Subgroups — C₂×#541×D₇₉ #35195080

Order 20224.

7110 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19099175	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099174	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099173	C₂	1	2	yes	maximal, complemented
5	C₂×#19099172	C₂	1	4	yes	maximal, complemented
6	C₂×#19099171	C₂	1	2	yes	maximal, complemented
7	C₂×#19099170	C₂	1	4	yes	maximal, complemented
8	#541×D₇₉	C₂	1	32	yes	maximal, direct product factor
9	C₂×C₄⋊Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#126×D₇₉	C₂	1	4	yes	maximal
11	C₂×#125×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×D₇₉	C₂	1	4	yes	maximal, complemented
13	C₂×C₂²⋊Q₈×D₇₉	C₂	1	2	yes	maximal
14	C₂×C₄×Q₈×D₇₉	C₂	1	2	yes	maximal, complemented
15	C₂×#117×D₇₉	C₂	1	1	yes	maximal, characteristic
16	C₂×#541×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₈×D₇₉	C₂²	1	2	yes	—
18	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
19	#19099176	C₂²	1	16	yes	complemented
20	#19099175	C₂²	1	16	yes	complemented
21	#19099174	C₂²	1	16	yes	complemented
22	#19099173	C₂²	1	32	yes	complemented
23	#19099172	C₂²	1	64	yes	complemented
24	#19099171	C₂²	1	32	yes	complemented
25	#19099170	C₂²	1	64	yes	complemented
26	C₂×#14579161	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14579160	C₂²	1	4	yes	complemented
28	C₂×#14579159	C₂²	1	2	yes	complemented
29	C₄⋊Q₈×D₇₉	C₂²	1	16	yes	complemented
30	C₂×#14579156	C₂²	1	4	yes	—
31	C₂×#14579156	C₂²	1	4	yes	—
32	C₂×#14579156	C₂²	1	4	yes	—
33	C₂×#14579155	C₂²	1	4	yes	—
34	C₂×#14579154	C₂²	1	4	yes	—
35	C₂×#14579154	C₂²	1	4	yes	—
36	C₂×#14579154	C₂²	1	4	yes	—
37	#126×D₇₉	C₂²	1	64	yes	—
38	C₂×#14579153	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14579153	C₂²	1	4	yes	complemented
40	C₂×#14579152	C₂²	1	4	yes	complemented
41	C₂×#14579152	C₂²	1	2	yes	complemented
42	C₂×#14579152	C₂²	1	4	yes	complemented
43	C₂×#14579151	C₂²	1	4	yes	complemented
44	C₂×#14579151	C₂²	1	4	yes	complemented
45	C₂×#14579151	C₂²	1	4	yes	complemented
46	C₂×#14579151	C₂²	1	4	yes	complemented
47	C₂×#14579151	C₂²	1	4	yes	complemented
48	#125×D₇₉	C₂²	1	64	yes	complemented
49	#125×D₇₉	C₂²	1	16	yes	complemented
50	C₂×#14579141	C₂²	1	2	yes	—
51	C₂×#14579140	C₂²	1	2	yes	—
52	C₂×#14579139	C₂²	1	4	yes	—
53	C₂×#14579138	C₂²	1	4	yes	—
54	C₂×#14579137	C₂²	1	2	yes	—
55	C₂²⋊Q₈×D₇₉	C₂²	1	32	yes	—
56	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
58	C₂×C₄×Dic₁₅₈	C₂²	1	4	yes	complemented
59	C₂×#14579126	C₂²	1	2	yes	complemented
60	C₂×#14579126	C₂²	1	4	yes	complemented
61	C₄×Q₈×D₇₉	C₂²	1	32	yes	complemented
62	C₂×#14579120	C₂²	1	1	yes	characteristic
63	C₂×#14579119	C₂²	1	2	yes	—
64	C₂×#14579118	C₂²	1	1	yes	characteristic
65	C₂×#14579118	C₂²	1	1	yes	characteristic
66	C₂×#14579117	C₂²	1	2	yes	—
67	#117×D₇₉	C₂²	1	16	yes	—
68	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
69	C₂×C₄⋊C₄×D₇₉	C₂²	1	2	yes	—
70	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
71	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
72	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
73	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
74	C₂×C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
75	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
76	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
77	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
78	C₂×C₄²×D₇₉	C₂²	1	4	yes	—
79	#541×C₇₉	C₂²	1	16	yes	complemented
80	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×#126×C₇₉	C₂²	1	4	yes	—
82	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
83	C₂×#125×C₇₉	C₂²	1	4	yes	complemented
84	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
85	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
86	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
87	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
88	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
89	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
90	C₂×Q₈×D₇₉	—	2	16	no	—
91	C₂×Q₈×D₇₉	C₂³	1	16	yes	—
92	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×D₇₉	—	2	8	no	—
94	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
95	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
96	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
97	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
98	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
100	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
103	#14579161	C₂³	1	8	yes	complemented
104	#14579160	C₂³	1	32	yes	complemented
105	#14579159	C₂³	1	16	yes	complemented
106	#14579156	C₂³	1	32	yes	—
107	#14579156	C₂³	1	32	yes	—
108	#14579156	C₂³	1	32	yes	—
109	#14579155	C₂³	1	32	yes	—
110	#14579154	C₂³	1	32	yes	—
111	#14579154	C₂³	1	32	yes	—
112	#14579154	C₂³	1	32	yes	—
113	#14579153	C₂³	1	32	yes	complemented
114	#14579153	C₂³	1	8	yes	complemented
115	#14579152	C₂³	1	32	yes	complemented
116	#14579152	C₂³	1	16	yes	complemented
117	#14579152	C₂³	1	32	yes	complemented
118	#14579151	C₂³	1	32	yes	complemented
119	#14579151	C₂³	1	32	yes	complemented
120	#14579151	C₂³	1	32	yes	complemented
121	#14579151	C₂³	1	32	yes	complemented
122	#14579151	C₂³	1	32	yes	complemented
123	#14579141	C₂³	1	16	yes	—
124	#14579140	C₂³	1	16	yes	—
125	#14579139	C₂³	1	32	yes	—
126	#14579138	C₂³	1	32	yes	—
127	#14579137	C₂³	1	16	yes	—
128	Q₈×Dic₇₉	C₂³	1	16	yes	complemented
129	C₄×Dic₁₅₈	C₂³	1	32	yes	complemented
130	C₄×Dic₁₅₈	C₂³	1	16	yes	complemented
131	#14579126	C₂³	1	32	yes	complemented
132	#14579126	C₂³	1	16	yes	complemented
133	#14579120	C₂³	1	8	yes	—
134	#14579119	C₂³	1	16	yes	—
135	#14579118	C₂³	1	8	yes	—
136	#14579118	C₂³	1	8	yes	—
137	#14579117	C₂³	1	16	yes	—
138	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
139	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
140	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
141	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
142	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
143	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
144	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
145	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
146	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
147	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
148	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
149	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
150	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
151	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
152	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
153	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
154	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
155	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
156	C₄⋊C₄×D₇₉	C₂³	1	16	yes	—
157	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
158	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
159	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
160	C₄⋊C₄×D₇₉	C₂³	1	32	yes	—
161	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
163	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
164	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
165	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
166	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
167	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	—
168	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
169	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
170	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
171	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
172	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
173	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
174	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
175	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
176	C₄²×D₇₉	C₂³	1	8	yes	—
177	C₄²×D₇₉	C₂³	1	8	yes	—
178	C₄²×D₇₉	C₂³	1	32	yes	—
179	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
180	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	complemented
182	#126×C₇₉	C₂³	1	32	yes	—
183	#125×C₇₉	C₂³	1	32	yes	complemented
184	#125×C₇₉	C₂³	1	8	yes	complemented
185	C₂²⋊Q₈×C₇₉	C₂³	1	16	yes	—
186	C₄×Q₈×C₇₉	C₂³	1	16	yes	complemented
187	#117×C₇₉	C₂³	1	8	yes	—
188	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
196	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
199	C₂³×D₇₉	—	2	4	no	—
200	C₂³×D₇₉	—	2	8	no	—
201	C₂³×D₇₉	C₂⁴	1	4	yes	—
202	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
203	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₁₅₈	—	2	16	no	—
205	C₂×Dic₁₅₈	—	2	8	no	—
206	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
207	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
208	Q₈×D₇₉	—	2	64	no	—
209	C₂²×Dic₇₉	—	2	4	no	—
210	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
211	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
212	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
213	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
214	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
215	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
216	C₂²×Dic₇₉	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×D₇₉	—	2	4	no	—
218	C₂×C₄×D₇₉	—	2	32	no	—
219	C₂×C₄×D₇₉	—	2	16	no	—
220	C₂×C₄×D₇₉	—	2	4	no	—
221	C₂×C₄×D₇₉	—	2	8	no	—
222	C₂×C₄×D₇₉	—	2	8	no	—
223	C₂×C₄×D₇₉	—	2	16	no	—
224	C₂×C₄×D₇₉	—	2	4	no	—
225	C₂×C₄×D₇₉	#41	1	8	yes	—
226	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
227	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
228	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
229	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
230	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
231	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
232	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
233	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
234	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
235	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
236	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
237	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
238	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
239	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
240	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
241	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
242	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
243	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
244	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
245	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
246	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
247	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
248	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
249	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
250	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
251	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
252	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
253	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
254	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
255	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
256	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
257	C₄×Dic₇₉	C₂⁴	1	8	yes	—
258	C₄×Dic₇₉	C₂⁴	1	8	yes	—
259	C₄×Dic₇₉	C₂⁴	1	4	yes	—
260	C₄×Dic₇₉	C₂⁴	1	4	yes	—
261	C₄×Dic₇₉	C₂⁴	1	16	yes	—
262	C₄×Dic₇₉	C₂⁴	1	16	yes	—
263	C₄×Dic₇₉	C₂⁴	1	16	yes	—
264	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
265	C₂×Q₈×C₇₉	—	2	8	no	—
266	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₇₉	—	2	4	no	—
268	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
276	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
278	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
280	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	—
281	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
283	C₄²×C₇₉	C₂⁴	1	4	yes	—
284	C₄²×C₇₉	C₂⁴	1	4	yes	—
285	C₄²×C₇₉	C₂⁴	1	16	yes	—
286	C₂³×C₇₉	—	2	2	no	—
287	C₂³×C₇₉	—	2	4	no	—
288	C₂³×C₇₉	C₂⁵	1	2	yes	—
289	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
290	C₂²×D₇₉	—	2	2	no	—
291	C₂²×D₇₉	—	2	4	no	—
292	C₂²×D₇₉	—	2	8	no	—
293	C₂²×D₇₉	—	2	16	no	—
294	C₂²×D₇₉	—	4	16	no	—
295	C₂²×D₇₉	C₂×#41	1	4	yes	—
296	C₂²×D₇₉	2₋¹⁺⁴	1	8	yes	—
297	C₂²×D₇₉	C₂⁵	1	2	yes	—
298	C₂²×D₇₉	C₂⁵	1	2	yes	—
299	Q₈×C₇₉	—	2	16	no	—
300	C₂×C₄×C₇₉	—	2	2	no	—
301	C₂×C₄×C₇₉	—	2	8	no	—
302	C₂×C₄×C₇₉	—	2	4	no	—
303	C₂×C₄×C₇₉	—	2	4	no	—
304	C₂×C₄×C₇₉	—	2	8	no	—
305	C₂×C₄×C₇₉	—	2	8	no	—
306	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
307	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
308	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
309	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
310	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
311	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
312	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
313	C₂×Dic₇₉	—	2	2	no	—
314	C₂×Dic₇₉	—	2	8	no	—
315	C₂×Dic₇₉	—	2	4	no	—
316	C₂×Dic₇₉	—	2	4	no	—
317	C₂×Dic₇₉	—	2	8	no	—
318	C₂×Dic₇₉	—	2	8	no	—
319	C₂×Dic₇₉	C₂×#41	1	4	yes	—
320	C₂×Dic₇₉	C₂⁵	1	4	yes	—
321	C₂×Dic₇₉	C₂⁵	1	4	yes	—
322	C₂×Dic₇₉	C₂⁵	1	8	yes	—
323	C₂×Dic₇₉	C₂⁵	1	8	yes	—
324	C₂×Dic₇₉	C₂⁵	1	2	yes	—
325	C₂×Dic₇₉	C₂⁵	1	2	yes	—
326	C₄×D₇₉	—	2	8	no	—
327	C₄×D₇₉	—	2	32	no	—
328	C₄×D₇₉	—	2	16	no	—
329	C₄×D₇₉	—	2	16	no	—
330	C₄×D₇₉	—	2	32	no	—
331	C₄×D₇₉	—	2	8	no	—
332	C₄×D₇₉	—	2	8	no	—
333	C₄×D₇₉	C₂×#41	1	16	yes	—
334	Dic₁₅₈	—	2	16	no	—
335	Dic₁₅₈	—	2	32	no	—
336	C₂²×C₇₉	—	2	2	no	—
337	C₂²×C₇₉	—	2	4	no	—
338	C₂²×C₇₉	—	4	4	no	—
339	C₂²×C₇₉	C₂²×#41	1	2	yes	—
340	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	4	yes	—
341	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
342	C₂×D₇₉	—	2	2	no	—
343	C₂×D₇₉	—	2	4	no	—
344	C₂×D₇₉	—	4	4	no	—
345	C₂×D₇₉	—	4	16	no	—
346	C₂×D₇₉	#541	1	16	yes	direct product factor
347	C₂×D₇₉	C₂²×#41	1	4	yes	—
348	C₂×D₇₉	C₂×2₋¹⁺⁴	1	8	yes	—
349	C₄×C₇₉	—	2	2	no	—
350	C₄×C₇₉	—	2	8	no	—
351	C₄×C₇₉	—	2	4	no	—
352	C₄×C₇₉	—	2	4	no	—
353	C₄×C₇₉	—	2	8	no	—
354	C₄×C₇₉	C₂²×#41	1	4	yes	—
355	Dic₇₉	—	2	8	no	—
356	Dic₇₉	—	2	2	no	—
357	Dic₇₉	—	2	4	no	—
358	Dic₇₉	—	2	4	no	—
359	Dic₇₉	—	2	8	no	—
360	Dic₇₉	C₂²×#41	1	4	yes	—
361	C₂²×#541	—	79	1	no	maximal, Sylow
362	C₂×C₇₉	—	4	2	no	—
363	C₂×C₇₉	C₂×#541	1	4	yes	complemented
364	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
365	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	2	yes	—
366	D₇₉	—	4	2	no	—
367	D₇₉	C₂×#541	1	8	yes	direct product factor
368	C₂×#541	—	79	32	no	—
369	C₂×#541	—	79	1	no	—
370	C₂×#541	—	79	4	no	—
371	C₂×#541	—	79	1	no	—
372	C₂×#541	—	79	4	no	—
373	C₂×#541	—	79	2	no	—
374	C₂×#541	—	79	2	no	—
375	C₂×#541	—	79	1	no	—
376	C₂×#541	D₇₉	1	1	yes	characteristic, direct product factor
377	C₂²×C₄⋊Q₈	—	79	1	no	—
378	C₂²×#126	—	79	4	no	—
379	C₂²×#125	—	79	4	no	—
380	C₂²×#125	—	79	1	no	—
381	C₂²×C₂²⋊Q₈	—	79	2	no	—
382	C₂²×C₄×Q₈	—	79	2	no	—
383	C₂²×#117	—	79	1	no	—
384	C₇₉	C₂²×#541	1	1	yes	characteristic, complemented, Sylow
385	C₂³×Q₈	—	79	2	no	—
386	C₂⁴×C₄	—	79	1	no	—
387	#541	—	79	16	no	—
388	#541	—	79	64	no	—
389	#541	—	79	64	no	—
390	#541	—	79	16	no	—
391	#541	—	79	32	no	—
392	#541	—	79	32	no	—
393	#541	—	79	16	no	—
394	#541	C₂×D₇₉	1	16	yes	direct product factor
395	C₂×C₄⋊Q₈	—	79	2	no	—
396	C₂×C₄⋊Q₈	—	79	16	no	—
397	C₂×C₄⋊Q₈	—	79	4	no	—
398	C₂×C₄⋊Q₈	—	79	1	no	—
399	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
400	C₂×#126	—	79	64	no	—
401	C₂×#126	—	79	4	no	—
402	C₂×#126	—	79	4	no	—
403	C₂×#126	—	79	4	no	—
404	C₂×#126	—	79	4	no	—
405	C₂×#126	—	79	4	no	—
406	C₂×#126	—	79	4	no	—
407	C₂×#126	—	79	4	no	—
408	C₂×#126	C₂×D₇₉	1	4	yes	—
409	C₂×#125	—	79	16	no	—
410	C₂×#125	—	79	64	no	—
411	C₂×#125	—	79	4	no	—
412	C₂×#125	—	79	4	no	—
413	C₂×#125	—	79	4	no	—
414	C₂×#125	—	79	4	no	—
415	C₂×#125	—	79	4	no	—
416	C₂×#125	—	79	2	no	—
417	C₂×#125	—	79	4	no	—
418	C₂×#125	—	79	4	no	—
419	C₂×#125	—	79	1	no	—
420	C₂×#125	—	79	4	no	—
421	C₂×#125	C₂×D₇₉	1	1	yes	characteristic, complemented
422	C₂×#125	C₂×D₇₉	1	4	yes	complemented
423	C₂×C₂²⋊Q₈	—	79	2	no	—
424	C₂×C₂²⋊Q₈	—	79	2	no	—
425	C₂×C₂²⋊Q₈	—	79	32	no	—
426	C₂×C₂²⋊Q₈	—	79	4	no	—
427	C₂×C₂²⋊Q₈	—	79	2	no	—
428	C₂×C₂²⋊Q₈	—	79	4	no	—
429	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
430	C₂×C₄×Q₈	—	79	2	no	—
431	C₂×C₄×Q₈	—	79	32	no	—
432	C₂×C₄×Q₈	—	79	4	no	—
433	C₂×C₄×Q₈	—	79	2	no	—
434	C₂×C₄×Q₈	—	79	4	no	—
435	C₂×C₄×Q₈	—	79	2	no	—
436	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	complemented
437	C₂×#117	—	79	1	no	—
438	C₂×#117	—	79	16	no	—
439	C₂×#117	—	79	2	no	—
440	C₂×#117	—	79	2	no	—
441	C₂×#117	—	79	1	no	—
442	C₂×#117	—	79	1	no	—
443	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	—	79	2	no	—
445	C₂²×C₄⋊C₄	—	79	2	no	—
446	C₂²×C₄⋊C₄	—	79	4	no	—
447	C₂²×C₄⋊C₄	—	79	4	no	—
448	C₂²×C₄⋊C₄	—	79	4	no	—
449	C₂²×C₄⋊C₄	—	79	4	no	—
450	C₂²×C₂²⋊C₄	—	79	2	no	—
451	C₂²×C₂²⋊C₄	—	79	4	no	—
452	C₂²×C₄²	—	79	1	no	—
453	C₂²×C₄²	—	79	1	no	—
454	C₂²×C₄²	—	79	4	no	—
455	C₂⁵	—	79	1	no	—
456	C₂²×Q₈	—	79	16	no	—
457	C₂²×Q₈	—	79	4	no	—
458	C₂²×Q₈	—	79	2	no	—
459	C₂²×Q₈	—	158	16	no	—
460	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
461	C₂³×C₄	—	79	1	no	—
462	C₂³×C₄	—	79	1	no	—
463	C₂³×C₄	—	79	2	no	—
464	C₂³×C₄	—	79	4	no	—
465	C₂³×C₄	—	79	4	no	—
466	C₂³×C₄	—	79	2	no	—
467	C₂³×C₄	—	79	1	no	—
468	C₂³×C₄	—	79	1	no	—
469	C₂³×C₄	—	79	8	no	—
470	C₂³×C₄	—	79	1	no	—
471	C₂³×C₄	—	158	8	no	—
472	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
473	C₄⋊Q₈	—	79	16	no	—
474	C₄⋊Q₈	—	79	32	no	—
475	C₄⋊Q₈	—	79	8	no	—
476	C₄⋊Q₈	C₂²×D₇₉	1	8	yes	complemented
477	#126	—	79	32	no	—
478	#126	—	79	32	no	—
479	#126	—	79	32	no	—
480	#126	—	79	32	no	—
481	#126	—	79	32	no	—
482	#126	—	79	32	no	—
483	#126	—	79	32	no	—
484	#126	C₂²×D₇₉	1	32	yes	—
485	#125	—	79	32	no	—
486	#125	—	79	32	no	—
487	#125	—	79	32	no	—
488	#125	—	79	32	no	—
489	#125	—	79	32	no	—
490	#125	—	79	16	no	—
491	#125	—	79	32	no	—
492	#125	—	79	32	no	—
493	#125	—	79	8	no	—
494	#125	—	79	32	no	—
495	#125	C₂²×D₇₉	1	8	yes	complemented
496	#125	C₂²×D₇₉	1	32	yes	complemented
497	C₂²⋊Q₈	—	79	16	no	—
498	C₂²⋊Q₈	—	79	16	no	—
499	C₂²⋊Q₈	—	79	32	no	—
500	C₂²⋊Q₈	—	79	16	no	—
501	C₂²⋊Q₈	—	79	32	no	—
502	C₂²⋊Q₈	C₂²×D₇₉	1	16	yes	—
503	C₄×Q₈	—	79	16	no	—
504	C₄×Q₈	—	79	32	no	—
505	C₄×Q₈	—	79	16	no	—
506	C₄×Q₈	—	79	32	no	—
507	C₄×Q₈	—	79	16	no	—
508	C₄×Q₈	C₂²×D₇₉	1	16	yes	complemented
509	#117	—	79	8	no	—
510	#117	—	79	16	no	—
511	#117	—	79	16	no	—
512	#117	—	79	8	no	—
513	#117	—	79	8	no	—
514	#117	C₂²×D₇₉	1	8	yes	—
515	C₂×C₄⋊C₄	—	79	2	no	—
516	C₂×C₄⋊C₄	—	79	2	no	—
517	C₂×C₄⋊C₄	—	79	2	no	—
518	C₂×C₄⋊C₄	—	79	4	no	—
519	C₂×C₄⋊C₄	—	79	2	no	—
520	C₂×C₄⋊C₄	—	79	4	no	—
521	C₂×C₄⋊C₄	—	79	4	no	—
522	C₂×C₄⋊C₄	—	79	4	no	—
523	C₂×C₄⋊C₄	—	79	4	no	—
524	C₂×C₄⋊C₄	—	79	4	no	—
525	C₂×C₄⋊C₄	—	79	4	no	—
526	C₂×C₄⋊C₄	—	79	4	no	—
527	C₂×C₄⋊C₄	—	79	4	no	—
528	C₂×C₄⋊C₄	—	79	4	no	—
529	C₂×C₄⋊C₄	—	79	4	no	—
530	C₂×C₄⋊C₄	—	79	4	no	—
531	C₂×C₄⋊C₄	—	79	4	no	—
532	C₂×C₄⋊C₄	—	79	16	no	—
533	C₂×C₄⋊C₄	—	79	16	no	—
534	C₂×C₄⋊C₄	—	79	32	no	—
535	C₂×C₄⋊C₄	—	79	32	no	—
536	C₂×C₄⋊C₄	—	79	32	no	—
537	C₂×C₄⋊C₄	—	79	32	no	—
538	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
541	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
542	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
543	C₂×C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
544	C₂×C₂²⋊C₄	—	79	2	no	—
545	C₂×C₂²⋊C₄	—	79	4	no	—
546	C₂×C₂²⋊C₄	—	79	2	no	—
547	C₂×C₂²⋊C₄	—	79	2	no	—
548	C₂×C₂²⋊C₄	—	79	4	no	—
549	C₂×C₂²⋊C₄	—	79	4	no	—
550	C₂×C₂²⋊C₄	—	79	16	no	—
551	C₂×C₂²⋊C₄	—	79	32	no	—
552	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
554	C₂×C₄²	—	79	2	no	—
555	C₂×C₄²	—	79	1	no	—
556	C₂×C₄²	—	79	2	no	—
557	C₂×C₄²	—	79	1	no	—
558	C₂×C₄²	—	79	4	no	—
559	C₂×C₄²	—	79	4	no	—
560	C₂×C₄²	—	79	4	no	—
561	C₂×C₄²	—	79	8	no	—
562	C₂×C₄²	—	79	8	no	—
563	C₂×C₄²	—	79	32	no	—
564	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
565	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
566	C₂×C₄²	C₂²×D₇₉	1	4	yes	—
567	C₂⁴	—	79	1	no	—
568	C₂⁴	—	79	4	no	—
569	C₂⁴	—	79	1	no	—
570	C₂⁴	—	158	4	no	—
571	C₂⁴	—	158	8	no	—
572	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
573	C₂×Q₈	—	2	8	no	—
574	C₂×Q₈	—	79	16	no	—
575	C₂×Q₈	—	79	8	no	—
576	C₂×Q₈	—	158	16	no	—
577	C₂×Q₈	—	158	64	no	—
578	C₂×Q₈	—	158	8	no	—
579	C₂×Q₈	C₂³×D₇₉	1	8	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	79	1	no	—
582	C₂²×C₄	—	79	8	no	—
583	C₂²×C₄	—	79	4	no	—
584	C₂²×C₄	—	79	4	no	—
585	C₂²×C₄	—	79	2	no	—
586	C₂²×C₄	—	79	2	no	—
587	C₂²×C₄	—	79	4	no	—
588	C₂²×C₄	—	79	4	no	—
589	C₂²×C₄	—	79	1	no	—
590	C₂²×C₄	—	79	8	no	—
591	C₂²×C₄	—	79	8	no	—
592	C₂²×C₄	—	79	16	no	—
593	C₂²×C₄	—	79	16	no	—
594	C₂²×C₄	—	79	4	no	—
595	C₂²×C₄	—	79	4	no	—
596	C₂²×C₄	—	79	4	no	—
597	C₂²×C₄	—	158	4	no	—
598	C₂²×C₄	—	158	32	no	—
599	C₂²×C₄	—	158	8	no	—
600	C₂²×C₄	—	158	16	no	—
601	C₂²×C₄	—	158	8	no	—
602	C₂²×C₄	—	158	4	no	—
603	C₂²×C₄	—	158	16	no	—
604	C₂²×C₄	—	158	4	no	—
605	C₂²×C₄	—	158	4	no	—
606	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
607	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
608	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
609	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
610	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
611	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
612	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
613	C₄⋊C₄	—	79	8	no	—
614	C₄⋊C₄	—	79	8	no	—
615	C₄⋊C₄	—	79	16	no	—
616	C₄⋊C₄	—	79	16	no	—
617	C₄⋊C₄	—	79	16	no	—
618	C₄⋊C₄	—	79	16	no	—
619	C₄⋊C₄	—	79	16	no	—
620	C₄⋊C₄	—	79	16	no	—
621	C₄⋊C₄	—	79	16	no	—
622	C₄⋊C₄	—	79	16	no	—
623	C₄⋊C₄	—	79	16	no	—
624	C₄⋊C₄	—	79	8	no	—
625	C₄⋊C₄	—	79	8	no	—
626	C₄⋊C₄	—	79	16	no	—
627	C₄⋊C₄	—	79	16	no	—
628	C₄⋊C₄	—	79	16	no	—
629	C₄⋊C₄	—	79	16	no	—
630	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
631	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
632	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
633	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
634	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
635	C₄⋊C₄	C₂³×D₇₉	1	16	yes	—
636	C₂²⋊C₄	—	79	8	no	—
637	C₂²⋊C₄	—	79	16	no	—
638	C₂²⋊C₄	—	79	8	no	—
639	C₂²⋊C₄	—	79	8	no	—
640	C₂²⋊C₄	—	79	16	no	—
641	C₂²⋊C₄	—	79	16	no	—
642	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
643	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
644	C₄²	—	79	8	no	—
645	C₄²	—	79	4	no	—
646	C₄²	—	79	8	no	—
647	C₄²	—	79	4	no	—
648	C₄²	—	79	16	no	—
649	C₄²	—	79	16	no	—
650	C₄²	—	79	16	no	—
651	C₄²	C₂³×D₇₉	1	4	yes	—
652	C₄²	C₂³×D₇₉	1	4	yes	—
653	C₄²	C₂³×D₇₉	1	16	yes	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	316	16	no	—
657	C₂³	—	79	8	no	—
658	C₂³	—	79	2	no	—
659	C₂³	—	79	4	no	—
660	C₂³	—	79	2	no	—
661	C₂³	—	158	8	no	—
662	C₂³	—	158	16	no	—
663	C₂³	—	158	4	no	—
664	C₂³	—	158	2	no	—
665	C₂³	C₂⁴×D₇₉	1	2	yes	—
666	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
667	Q₈	—	2	16	no	—
668	Q₈	—	158	32	no	—
669	Q₈	—	158	16	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	79	2	no	—
677	C₂×C₄	—	79	4	no	—
678	C₂×C₄	—	79	16	no	—
679	C₂×C₄	—	79	4	no	—
680	C₂×C₄	—	79	4	no	—
681	C₂×C₄	—	79	8	no	—
682	C₂×C₄	—	79	8	no	—
683	C₂×C₄	—	79	2	no	—
684	C₂×C₄	—	158	8	no	—
685	C₂×C₄	—	158	8	no	—
686	C₂×C₄	—	158	32	no	—
687	C₂×C₄	—	158	16	no	—
688	C₂×C₄	—	158	16	no	—
689	C₂×C₄	—	158	32	no	—
690	C₂×C₄	—	158	8	no	—
691	C₂×C₄	—	158	4	no	—
692	C₂×C₄	—	158	4	no	—
693	C₂×C₄	—	158	8	no	—
694	C₂×C₄	—	158	2	no	—
695	C₂×C₄	—	158	8	no	—
696	C₂×C₄	—	158	8	no	—
697	C₂×C₄	#41×D₇₉	1	4	yes	—
698	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
699	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
700	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
701	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
702	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
703	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	316	16	no	—
708	C₂²	—	316	4	no	—
709	C₂²	—	79	4	no	—
710	C₂²	—	79	8	no	—
711	C₂²	—	79	16	no	—
712	C₂²	—	158	2	no	—
713	C₂²	—	158	4	no	—
714	C₂²	C₂×#41×D₇₉	1	2	yes	—
715	C₂²	2₋¹⁺⁴×D₇₉	1	4	yes	—
716	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
717	C₄	—	2	2	no	—
718	C₄	—	2	8	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	8	no	—
722	C₄	—	79	4	no	—
723	C₄	—	158	2	no	—
724	C₄	—	158	8	no	—
725	C₄	—	158	4	no	—
726	C₄	—	158	4	no	—
727	C₄	—	158	8	no	—
728	C₄	C₂×#41×D₇₉	1	4	yes	—
729	C₂	—	4	2	no	—
730	C₂	—	316	2	no	—
731	C₂	—	79	8	no	—
732	C₂	#541×D₇₉	1	4	yes	direct product factor
733	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
734	C₂	C₂×2₋¹⁺⁴×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#541×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
prime radical	C₂⁴×D₇₉	C₂³
hypercenter	C₂×#541	D₇₉
hypocenter	C₇₉	C₂²×#541
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#541

Complements

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

N	H ≅ G/N	type
1. C₂×#19099176	C₂	semidirect
2. C₂×#19099175	C₂	semidirect
3. C₂×#19099174	C₂	semidirect
4. C₂×#19099173	C₂	semidirect
5. C₂×#19099172	C₂	semidirect
6. C₂×#19099171	C₂	semidirect
7. C₂×#19099170	C₂	semidirect
8. #541×D₇₉	C₂	direct (N × H)
9. C₂×C₄⋊Q₈×D₇₉	C₂	semidirect
11. C₂×#125×D₇₉	C₂	semidirect
12. C₂×#125×D₇₉	C₂	semidirect
14. C₂×C₄×Q₈×D₇₉	C₂	semidirect
16. C₂×#541×C₇₉	C₂	semidirect
19. #19099176	C₂²	semidirect
20. #19099175	C₂²	semidirect
21. #19099174	C₂²	semidirect
22. #19099173	C₂²	semidirect
23. #19099172	C₂²	semidirect
24. #19099171	C₂²	semidirect
25. #19099170	C₂²	semidirect
26. C₂×#14579161	C₂²	semidirect
27. C₂×#14579160	C₂²	semidirect
28. C₂×#14579159	C₂²	semidirect
29. C₄⋊Q₈×D₇₉	C₂²	semidirect
38. C₂×#14579153	C₂²	semidirect
39. C₂×#14579153	C₂²	semidirect
40. C₂×#14579152	C₂²	semidirect
41. C₂×#14579152	C₂²	semidirect
42. C₂×#14579152	C₂²	semidirect
43. C₂×#14579151	C₂²	semidirect
44. C₂×#14579151	C₂²	semidirect
45. C₂×#14579151	C₂²	semidirect
46. C₂×#14579151	C₂²	semidirect
47. C₂×#14579151	C₂²	semidirect
48. #125×D₇₉	C₂²	semidirect
49. #125×D₇₉	C₂²	semidirect
56. C₂×Q₈×Dic₇₉	C₂²	semidirect
57. C₂×C₄×Dic₁₅₈	C₂²	semidirect
58. C₂×C₄×Dic₁₅₈	C₂²	semidirect
59. C₂×#14579126	C₂²	semidirect
60. C₂×#14579126	C₂²	semidirect
61. C₄×Q₈×D₇₉	C₂²	semidirect
79. #541×C₇₉	C₂²	semidirect
80. C₂×C₄⋊Q₈×C₇₉	C₂²	semidirect
82. C₂×#125×C₇₉	C₂²	semidirect
83. C₂×#125×C₇₉	C₂²	semidirect
85. C₂×C₄×Q₈×C₇₉	C₂²	semidirect
103. #14579161	C₂³	semidirect
104. #14579160	C₂³	semidirect
105. #14579159	C₂³	semidirect
113. #14579153	C₂³	semidirect
114. #14579153	C₂³	semidirect
115. #14579152	C₂³	semidirect
116. #14579152	C₂³	semidirect
117. #14579152	C₂³	semidirect
118. #14579151	C₂³	semidirect
119. #14579151	C₂³	semidirect
120. #14579151	C₂³	semidirect
121. #14579151	C₂³	semidirect
122. #14579151	C₂³	semidirect
128. Q₈×Dic₇₉	C₂³	semidirect
129. C₄×Dic₁₅₈	C₂³	semidirect
130. C₄×Dic₁₅₈	C₂³	semidirect
131. #14579126	C₂³	semidirect
132. #14579126	C₂³	semidirect
181. C₄⋊Q₈×C₇₉	C₂³	semidirect
183. #125×C₇₉	C₂³	semidirect
184. #125×C₇₉	C₂³	semidirect
186. C₄×Q₈×C₇₉	C₂³	semidirect
346. C₂×D₇₉	#541	direct (N × H)
363. C₂×C₇₉	C₂×#541	semidirect
367. D₇₉	C₂×#541	direct (N × H)
376. C₂×#541	D₇₉	direct (N × H)
384. C₇₉	C₂²×#541	semidirect
394. #541	C₂×D₇₉	direct (N × H)
399. C₂×C₄⋊Q₈	C₂×D₇₉	semidirect
421. C₂×#125	C₂×D₇₉	semidirect
422. C₂×#125	C₂×D₇₉	semidirect
436. C₂×C₄×Q₈	C₂×D₇₉	semidirect
476. C₄⋊Q₈	C₂²×D₇₉	semidirect
495. #125	C₂²×D₇₉	semidirect
496. #125	C₂²×D₇₉	semidirect
508. C₄×Q₈	C₂²×D₇₉	semidirect
732. C₂	#541×D₇₉	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×#19099176	2
C₂×#19099175	2
C₂×#19099174	2
C₂×#19099173	2
C₂×#19099172	2
C₂×#19099171	2
C₂×#19099170	2
#541×D₇₉	2
C₂×C₄⋊Q₈×D₇₉	2
C₂×#126×D₇₉	2
C₂×#125×D₇₉	2
C₂×C₂²⋊Q₈×D₇₉	2
C₂×C₄×Q₈×D₇₉	2
C₂×#117×D₇₉	2
C₂×#541×C₇₉	2
C₂²×#541	79

Subgroups — C2×#541×D79 #35195080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#541×D₇₉ #35195080