Subgroups — C₂×C₇₃×#1495 #32926880

Order 18688.

1066 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#423×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1495	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×D₄⋊C₈×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂²×M₁₆×C₇₃	—	2	1	no	—
8	#529×C₇₃	—	2	2	no	—
9	#529×C₇₃	—	2	2	no	—
10	#529×C₇₃	C₄	1	4	yes	—
11	#529×C₇₃	C₂²	1	4	yes	—
12	C₂×#126×C₇₃	—	2	1	no	—
13	C₂×#125×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#124×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#123×C₇₃	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
17	C₂×#121×C₇₃	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₇₃	—	2	1	no	—
20	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₃	—	2	1	no	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	#431×C₇₃	—	2	2	no	—
24	#431×C₇₃	C₂²	1	4	yes	complemented
25	#423×C₇₃	—	2	2	no	—
26	#423×C₇₃	C₂²	1	4	yes	complemented
27	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
28	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
29	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₇₃	—	2	1	no	—
31	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
32	Q₈⋊C₈×C₇₃	C₂²	1	8	yes	complemented
33	D₄⋊C₈×C₇₃	C₂²	1	8	yes	complemented
34	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₇₃	—	2	1	no	—
36	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₃	—	2	1	no	—
38	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
41	C₂×M₁₆×C₇₃	—	2	4	no	—
42	C₂×M₁₆×C₇₃	—	4	4	no	—
43	C₂²×C₈×C₇₃	—	2	2	no	—
44	C₂²×C₈×C₇₃	—	2	2	no	—
45	#126×C₇₃	—	2	4	no	—
46	#126×C₇₃	—	2	4	no	—
47	#125×C₇₃	—	2	2	no	—
48	#125×C₇₃	C₂×C₄	1	4	yes	—
49	#124×C₇₃	—	2	2	no	—
50	#124×C₇₃	C₂×C₄	1	4	yes	—
51	#123×C₇₃	—	2	4	no	—
52	#123×C₇₃	—	2	4	no	—
53	C₂²⋊Q₈×C₇₃	—	2	2	no	—
54	C₂²⋊Q₈×C₇₃	C₂×C₄	1	4	yes	—
55	#121×C₇₃	—	2	2	no	—
56	#121×C₇₃	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₇₃	—	2	1	no	—
58	C₄×Q₈×C₇₃	—	2	1	no	—
59	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
61	C₄×D₄×C₇₃	—	2	4	no	—
62	C₄×D₄×C₇₃	—	2	4	no	—
63	C₄×D₄×C₇₃	—	2	1	no	—
64	C₄×D₄×C₇₃	—	2	1	no	—
65	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₇₃	C₂³	1	2	yes	—
67	#117×C₇₃	—	2	4	no	—
68	#117×C₇₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	D₄	1	2	yes	—
85	C₂×C₄²×C₇₃	D₄	1	2	yes	—
86	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	—	2	4	no	—
90	C₄⋊C₈×C₇₃	—	2	4	no	—
91	C₄⋊C₈×C₇₃	—	2	2	no	—
92	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
93	C₂²⋊C₈×C₇₃	—	2	4	no	—
94	C₄×C₈×C₇₃	—	2	2	no	—
95	C₄×C₈×C₇₃	C₂³	1	4	yes	—
96	C₂⁴×C₇₃	—	2	1	no	—
97	C₂⁴×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×Q₈×C₇₃	—	2	1	no	—
99	C₂×Q₈×C₇₃	—	2	4	no	—
100	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₇₃	—	2	4	no	—
102	C₂×D₄×C₇₃	—	2	1	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	4	4	no	—
105	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₇₃	—	2	4	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	—	2	1	no	—
110	C₂²×C₄×C₇₃	—	2	1	no	—
111	C₂²×C₄×C₇₃	—	2	1	no	—
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	—	2	2	no	—
114	C₂²×C₄×C₇₃	—	4	2	no	—
115	C₂²×C₄×C₇₃	—	4	2	no	—
116	C₂²×C₄×C₇₃	—	4	2	no	—
117	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	M₁₆×C₇₃	—	4	8	no	—
130	C₂×C₈×C₇₃	—	2	4	no	—
131	C₂×C₈×C₇₃	—	2	4	no	—
132	C₂×C₈×C₇₃	—	4	4	no	—
133	C₂×C₈×C₇₃	—	4	4	no	—
134	C₄⋊C₄×C₇₃	—	2	4	no	—
135	C₄⋊C₄×C₇₃	—	2	4	no	—
136	C₄⋊C₄×C₇₃	—	2	4	no	—
137	C₄⋊C₄×C₇₃	—	2	2	no	—
138	C₄⋊C₄×C₇₃	—	2	1	no	—
139	C₄⋊C₄×C₇₃	—	2	1	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
142	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
143	C₂²⋊C₄×C₇₃	—	2	4	no	—
144	C₂²⋊C₄×C₇₃	—	2	4	no	—
145	C₂²⋊C₄×C₇₃	—	2	4	no	—
146	C₂²⋊C₄×C₇₃	—	2	4	no	—
147	C₂²⋊C₄×C₇₃	—	2	2	no	—
148	C₂²⋊C₄×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
153	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
154	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₃	C₂×D₄	1	2	yes	—
158	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₇₃	C₂×D₄	1	2	yes	—
160	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
161	C₂³×C₇₃	—	2	2	no	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	4	2	no	—
166	C₂³×C₇₃	—	4	2	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	Q₈×C₇₃	—	2	4	no	—
171	Q₈×C₇₃	—	4	2	no	—
172	D₄×C₇₃	—	2	4	no	—
173	D₄×C₇₃	—	4	8	no	—
174	D₄×C₇₃	—	4	2	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	2	4	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	4	no	—
183	C₂×C₄×C₇₃	—	2	4	no	—
184	C₂×C₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	—	4	2	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	4	no	—
195	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₇₃	#131	1	4	yes	—
202	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₇₃	#137	1	2	yes	—
204	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₇₃	—	4	4	no	—
208	C₈×C₇₃	—	4	4	no	—
209	C₂²×C₇₃	—	2	2	no	—
210	C₂²×C₇₃	—	2	2	no	—
211	C₂²×C₇₃	—	2	2	no	—
212	C₂²×C₇₃	—	4	4	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	4	2	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	8	4	no	—
217	C₂²×C₇₃	#408	1	2	yes	—
218	C₂²×C₇₃	#417	1	2	yes	—
219	C₂²×C₇₃	#421	1	2	yes	—
220	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₇₃	—	2	2	no	—
222	C₄×C₇₃	—	2	2	no	—
223	C₄×C₇₃	—	2	1	no	—
224	C₄×C₇₃	—	2	1	no	—
225	C₄×C₇₃	—	2	2	no	—
226	C₄×C₇₃	—	4	2	no	—
227	C₄×C₇₃	—	4	2	no	—
228	C₄×C₇₃	—	4	2	no	—
229	C₄×C₇₃	#408	1	2	yes	—
230	C₄×C₇₃	#417	1	2	yes	—
231	C₄×C₇₃	C₂×#131	1	2	yes	—
232	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
234	C₂×#1495	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₇₃	—	4	2	no	—
236	C₂×C₇₃	—	8	2	no	—
237	C₂×C₇₃	#1495	1	4	yes	direct product factor
238	C₂×C₇₃	C₂×#408	1	1	yes	characteristic
239	C₂×C₇₃	C₂×#417	1	1	yes	characteristic
240	C₂×C₇₃	C₂×#421	1	1	yes	characteristic
241	C₂×#529	C₂×C₇₃	1	1	yes	characteristic
242	C₂×#431	C₂×C₇₃	1	1	yes	characteristic, complemented
243	C₂×#423	C₂×C₇₃	1	1	yes	characteristic, complemented
244	#1495	C₂×C₇₃	1	8	yes	direct product factor
245	C₂×Q₈⋊C₈	C₂×C₇₃	1	2	yes	complemented
246	C₂×D₄⋊C₈	C₂×C₇₃	1	2	yes	complemented
247	C₇₃	C₂×#1495	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×M₁₆	—	2	1	no	—
249	#529	—	2	2	no	—
250	#529	—	2	2	no	—
251	#529	C₄×C₇₃	1	4	yes	—
252	#529	C₂²×C₇₃	1	4	yes	—
253	C₂×#126	—	2	1	no	—
254	C₂×#125	C₄×C₇₃	1	1	yes	characteristic
255	C₂×#124	C₄×C₇₃	1	1	yes	characteristic
256	C₂×#123	—	2	1	no	—
257	C₂×C₂²⋊Q₈	C₄×C₇₃	1	1	yes	characteristic
258	C₂×#121	C₄×C₇₃	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×C₄×D₄	—	2	1	no	—
261	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
262	C₂×#117	—	2	1	no	—
263	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
264	#431	—	2	2	no	—
265	#431	C₂²×C₇₃	1	4	yes	complemented
266	#423	—	2	2	no	—
267	#423	C₂²×C₇₃	1	4	yes	complemented
268	C₂×C₄⋊C₈	—	2	1	no	—
269	C₂×C₄⋊C₈	—	2	1	no	—
270	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
271	C₂×C₂²⋊C₈	—	2	1	no	—
272	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
273	Q₈⋊C₈	C₂²×C₇₃	1	8	yes	complemented
274	D₄⋊C₈	C₂²×C₇₃	1	8	yes	complemented
275	C₂²×Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
280	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
281	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	—	4	4	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	#126	—	2	4	no	—
287	#126	—	2	4	no	—
288	#125	—	2	2	no	—
289	#125	C₂×C₄×C₇₃	1	4	yes	—
290	#124	—	2	2	no	—
291	#124	C₂×C₄×C₇₃	1	4	yes	—
292	#123	—	2	4	no	—
293	#123	—	2	4	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	C₂×C₄×C₇₃	1	4	yes	—
296	#121	—	2	2	no	—
297	#121	C₂×C₄×C₇₃	1	4	yes	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	C₂×C₄×C₇₃	1	2	yes	—
301	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	C₂×C₄×C₇₃	1	2	yes	—
307	C₄×D₄	C₂³×C₇₃	1	2	yes	—
308	#117	—	2	4	no	—
309	#117	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
323	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
324	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
325	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₇₃	1	2	yes	—
327	C₂×C₄²	D₄×C₇₃	1	2	yes	—
328	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
330	C₄⋊C₈	—	2	4	no	—
331	C₄⋊C₈	—	2	4	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
334	C₂²⋊C₈	—	2	4	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	C₂³×C₇₃	1	4	yes	—
337	C₂⁴	—	2	1	no	—
338	C₂⁴	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	C₂²×C₄×C₇₃	1	2	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
359	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
361	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
362	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
363	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
365	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
370	M₁₆	—	4	8	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	4	4	no	—
374	C₂×C₈	—	4	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
383	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
393	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
394	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
395	C₄²	C₂²×C₄×C₇₃	1	1	yes	characteristic
396	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
397	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
398	C₄²	C₂×D₄×C₇₃	1	2	yes	—
399	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₄²	C₂×D₄×C₇₃	1	2	yes	—
401	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
410	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
438	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
440	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
441	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
442	C₂×C₄	#131×C₇₃	1	4	yes	—
443	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
444	C₂×C₄	#137×C₇₃	1	2	yes	—
445	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
448	C₈	—	4	4	no	—
449	C₈	—	4	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	4	no	—
458	C₂²	#408×C₇₃	1	2	yes	—
459	C₂²	#417×C₇₃	1	2	yes	—
460	C₂²	#421×C₇₃	1	2	yes	—
461	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	#408×C₇₃	1	2	yes	—
471	C₄	#417×C₇₃	1	2	yes	—
472	C₄	C₂×#131×C₇₃	1	2	yes	—
473	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
474	C₄	C₂×#137×C₇₃	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	—	8	2	no	—
477	C₂	C₇₃×#1495	1	4	yes	direct product factor
478	C₂	C₂×#408×C₇₃	1	1	yes	characteristic
479	C₂	C₂×#417×C₇₃	1	1	yes	characteristic
480	C₂	C₂×#421×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₄²	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₇₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₇₃	C₂	semidirect
3. C₂×#423×C₇₃	C₂	semidirect
4. C₇₃×#1495	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₇₃	C₂	semidirect
6. C₂×D₄⋊C₈×C₇₃	C₂	semidirect
24. #431×C₇₃	C₂²	semidirect
26. #423×C₇₃	C₂²	semidirect
32. Q₈⋊C₈×C₇₃	C₂²	semidirect
33. D₄⋊C₈×C₇₃	C₂²	semidirect
234. C₂×#1495	C₇₃	direct (N × H)
237. C₂×C₇₃	#1495	direct (N × H)
242. C₂×#431	C₂×C₇₃	semidirect
243. C₂×#423	C₂×C₇₃	semidirect
244. #1495	C₂×C₇₃	direct (N × H)
245. C₂×Q₈⋊C₈	C₂×C₇₃	semidirect
246. C₂×D₄⋊C₈	C₂×C₇₃	semidirect
247. C₇₃	C₂×#1495	direct (N × H)
265. #431	C₂²×C₇₃	semidirect
267. #423	C₂²×C₇₃	semidirect
273. Q₈⋊C₈	C₂²×C₇₃	semidirect
274. D₄⋊C₈	C₂²×C₇₃	semidirect
477. C₂	C₇₃×#1495	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×#529×C₇₃	2
C₂×#431×C₇₃	2
C₂×#423×C₇₃	2
C₇₃×#1495	2
C₂×Q₈⋊C₈×C₇₃	2
C₂×D₄⋊C₈×C₇₃	2
C₂×#1495	73

Subgroups — C2×C73×#1495 #32926880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#1495 #32926880