2	yes	—
42	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
43	#339×C₇₉	C₂²	1	2	yes	—
44	C₂×#11929624	C₂³	1	2	yes	—
45	#14579183	C₂×C₄	1	4	yes	—
46	#14579183	C₂×C₄	1	4	yes	—
47	C₂×Dic₃₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#11929613	C₂×C₄	1	2	yes	—
49	C₂×D₆₃₂	C₂×C₄	1	1	yes	characteristic
50	#14579169	—	2	4	no	—
51	#14579169	C₂×C₄	1	8	yes	complemented
52	#14579167	—	2	4	no	—
53	#14579167	C₂×C₄	1	8	yes	complemented
54	C₂×#11929608	C₂³	1	2	yes	—
55	C₂×#11929607	—	2	2	no	—
56	C₂×#11929607	—	2	2	no	—
57	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₇₉	—	2	2	no	—
60	C₂×C₈×D₇₉	—	2	2	no	—
61	#14579126	C₂×C₄	1	4	yes	—
62	#14579123	C₂×C₄	1	4	yes	—
63	(C₂²⋊D₇₉)⋊C₄	—	2	4	no	—
64	#14579118	—	2	2	no	—
65	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
67	C₄²×D₇₉	—	2	2	no	—
68	#14579097	C₂×C₄	1	4	yes	complemented
69	#14579089	C₂×C₄	1	8	yes	complemented
70	#14579087	C₂×C₄	1	8	yes	complemented
71	#14579084	C₂×C₄	1	4	yes	—
72	#14579081	C₂×C₄	1	4	yes	—
73	#14579072	—	2	2	no	—
74	#14579071	—	2	2	no	—
75	#14579071	—	2	2	no	—
76	#14579071	C₂×C₄	1	2	yes	—
77	#14579071	C₂×C₄	1	2	yes	—
78	C₄×C₇₉⋊C₈	—	2	2	no	—
79	C₄×C₇₉⋊C₈	—	2	2	no	—
80	C₈×Dic₇₉	—	2	2	no	—
81	C₈×Dic₇₉	C₂×C₄	1	4	yes	complemented
82	C₈×Dic₇₉	D₄	1	2	yes	—
83	C₈×Dic₇₉	D₄	1	2	yes	—
84	C₇₉⋊#95	—	2	2	no	—
85	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
86	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	#117×C₇₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
90	#108×C₇₉	C₂×C₄	1	4	yes	complemented
91	#107×C₇₉	C₂×C₄	1	2	yes	—
92	#106×C₇₉	C₂×C₄	1	2	yes	—
93	#97×C₇₉	—	2	2	no	—
94	#97×C₇₉	C₂×C₄	1	4	yes	complemented
95	C₄×C₈×C₇₉	—	2	2	no	—
96	#11929624	—	2	2	no	—
97	#11929624	—	2	2	no	—
98	#11929624	C₂²×C₄	1	4	yes	—
99	#11929624	C₂²×C₄	1	4	yes	—
100	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
101	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₇₉	—	2	2	no	—
103	C₂²×Dic₇₉	—	2	1	no	—
104	C₂²×Dic₇₉	#41	1	2	yes	—
105	C₂×C₄×D₇₉	—	2	4	no	—
106	C₂×C₄×D₇₉	—	2	2	no	—
107	Dic₃₁₆	C₄²	1	4	yes	—
108	#11929613	C₄²	1	8	yes	—
109	D₆₃₂	C₄²	1	4	yes	—
110	#11929608	—	2	2	no	—
111	#11929608	C₂²×C₄	1	4	yes	—
112	#11929607	—	2	8	no	—
113	#11929607	—	2	8	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	1	no	—
117	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇₉⋊C₈	#41	1	2	yes	—
122	C₈×D₇₉	—	2	8	no	—
123	C₈×D₇₉	—	2	8	no	—
124	Dic₇₉⋊C₄	—	2	4	no	—
125	(C₂×D₇₉)⋊C₄	—	2	4	no	—
126	C₄×Dic₇₉	—	2	4	no	—
127	C₄×Dic₇₉	—	2	1	no	—
128	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
129	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
130	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₇₉	—	2	2	no	—
134	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₇₉	#41	1	2	yes	—
143	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
144	C₂²⋊C₄×C₇₉	—	2	2	no	—
145	C₄²×C₇₉	—	2	2	no	—
146	C₄²×C₇₉	—	2	1	no	—
147	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
148	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
149	C₂²×D₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	4	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
159	C₂²⋊D₇₉	—	2	4	no	—
160	C₂²⋊D₇₉	—	2	4	no	—
161	C₂×Dic₇₉	—	2	2	no	—
162	C₂×Dic₇₉	—	2	2	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	2	no	—
165	C₂×Dic₇₉	C₄×D₄	1	4	yes	—
166	D₃₁₆	—	2	2	no	—
167	D₃₁₆	C₂×C₄²	1	4	yes	—
168	C₄×D₇₉	—	2	4	no	—
169	C₄×D₇₉	—	2	4	no	—
170	C₄×D₇₉	—	4	8	no	—
171	Dic₁₅₈	—	2	2	no	—
172	Dic₁₅₈	C₂×C₄²	1	4	yes	—
173	C₈×C₇₉	—	2	4	no	—
174	C₈×C₇₉	C₂×C₄²	1	2	yes	—
175	C₈×C₇₉	C₂×C₄²	1	2	yes	—
176	C₈×C₇₉	C₄×D₄	1	4	yes	—
177	C₇₉⋊C₈	—	2	4	no	—
178	C₇₉⋊C₈	—	2	2	no	—
179	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
180	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
181	C₂²×C₇₉	—	2	2	no	—
182	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
184	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
185	C₂×D₇₉	—	2	4	no	—
186	C₂×D₇₉	—	4	4	no	—
187	C₄×C₇₉	—	4	2	no	—
188	C₄×C₇₉	—	4	4	no	—
189	C₄×C₇₉	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
193	Dic₇₉	—	2	4	no	—
194	Dic₇₉	—	2	4	no	—
195	Dic₇₉	—	4	2	no	—
196	#20510	—	79	1	no	maximal, Sylow
197	C₂×C₇₉	—	2	1	no	—
198	C₂×C₇₉	—	2	1	no	—
199	C₂×C₇₉	C₄²×D₄	1	1	yes	characteristic
200	C₂×C₇₉	#2955	1	2	yes	—
201	D₇₉	—	4	4	no	—
202	C₂×#444	—	79	1	no	—
203	C₂×#443	—	79	1	no	—
204	#2943	—	79	1	no	—
205	C₄×#131	—	79	2	no	—
206	#1778	—	79	1	no	—
207	#1773	D₇₉	1	1	yes	characteristic, complemented
208	#1772	—	79	1	no	—
209	#1765	—	79	2	no	—
210	#1764	—	79	2	no	—
211	#1759	—	79	2	no	—
212	#1726	—	79	1	no	—
213	C₇₉	#20510	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	—	79	1	no	—
215	C₂×#131	—	79	2	no	—
216	C₂×#131	—	79	2	no	—
217	C₄×#41	—	79	2	no	—
218	#444	—	79	8	no	—
219	#443	—	79	8	no	—
220	#442	—	79	2	no	—
221	#441	—	79	2	no	—
222	#440	—	79	4	no	—
223	C₂×#108	—	79	1	no	—
224	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
225	#427	C₂×D₇₉	1	1	yes	characteristic
226	C₂×#104	—	79	2	no	—
227	C₂×#104	—	79	2	no	—
228	#416	—	79	2	no	—
229	#405	—	79	2	no	—
230	#405	—	158	2	no	—
231	#405	—	158	2	no	—
232	#405	C₂×D₇₉	1	2	yes	—
233	C₄×M₁₆	—	79	2	no	—
234	C₄×M₁₆	—	158	2	no	—
235	C₂×#97	—	79	1	no	—
236	C₂×#97	—	79	1	no	—
237	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
238	C₂×C₄×C₈	—	79	1	no	—
239	C₂×C₄×C₈	—	79	1	no	—
240	C₂×C₄×C₈	—	79	1	no	—
241	C₂×C₄×C₈	—	158	2	no	—
242	#376	—	79	1	no	—
243	#341	—	79	2	no	—
244	#339	—	79	2	no	—
245	#339	C₂×D₇₉	1	2	yes	—
246	C₂×#41	—	79	2	no	—
247	#135	—	79	4	no	—
248	#135	—	79	4	no	—
249	C₂×Q₁₆	—	79	1	no	—
250	C₂×SD₁₆	—	79	2	no	—
251	C₂×D₈	—	79	1	no	—
252	#131	—	79	8	no	—
253	#131	—	79	8	no	—
254	#131	—	158	4	no	—
255	#131	—	158	4	no	—
256	C₂×M₁₆	—	79	2	no	—
257	C₂×M₁₆	—	158	2	no	—
258	C₂×M₁₆	—	158	2	no	—
259	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
260	C₂²×C₈	—	79	1	no	—
261	C₂²×C₈	—	79	1	no	—
262	C₂²×C₈	—	158	2	no	—
263	C₂²×C₈	—	158	2	no	—
264	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₄×Q₈	—	79	4	no	—
267	C₄×D₄	—	79	4	no	—
268	C₄×D₄	—	158	4	no	—
269	#117	—	158	2	no	—
270	#117	C₂²×D₇₉	1	2	yes	—
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	158	2	no	—
274	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
275	#108	—	79	4	no	—
276	#108	C₄×D₇₉	1	4	yes	complemented
277	#107	C₄×D₇₉	1	2	yes	—
278	#106	C₄×D₇₉	1	2	yes	—
279	#104	—	79	8	no	—
280	#104	—	79	8	no	—
281	#103	—	79	4	no	—
282	#102	—	79	4	no	—
283	#97	—	2	2	no	—
284	#97	—	79	2	no	—
285	#97	—	79	2	no	—
286	#97	—	158	2	no	—
287	#97	—	158	2	no	—
288	#97	—	158	2	no	—
289	#97	C₄×D₇₉	1	4	yes	complemented
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	79	4	no	—
292	C₄×C₈	—	79	2	no	—
293	C₄×C₈	—	79	2	no	—
294	C₄×C₈	—	158	2	no	—
295	C₄×C₈	—	158	2	no	—
296	C₄×C₈	—	158	2	no	—
297	#95	—	158	2	no	—
298	#41	—	79	4	no	—
299	#41	—	79	4	no	—
300	#41	—	158	2	no	—
301	#41	—	158	2	no	—
302	C₂×Q₈	—	79	2	no	—
303	C₂×D₄	—	79	2	no	—
304	C₂×D₄	—	158	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	79	2	no	—
307	C₂²×C₄	—	158	4	no	—
308	C₂²×C₄	—	158	1	no	—
309	C₂²×C₄	—	158	2	no	—
310	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
311	Q₁₆	—	79	4	no	—
312	SD₁₆	—	79	8	no	—
313	D₈	—	79	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	79	4	no	—
316	M₁₆	—	158	8	no	—
317	M₁₆	—	158	2	no	—
318	M₁₆	—	158	8	no	—
319	M₁₆	C₂×C₄×D₇₉	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	79	2	no	—
322	C₂×C₈	—	79	2	no	—
323	C₂×C₈	—	79	1	no	—
324	C₂×C₈	—	79	1	no	—
325	C₂×C₈	—	79	2	no	—
326	C₂×C₈	—	158	8	no	—
327	C₂×C₈	—	158	1	no	—
328	C₂×C₈	—	158	1	no	—
329	C₂×C₈	—	158	2	no	—
330	C₂×C₈	—	158	8	no	—
331	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
336	C₂×C₈	D₄×D₇₉	1	2	yes	—
337	C₂×C₈	#11929625	1	2	yes	—
338	C₄⋊C₄	—	158	4	no	—
339	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	158	4	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	79	2	no	—
345	C₄²	—	79	2	no	—
346	C₄²	—	79	2	no	—
347	C₄²	—	158	4	no	—
348	C₄²	—	158	1	no	—
349	C₄²	C₂×C₄×D₇₉	1	2	yes	—
350	C₂³	—	158	2	no	—
351	C₂³	#41×D₇₉	1	1	yes	characteristic
352	Q₈	—	79	4	no	—
353	Q₈	—	158	2	no	—
354	D₄	—	79	4	no	—
355	D₄	—	158	4	no	—
356	D₄	—	158	4	no	—
357	D₄	—	158	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	316	8	no	—
362	C₂×C₄	—	316	2	no	—
363	C₂×C₄	—	316	2	no	—
364	C₂×C₄	—	79	4	no	—
365	C₂×C₄	—	158	2	no	—
366	C₂×C₄	—	158	2	no	—
367	C₂×C₄	—	158	4	no	—
368	C₂×C₄	—	158	4	no	—
369	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
373	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	79	2	no	—
377	C₈	—	79	2	no	—
378	C₈	—	158	4	no	—
379	C₈	—	158	2	no	—
380	C₈	C₄²×D₇₉	1	2	yes	—
381	C₈	C₄²×D₇₉	1	2	yes	—
382	C₈	#14579123	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	316	4	no	—
385	C₂²	—	158	4	no	—
386	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
387	C₂²	#19099031	1	1	yes	characteristic
388	C₂²	C₄×#11929625	1	1	yes	characteristic
389	C₄	—	4	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	316	2	no	—
392	C₄	—	158	4	no	—
393	C₄	—	158	4	no	—
394	C₄	C₂×C₄²×D₇₉	1	1	yes	characteristic
395	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
396	C₄	C₂×#14579123	1	1	yes	characteristic
397	C₄	C₄×#11929625	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	316	4	no	—
401	C₂	C₄×#14579123	1	1	yes	characteristic
402	C₂	#23772300	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₄×C₇₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1773	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579183	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1773	D₇₉
hypocenter	C₇₉	#20510
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
4. #23771822	C₂	semidirect
5. #23763308	C₂	semidirect
6. #23763281	C₂	semidirect
7. #23763246	C₂	semidirect
8. #23763234	C₂	semidirect
9. #23763209	C₂	semidirect
10. #23763088	C₂	semidirect
11. C₇₉×#1773	C₂	semidirect
16. #19098686	C₄	semidirect
17. #19098679	C₄	semidirect
18. #19098674	C₄	semidirect
19. #19098669	C₄	semidirect
20. #19098662	C₄	semidirect
51. #14579169	C₂×C₄	semidirect
53. #14579167	C₂×C₄	semidirect
68. #14579097	C₂×C₄	semidirect
69. #14579089	C₂×C₄	semidirect
70. #14579087	C₂×C₄	semidirect
81. C₈×Dic₇₉	C₂×C₄	semidirect
90. #108×C₇₉	C₂×C₄	semidirect
94. #97×C₇₉	C₂×C₄	semidirect
207. #1773	D₇₉	semidirect
213. C₇₉	#20510	semidirect
276. #108	C₄×D₇₉	semidirect
289. #97	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098686	2
C₂×#19098679	2
#23772200	2
#23771822	2
#23763308	2
#23763281	2
#23763246	2
#23763234	2
#23763209	2
#23763088	2
C₇₉×#1773	2
#20510	79