Subgroups — #34286302

Order 20224.

1010 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579097	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098601	C₂	1	1	yes	maximal, characteristic
3	#23771818	C₂	1	2	yes	maximal
4	#23763284	C₂	1	4	yes	maximal, complemented
5	#23763279	C₂	1	4	yes	maximal, complemented
6	#23763110	C₂	1	2	yes	maximal
7	C₂×#405×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11929608	C₂²	1	2	yes	—
9	C₂×#14579120	C₂²	1	2	yes	—
10	C₂×#14579097	C₄	1	8	yes	complemented
11	C₂×#14579097	C₂²	1	2	yes	—
12	C₂×#14579097	C₂²	1	2	yes	—
13	#19098601	C₄	1	2	yes	complemented
14	#19098601	C₄	1	2	yes	complemented
15	#19098601	C₂²	1	2	yes	—
16	#19098601	C₂²	1	2	yes	—
17	C₂×#14579095	C₄	1	2	yes	complemented
18	C₂×#14579093	C₄	1	2	yes	complemented
19	#19098521	—	2	4	no	—
20	#19098518	C₂²	1	8	yes	—
21	M₁₆×Dic₇₉	—	2	4	no	—
22	#19098323	C₂²	1	8	yes	—
23	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
26	#405×C₇₉	C₄	1	8	yes	complemented
27	C₂×#97×C₇₉	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
29	C₂×#11929608	—	2	2	no	—
30	C₂×#11929608	—	2	4	no	—
31	C₂×#11929608	C₂×C₄	1	8	yes	—
32	C₂×#11929608	C₂³	1	4	yes	—
33	C₂²×C₇₉⋊C₈	—	2	2	no	—
34	#14579120	—	2	2	no	—
35	#14579120	—	2	2	no	—
36	#14579120	C₂×C₄	1	4	yes	—
37	#14579120	C₂³	1	4	yes	—
38	C₂×C₄⋊Dic₇₉	C₂×C₄	1	4	yes	—
39	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
40	C₂×C₄×Dic₇₉	—	2	2	no	—
41	#14579097	C₂×C₄	1	8	yes	complemented
42	#14579097	C₂×C₄	1	8	yes	complemented
43	#14579095	C₂×C₄	1	4	yes	—
44	#14579095	C₂×C₄	1	4	yes	—
45	#14579093	C₂×C₄	1	4	yes	—
46	#14579093	C₂×C₄	1	4	yes	—
47	#14579071	—	2	8	no	—
48	C₈×Dic₇₉	—	2	8	no	—
49	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₇₉	C₂×C₄	1	4	yes	—
51	C₂×M₁₆×C₇₉	D₄	1	2	yes	—
52	C₂×M₁₆×C₇₉	D₄	1	2	yes	—
53	C₂×M₁₆×C₇₉	Q₈	1	4	yes	—
54	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₉	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₇₉	C₂×C₄	1	4	yes	—
60	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
63	#117×C₇₉	—	2	2	no	—
64	#117×C₇₉	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
67	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
68	#97×C₇₉	C₂×C₄	1	8	yes	complemented
69	C₄×C₈×C₇₉	C₂×C₄	1	8	yes	complemented
70	C₂²×Dic₇₉	—	2	4	no	—
71	#11929608	—	2	8	no	—
72	#11929608	—	2	4	no	—
73	#11929608	C₂²×C₄	1	8	yes	—
74	C₂×C₇₉⋊C₈	—	2	8	no	—
75	C₂×C₇₉⋊C₈	—	2	4	no	—
76	C₄⋊Dic₇₉	—	2	4	no	—
77	C₄⋊Dic₇₉	C₂²×C₄	1	8	yes	—
78	C₂²⋊Dic₇₉	—	2	4	no	—
79	C₂²⋊Dic₇₉	—	2	4	no	—
80	C₄×Dic₇₉	—	2	4	no	—
81	C₄×Dic₇₉	—	2	4	no	—
82	C₂⁴×C₇₉	#41	1	1	yes	characteristic
83	C₂²×C₄×C₇₉	—	2	2	no	—
84	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	#41	1	2	yes	—
93	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₇₉	C₄⋊C₄	1	8	yes	—
95	M₁₆×C₇₉	C₄⋊C₄	1	8	yes	—
96	C₂×C₈×C₇₉	C₄²	1	4	yes	—
97	C₂×C₈×C₇₉	C₄²	1	4	yes	—
98	C₂×C₈×C₇₉	C₄²	1	4	yes	—
99	C₂×C₈×C₇₉	C₄²	1	4	yes	—
100	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	—
111	C₄⋊C₄×C₇₉	—	2	4	no	—
112	C₂²⋊C₄×C₇₉	—	2	4	no	—
113	C₄²×C₇₉	—	2	2	no	—
114	C₄²×C₇₉	C₂²×C₄	1	4	yes	—
115	C₂³×C₇₉	—	4	2	no	—
116	C₂³×C₇₉	#117	1	2	yes	—
117	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
118	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
119	C₂³×C₇₉	C₄×Q₈	1	2	yes	—
120	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
121	C₂×C₄×C₇₉	—	2	4	no	—
122	C₂×C₄×C₇₉	—	4	4	no	—
123	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
124	C₂×C₄×C₇₉	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₇₉	#117	1	2	yes	—
128	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
135	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
138	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
141	C₂×Dic₇₉	—	2	8	no	—
142	C₂×Dic₇₉	—	8	4	no	—
143	C₈×C₇₉	C₂×C₄²	1	2	yes	—
144	C₈×C₇₉	C₂×C₄²	1	2	yes	—
145	C₈×C₇₉	C₂×C₄²	1	2	yes	—
146	C₈×C₇₉	C₂×C₄²	1	2	yes	—
147	C₈×C₇₉	C₂×C₄⋊C₄	1	8	yes	—
148	C₇₉⋊C₈	—	2	8	no	—
149	C₂²×C₇₉	—	2	2	no	—
150	C₂²×C₇₉	—	2	2	no	—
151	C₂²×C₇₉	—	2	2	no	—
152	C₂²×C₇₉	—	4	2	no	—
153	C₂²×C₇₉	—	4	2	no	—
154	C₂²×C₇₉	C₄×C₄⋊C₄	1	2	yes	—
155	C₂²×C₇₉	C₄×C₄⋊C₄	1	2	yes	—
156	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
157	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
158	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
159	C₄×C₇₉	—	4	4	no	—
160	C₄×C₇₉	C₄×C₄⋊C₄	1	2	yes	—
161	C₄×C₇₉	C₄×C₄⋊C₄	1	2	yes	—
162	C₄×C₇₉	C₂²×C₄²	1	1	yes	characteristic
163	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
164	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
165	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
166	Dic₇₉	—	4	8	no	—
167	#20446	—	79	1	no	maximal, Sylow
168	C₂×C₇₉	—	2	1	no	—
169	C₂×C₇₉	—	2	1	no	—
170	C₂×C₇₉	—	2	2	no	—
171	C₂×C₇₉	—	2	2	no	—
172	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₇₉	#2957	1	2	yes	—
174	C₂²×#108	—	79	1	no	—
175	C₂×#427	—	79	1	no	—
176	#2873	—	79	2	no	—
177	C₂×#405	D₇₉	1	1	yes	characteristic
178	#1773	—	79	4	no	—
179	#1772	—	79	4	no	—
180	#1733	—	79	2	no	—
181	C₇₉	#20446	1	1	yes	characteristic, complemented, Sylow
182	C₂²×M₁₆	—	79	2	no	—
183	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
184	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
185	C₂×#117	—	79	2	no	—
186	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
187	C₂×#108	—	79	2	no	—
188	C₂×#108	—	79	2	no	—
189	C₂×#108	—	79	8	no	—
190	#427	—	79	2	no	—
191	#427	—	79	2	no	—
192	#427	—	79	2	no	—
193	#427	—	79	2	no	—
194	C₂×#107	—	79	2	no	—
195	C₂×#106	—	79	2	no	—
196	#405	—	79	8	no	—
197	#405	—	158	4	no	—
198	#405	Dic₇₉	1	8	yes	complemented
199	C₄×M₁₆	—	158	4	no	—
200	C₂×#97	C₂×D₇₉	1	2	yes	—
201	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
202	#339	—	79	8	no	—
203	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
204	C₂×M₁₆	—	79	8	no	—
205	C₂×M₁₆	—	79	4	no	—
206	C₂×M₁₆	—	158	2	no	—
207	C₂×M₁₆	—	158	4	no	—
208	C₂×M₁₆	Dic₁₅₈	1	4	yes	—
209	C₂×M₁₆	D₃₁₆	1	2	yes	—
210	C₂×M₁₆	D₃₁₆	1	2	yes	—
211	C₂×M₁₆	C₂×Dic₇₉	1	4	yes	—
212	C₂²×C₈	—	158	2	no	—
213	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
214	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
215	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
216	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
217	C₂²×C₈	C₄×D₇₉	1	4	yes	—
218	C₂²×C₈	C₂×Dic₇₉	1	4	yes	—
219	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
220	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
221	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
222	#117	—	2	2	no	—
223	#117	—	79	4	no	—
224	#117	—	79	4	no	—
225	#117	—	158	2	no	—
226	#117	—	158	2	no	—
227	#117	C₂×Dic₇₉	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	—	79	4	no	—
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	158	2	no	—
232	C₂×C₄²	—	158	2	no	—
233	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
234	#108	—	79	8	no	—
235	#108	—	79	8	no	—
236	#107	—	79	4	no	—
237	#107	—	79	4	no	—
238	#106	—	79	4	no	—
239	#106	—	79	4	no	—
240	#97	—	158	8	no	—
241	#97	C₂×Dic₇₉	1	8	yes	complemented
242	C₄×C₈	—	158	8	no	—
243	C₄×C₈	C₂×Dic₇₉	1	8	yes	complemented
244	C₂⁴	#11929624	1	1	yes	characteristic
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	158	4	no	—
247	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
248	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
250	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
251	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
253	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
254	C₂²×C₄	#11929624	1	2	yes	—
255	C₂²×C₄	#11929624	1	1	yes	characteristic
256	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
257	M₁₆	—	79	8	no	—
258	M₁₆	—	158	4	no	—
259	M₁₆	—	158	8	no	—
260	M₁₆	C₄⋊Dic₇₉	1	8	yes	—
261	M₁₆	C₄⋊Dic₇₉	1	8	yes	—
262	C₂×C₈	—	158	8	no	—
263	C₂×C₈	—	158	4	no	—
264	C₂×C₈	C₄×Dic₇₉	1	4	yes	—
265	C₂×C₈	C₄×Dic₇₉	1	4	yes	—
266	C₂×C₈	C₄×Dic₇₉	1	4	yes	—
267	C₂×C₈	C₄×Dic₇₉	1	4	yes	—
268	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
269	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
270	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
271	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
272	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
273	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
274	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
275	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
276	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
277	C₂×C₈	C₂×D₃₁₆	1	4	yes	—
278	C₂×C₈	C₂×Dic₁₅₈	1	4	yes	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	79	8	no	—
281	C₄⋊C₄	—	158	4	no	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₂²⋊C₄	—	158	4	no	—
284	C₂²⋊C₄	—	158	4	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	158	4	no	—
287	C₄²	—	158	4	no	—
288	C₄²	C₂²×Dic₇₉	1	4	yes	—
289	C₂³	—	4	2	no	—
290	C₂³	#14579120	1	2	yes	—
291	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
292	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
293	C₂³	C₄×Dic₁₅₈	1	2	yes	—
294	C₂³	C₂×#11929624	1	1	yes	characteristic
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	632	4	no	—
298	C₂×C₄	—	158	8	no	—
299	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
300	C₂×C₄	C₂×C₄×Dic₇₉	1	2	yes	—
301	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
302	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
303	C₂×C₄	#14579120	1	2	yes	—
304	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
305	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
306	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
307	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
308	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
309	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
310	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
311	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
312	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
313	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
315	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
316	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
317	C₈	—	158	8	no	—
318	C₈	C₂×C₄×Dic₇₉	1	2	yes	—
319	C₈	C₂×C₄×Dic₇₉	1	2	yes	—
320	C₈	C₂×C₄×Dic₇₉	1	2	yes	—
321	C₈	C₂×C₄×Dic₇₉	1	2	yes	—
322	C₈	C₂×C₄⋊Dic₇₉	1	8	yes	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	C₄×C₄⋊Dic₇₉	1	2	yes	—
329	C₂²	C₄×C₄⋊Dic₇₉	1	2	yes	—
330	C₂²	C₂×#14579120	1	1	yes	characteristic
331	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
332	C₂²	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
333	C₄	—	4	4	no	—
334	C₄	—	316	8	no	—
335	C₄	C₄×C₄⋊Dic₇₉	1	2	yes	—
336	C₄	C₄×C₄⋊Dic₇₉	1	2	yes	—
337	C₄	C₂²×C₄×Dic₇₉	1	1	yes	characteristic
338	C₄	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
339	C₄	C₂×C₄×D₃₁₆	1	1	yes	characteristic
340	C₄	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
341	C₂	—	2	1	no	—
342	C₂	—	2	2	no	—
343	C₂	—	2	2	no	—
344	C₂	—	2	1	no	—
345	C₂	C₂×C₄×C₄⋊Dic₇₉	1	1	yes	characteristic
346	C₂	#23772318	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₁₆
commutator	C₄×C₇₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#405×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂⁴×C₇₉	#41
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#405	D₇₉
hypocenter	C₇₉	#20446
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. #23763284	C₂	semidirect
5. #23763279	C₂	semidirect
10. C₂×#14579097	C₄	semidirect
13. #19098601	C₄	semidirect
14. #19098601	C₄	semidirect
17. C₂×#14579095	C₄	semidirect
18. C₂×#14579093	C₄	semidirect
26. #405×C₇₉	C₄	semidirect
41. #14579097	C₂×C₄	semidirect
42. #14579097	C₂×C₄	semidirect
68. #97×C₇₉	C₂×C₄	semidirect
69. C₄×C₈×C₇₉	C₂×C₄	semidirect
181. C₇₉	#20446	semidirect
198. #405	Dic₇₉	semidirect
241. #97	C₂×Dic₇₉	semidirect
243. C₄×C₈	C₂×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579097	2
C₂×#19098601	2
#23771818	2
#23763284	2
#23763279	2
#23763110	2
C₂×#405×C₇₉	2
#20446	79