Subgroups — C₂×C₇₉×#2816 #34148337

Order 20224.

2998 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2816	C₂	1	16	yes	maximal, direct product factor
4	C₂×#399×C₇₉	C₂	1	2	yes	maximal, complemented
5	C₂×#398×C₇₉	C₂	1	2	yes	maximal, complemented
6	C₂×#394×C₇₉	C₂	1	4	yes	maximal, complemented
7	C₂×#394×C₇₉	C₂	1	2	yes	maximal, complemented
8	C₂×#393×C₇₉	C₂	1	2	yes	maximal, complemented
9	C₂×#381×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₇₉	C₂²	1	2	yes	—
12	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₇₉	—	2	8	no	—
15	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	8	yes	complemented
16	C₂×#121×C₇₉	—	2	8	no	—
17	C₂×#121×C₇₉	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₇₉	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	—
26	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	—
27	#399×C₇₉	C₂²	1	16	yes	complemented
28	#398×C₇₉	C₂²	1	16	yes	complemented
29	#394×C₇₉	C₂²	1	16	yes	complemented
30	#394×C₇₉	C₂²	1	32	yes	complemented
31	#393×C₇₉	C₂²	1	16	yes	complemented
32	#381×C₇₉	C₂²	1	8	yes	complemented
33	C₂×#95×C₇₉	C₂²	1	2	yes	—
34	C₂×#95×C₇₉	C₂²	1	2	yes	—
35	C₂×#95×C₇₉	C₂²	1	4	yes	—
36	C₂⁵×C₇₉	C₂³	1	2	yes	—
37	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₇₉	—	2	4	no	—
39	C₂²×Q₈×C₇₉	—	4	4	no	—
40	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
41	C₂²×D₄×C₇₉	—	2	8	no	—
42	C₂²×D₄×C₇₉	—	2	4	no	—
43	C₂²×D₄×C₇₉	—	4	4	no	—
44	C₂²×D₄×C₇₉	—	4	8	no	—
45	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
46	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₇₉	—	4	4	no	—
48	C₂³×C₄×C₇₉	D₄	1	8	yes	—
49	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	C₂³	1	4	yes	—
56	C₂²⋊Q₈×C₇₉	—	2	32	no	—
57	#121×C₇₉	—	2	32	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₇₉	—	4	8	no	—
62	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₇₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₇₉	C₂³	1	16	yes	—
66	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₇₉	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
69	C₂×C₂²⋊C₄×C₇₉	—	4	8	no	—
70	C₂×C₂²⋊C₄×C₇₉	—	4	8	no	—
71	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₇₉	C₂³	1	16	yes	—
76	#95×C₇₉	C₂³	1	8	yes	—
77	#95×C₇₉	C₂³	1	8	yes	—
78	#95×C₇₉	C₂³	1	16	yes	—
79	C₂⁴×C₇₉	—	2	4	no	—
80	C₂⁴×C₇₉	—	2	4	no	—
81	C₂⁴×C₇₉	—	2	4	no	—
82	C₂⁴×C₇₉	—	2	4	no	—
83	C₂⁴×C₇₉	—	2	8	no	—
84	C₂⁴×C₇₉	—	2	8	no	—
85	C₂⁴×C₇₉	—	2	8	no	—
86	C₂⁴×C₇₉	C₂×D₄	1	4	yes	—
87	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
88	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
89	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
90	C₂×Q₈×C₇₉	—	2	8	no	—
91	C₂×Q₈×C₇₉	—	4	8	no	—
92	C₂×Q₈×C₇₉	—	4	16	no	—
93	C₂×D₄×C₇₉	—	2	16	no	—
94	C₂×D₄×C₇₉	—	2	8	no	—
95	C₂×D₄×C₇₉	—	4	8	no	—
96	C₂×D₄×C₇₉	—	4	16	no	—
97	C₂×D₄×C₇₉	—	4	16	no	—
98	C₂×D₄×C₇₉	—	4	32	no	—
99	C₂²×C₄×C₇₉	—	2	4	no	—
100	C₂²×C₄×C₇₉	—	2	4	no	—
101	C₂²×C₄×C₇₉	—	2	4	no	—
102	C₂²×C₄×C₇₉	—	2	4	no	—
103	C₂²×C₄×C₇₉	—	2	4	no	—
104	C₂²×C₄×C₇₉	—	2	4	no	—
105	C₂²×C₄×C₇₉	—	2	8	no	—
106	C₂²×C₄×C₇₉	—	2	8	no	—
107	C₂²×C₄×C₇₉	—	2	8	no	—
108	C₂²×C₄×C₇₉	—	2	4	no	—
109	C₂²×C₄×C₇₉	—	2	8	no	—
110	C₂²×C₄×C₇₉	—	2	8	no	—
111	C₂²×C₄×C₇₉	—	4	16	no	—
112	C₂²×C₄×C₇₉	—	4	8	no	—
113	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₇₉	C₂×D₄	1	16	yes	—
116	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
122	C₄⋊C₄×C₇₉	—	2	8	no	—
123	C₄⋊C₄×C₇₉	—	2	8	no	—
124	C₄⋊C₄×C₇₉	—	2	16	no	—
125	C₄⋊C₄×C₇₉	—	4	16	no	—
126	C₂²⋊C₄×C₇₉	—	2	16	no	—
127	C₂²⋊C₄×C₇₉	—	2	16	no	—
128	C₂²⋊C₄×C₇₉	—	4	8	no	—
129	C₂²⋊C₄×C₇₉	—	4	16	no	—
130	C₂²⋊C₄×C₇₉	—	4	16	no	—
131	C₂³×C₇₉	—	2	8	no	—
132	C₂³×C₇₉	—	2	8	no	—
133	C₂³×C₇₉	—	2	8	no	—
134	C₂³×C₇₉	—	2	4	no	—
135	C₂³×C₇₉	—	2	4	no	—
136	C₂³×C₇₉	—	2	4	no	—
137	C₂³×C₇₉	—	2	4	no	—
138	C₂³×C₇₉	—	2	8	no	—
139	C₂³×C₇₉	—	2	8	no	—
140	C₂³×C₇₉	—	2	8	no	—
141	C₂³×C₇₉	—	4	16	no	—
142	C₂³×C₇₉	—	4	8	no	—
143	C₂³×C₇₉	—	4	8	no	—
144	C₂³×C₇₉	—	4	8	no	—
145	C₂³×C₇₉	—	4	32	no	—
146	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
147	C₂³×C₇₉	C₂²×D₄	1	2	yes	—
148	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
149	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
150	C₂³×C₇₉	2₋¹⁺⁴	1	4	yes	—
151	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
152	Q₈×C₇₉	—	4	16	no	—
153	D₄×C₇₉	—	4	16	no	—
154	D₄×C₇₉	—	4	32	no	—
155	C₂×C₄×C₇₉	—	2	8	no	—
156	C₂×C₄×C₇₉	—	2	8	no	—
157	C₂×C₄×C₇₉	—	2	4	no	—
158	C₂×C₄×C₇₉	—	2	4	no	—
159	C₂×C₄×C₇₉	—	2	4	no	—
160	C₂×C₄×C₇₉	—	2	4	no	—
161	C₂×C₄×C₇₉	—	2	4	no	—
162	C₂×C₄×C₇₉	—	2	4	no	—
163	C₂×C₄×C₇₉	—	2	8	no	—
164	C₂×C₄×C₇₉	—	2	8	no	—
165	C₂×C₄×C₇₉	—	2	8	no	—
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	8	no	—
168	C₂×C₄×C₇₉	—	2	8	no	—
169	C₂×C₄×C₇₉	—	4	16	no	—
170	C₂×C₄×C₇₉	—	4	8	no	—
171	C₂×C₄×C₇₉	—	4	8	no	—
172	C₂×C₄×C₇₉	—	4	8	no	—
173	C₂×C₄×C₇₉	—	4	16	no	—
174	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
176	C₂²×C₇₉	—	2	4	no	—
177	C₂²×C₇₉	—	2	4	no	—
178	C₂²×C₇₉	—	2	4	no	—
179	C₂²×C₇₉	—	4	16	no	—
180	C₂²×C₇₉	—	4	8	no	—
181	C₂²×C₇₉	—	4	4	no	—
182	C₂²×C₇₉	—	4	4	no	—
183	C₂²×C₇₉	—	4	4	no	—
184	C₂²×C₇₉	—	4	16	no	—
185	C₂²×C₇₉	—	8	16	no	—
186	C₂²×C₇₉	#534	1	4	yes	—
187	C₂²×C₇₉	#535	1	4	yes	—
188	C₂²×C₇₉	#536	1	4	yes	—
189	C₂²×C₇₉	#562	1	16	yes	—
190	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
191	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	2	yes	—
194	C₄×C₇₉	—	2	4	no	—
195	C₄×C₇₉	—	2	4	no	—
196	C₄×C₇₉	—	4	4	no	—
197	C₄×C₇₉	—	4	4	no	—
198	C₄×C₇₉	—	4	4	no	—
199	C₄×C₇₉	—	4	8	no	—
200	C₂×#2816	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂×C₇₉	—	4	4	no	—
202	C₂×C₇₉	—	8	4	no	—
203	C₂×C₇₉	#2816	1	8	yes	direct product factor
204	C₂×C₇₉	C₂×#534	1	1	yes	characteristic
205	C₂×C₇₉	C₂×#535	1	1	yes	characteristic
206	C₂×C₇₉	C₂×#536	1	1	yes	characteristic
207	C₂×C₇₉	C₂×#562	1	4	yes	—
208	C₂²×C₂²⋊Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
209	C₂²×#121	C₂×C₇₉	1	1	yes	characteristic
210	#2816	C₂×C₇₉	1	16	yes	direct product factor
211	C₂×#399	C₂×C₇₉	1	2	yes	complemented
212	C₂×#398	C₂×C₇₉	1	2	yes	complemented
213	C₂×#394	C₂×C₇₉	1	4	yes	complemented
214	C₂×#394	C₂×C₇₉	1	2	yes	complemented
215	C₂×#393	C₂×C₇₉	1	2	yes	complemented
216	C₂×#381	C₂×C₇₉	1	1	yes	characteristic, complemented
217	C₇₉	C₂×#2816	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
219	C₂³×D₄	C₂²×C₇₉	1	2	yes	—
220	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
221	C₂⁴×C₄	C₂²×C₇₉	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	—	2	8	no	—
223	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	8	yes	complemented
224	C₂×#121	—	2	8	no	—
225	C₂×#121	C₂²×C₇₉	1	8	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₇₉	1	4	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	4	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	4	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₇₉	1	2	yes	—
235	#399	C₂²×C₇₉	1	16	yes	complemented
236	#398	C₂²×C₇₉	1	16	yes	complemented
237	#394	C₂²×C₇₉	1	16	yes	complemented
238	#394	C₂²×C₇₉	1	32	yes	complemented
239	#393	C₂²×C₇₉	1	16	yes	complemented
240	#381	C₂²×C₇₉	1	8	yes	complemented
241	C₂×#95	C₂²×C₇₉	1	4	yes	—
242	C₂×#95	C₂²×C₇₉	1	2	yes	—
243	C₂×#95	C₂²×C₇₉	1	2	yes	—
244	C₂⁵	C₂³×C₇₉	1	2	yes	—
245	C₂⁵	C₂³×C₇₉	1	1	yes	characteristic
246	C₂²×Q₈	—	2	4	no	—
247	C₂²×Q₈	—	4	4	no	—
248	C₂²×Q₈	C₂³×C₇₉	1	4	yes	—
249	C₂²×D₄	—	2	8	no	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	4	4	no	—
252	C₂²×D₄	—	4	8	no	—
253	C₂²×D₄	C₂³×C₇₉	1	8	yes	—
254	C₂²×D₄	C₂³×C₇₉	1	4	yes	—
255	C₂³×C₄	—	4	4	no	—
256	C₂³×C₄	D₄×C₇₉	1	8	yes	—
257	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
258	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
259	C₂³×C₄	C₂³×C₇₉	1	4	yes	—
260	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₇₉	1	4	yes	—
264	C₂²⋊Q₈	—	2	32	no	—
265	#121	—	2	32	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	8	no	—
269	C₂×C₄⋊C₄	—	4	8	no	—
270	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇₉	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₇₉	1	16	yes	—
274	C₂×C₂²⋊C₄	—	2	8	no	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	—	4	4	no	—
277	C₂×C₂²⋊C₄	—	4	8	no	—
278	C₂×C₂²⋊C₄	—	4	8	no	—
279	C₂×C₂²⋊C₄	C₂³×C₇₉	1	8	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₇₉	1	8	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₇₉	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₇₉	1	16	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₇₉	1	16	yes	—
284	#95	C₂³×C₇₉	1	8	yes	—
285	#95	C₂³×C₇₉	1	8	yes	—
286	#95	C₂³×C₇₉	1	16	yes	—
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	C₂×D₄×C₇₉	1	4	yes	—
295	C₂⁴	C₂⁴×C₇₉	1	4	yes	—
296	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
297	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	—	4	16	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	4	8	no	—
304	C₂×D₄	—	4	16	no	—
305	C₂×D₄	—	4	16	no	—
306	C₂×D₄	—	4	32	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	4	16	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
322	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
323	C₂²×C₄	C₂×D₄×C₇₉	1	16	yes	—
324	C₂²×C₄	C₂⁴×C₇₉	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₇₉	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	16	no	—
333	C₄⋊C₄	—	4	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	2	16	no	—
336	C₂²⋊C₄	—	4	8	no	—
337	C₂²⋊C₄	—	4	16	no	—
338	C₂²⋊C₄	—	4	16	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	4	16	no	—
350	C₂³	—	4	8	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	32	no	—
354	C₂³	C₂²×D₄×C₇₉	1	4	yes	—
355	C₂³	C₂²×D₄×C₇₉	1	2	yes	—
356	C₂³	H(5,𝔽₂)×C₇₉	1	4	yes	—
357	C₂³	H(5,𝔽₂)×C₇₉	1	4	yes	—
358	C₂³	2₋¹⁺⁴×C₇₉	1	4	yes	—
359	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
360	Q₈	—	4	16	no	—
361	D₄	—	4	16	no	—
362	D₄	—	4	32	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	4	16	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	8	16	no	—
394	C₂²	#534×C₇₉	1	4	yes	—
395	C₂²	#535×C₇₉	1	4	yes	—
396	C₂²	#536×C₇₉	1	4	yes	—
397	C₂²	#562×C₇₉	1	16	yes	—
398	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
399	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	2	yes	—
400	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	2	yes	—
401	C₂²	C₂×2₋¹⁺⁴×C₇₉	1	2	yes	—
402	C₄	—	2	4	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	8	no	—
408	C₂	—	4	4	no	—
409	C₂	—	8	4	no	—
410	C₂	C₇₉×#2816	1	8	yes	direct product factor
411	C₂	C₂×#534×C₇₉	1	1	yes	characteristic
412	C₂	C₂×#535×C₇₉	1	1	yes	characteristic
413	C₂	C₂×#536×C₇₉	1	1	yes	characteristic
414	C₂	C₂×#562×C₇₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
prime radical	C₂²×#121×C₇₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₇₉	C₂	semidirect
3. C₇₉×#2816	C₂	direct (N × H)
4. C₂×#399×C₇₉	C₂	semidirect
5. C₂×#398×C₇₉	C₂	semidirect
6. C₂×#394×C₇₉	C₂	semidirect
7. C₂×#394×C₇₉	C₂	semidirect
8. C₂×#393×C₇₉	C₂	semidirect
9. C₂×#381×C₇₉	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₇₉	C₂²	semidirect
27. #399×C₇₉	C₂²	semidirect
28. #398×C₇₉	C₂²	semidirect
29. #394×C₇₉	C₂²	semidirect
30. #394×C₇₉	C₂²	semidirect
31. #393×C₇₉	C₂²	semidirect
32. #381×C₇₉	C₂²	semidirect
200. C₂×#2816	C₇₉	direct (N × H)
203. C₂×C₇₉	#2816	direct (N × H)
208. C₂²×C₂²⋊Q₈	C₂×C₇₉	semidirect
210. #2816	C₂×C₇₉	direct (N × H)
211. C₂×#399	C₂×C₇₉	semidirect
212. C₂×#398	C₂×C₇₉	semidirect
213. C₂×#394	C₂×C₇₉	semidirect
214. C₂×#394	C₂×C₇₉	semidirect
215. C₂×#393	C₂×C₇₉	semidirect
216. C₂×#381	C₂×C₇₉	semidirect
217. C₇₉	C₂×#2816	direct (N × H)
223. C₂×C₂²⋊Q₈	C₂²×C₇₉	semidirect
235. #399	C₂²×C₇₉	semidirect
236. #398	C₂²×C₇₉	semidirect
237. #394	C₂²×C₇₉	semidirect
238. #394	C₂²×C₇₉	semidirect
239. #393	C₂²×C₇₉	semidirect
240. #381	C₂²×C₇₉	semidirect
410. C₂	C₇₉×#2816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₇₉	2
C₂²×#121×C₇₉	2
C₇₉×#2816	2
C₂×#399×C₇₉	2
C₂×#398×C₇₉	2
C₂×#394×C₇₉	2
C₂×#393×C₇₉	2
C₂×#381×C₇₉	2
C₂×#2816	79

Subgroups — C2×C79×#2816 #34148337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#2816 #34148337