Subgroups — C₇₃×#22272 #32931676

Order 18688.

1074 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#496×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1880	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1879	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1879	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₃	—	2	1	no	—
18	C₂×C₄×D₄×C₇₃	—	2	1	no	—
19	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
21	#496×C₇₃	C₄	1	8	yes	complemented
22	C₂×#103×C₇₃	C₂²	1	2	yes	—
23	C₂×#102×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
28	#391×C₇₃	C₂²	1	1	yes	characteristic
29	#390×C₇₃	—	2	1	no	—
30	#390×C₇₃	—	2	1	no	—
31	#390×C₇₃	C₂²	1	1	yes	characteristic
32	#390×C₇₃	C₂²	1	2	yes	—
33	#388×C₇₃	—	2	1	no	—
34	#388×C₇₃	—	2	1	no	—
35	#384×C₇₃	C₂²	1	1	yes	characteristic
36	#382×C₇₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
39	C₄³×C₇₃	C₂²	1	1	yes	characteristic
40	#340×C₇₃	C₂²	1	2	yes	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	#336×C₇₃	C₂²	1	2	yes	—
44	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₇₃	—	2	1	no	—
50	C₂³×C₄×C₇₃	—	2	2	no	—
51	C₂×SD₁₆×C₇₃	—	4	2	no	—
52	C₂×SD₁₆×C₇₃	—	4	2	no	—
53	C₂×SD₁₆×C₇₃	C₂×C₄	1	8	yes	complemented
54	C₂×D₈×C₇₃	—	4	2	no	—
55	C₂×D₈×C₇₃	—	4	2	no	—
56	C₂×D₈×C₇₃	C₂×C₄	1	8	yes	complemented
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	#127×C₇₃	—	2	2	no	—
60	#127×C₇₃	C₂×C₄	1	4	yes	complemented
61	#124×C₇₃	—	2	2	no	—
62	#124×C₇₃	C₂×C₄	1	4	yes	complemented
63	C₄×Q₈×C₇₃	—	4	2	no	—
64	C₄×D₄×C₇₃	—	4	2	no	—
65	C₄×D₄×C₇₃	—	4	2	no	—
66	C₄×D₄×C₇₃	—	4	2	no	—
67	C₄×D₄×C₇₃	—	4	4	no	—
68	C₄×D₄×C₇₃	—	4	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	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₄²×C₇₃	—	2	1	no	—
84	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	#103×C₇₃	—	4	2	no	—
92	#102×C₇₃	—	4	2	no	—
93	#102×C₇₃	—	4	2	no	—
94	#102×C₇₃	—	4	2	no	—
95	#97×C₇₃	—	2	2	no	—
96	#97×C₇₃	C₂×C₄	1	4	yes	complemented
97	#95×C₇₃	—	2	1	no	—
98	#95×C₇₃	—	2	1	no	—
99	#95×C₇₃	—	2	1	no	—
100	#95×C₇₃	—	2	1	no	—
101	C₂⁴×C₇₃	—	2	1	no	—
102	C₂⁴×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	1	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	1	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	4	2	no	—
120	C₂×D₄×C₇₃	—	4	2	no	—
121	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	4	2	no	—
128	C₂²×C₄×C₇₃	—	4	4	no	—
129	C₂²×C₄×C₇₃	—	4	4	no	—
130	C₂²×C₄×C₇₃	—	4	2	no	—
131	C₂²×C₄×C₇₃	—	4	4	no	—
132	C₂²×C₄×C₇₃	—	4	2	no	—
133	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₇₃	—	4	8	no	—
141	D₈×C₇₃	—	4	8	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	2	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	4	2	no	—
153	C₄⋊C₄×C₇₃	—	4	2	no	—
154	C₄⋊C₄×C₇₃	—	4	2	no	—
155	C₂²⋊C₄×C₇₃	—	2	4	no	—
156	C₂²⋊C₄×C₇₃	—	2	4	no	—
157	C₂²⋊C₄×C₇₃	—	4	2	no	—
158	C₂²⋊C₄×C₇₃	—	4	4	no	—
159	C₂²⋊C₄×C₇₃	—	4	2	no	—
160	C₂²⋊C₄×C₇₃	—	4	4	no	—
161	C₂²⋊C₄×C₇₃	—	4	2	no	—
162	C₂²⋊C₄×C₇₃	—	4	4	no	—
163	C₄²×C₇₃	—	2	2	no	—
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	4	1	no	—
168	C₄²×C₇₃	—	4	1	no	—
169	C₄²×C₇₃	—	4	2	no	—
170	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
171	C₄²×C₇₃	#41	1	2	yes	—
172	C₂³×C₇₃	—	2	2	no	—
173	C₂³×C₇₃	—	2	4	no	—
174	C₂³×C₇₃	—	4	1	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	1	no	—
178	C₂³×C₇₃	—	4	2	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	1	no	—
181	C₂³×C₇₃	—	4	1	no	—
182	C₂³×C₇₃	—	4	1	no	—
183	C₂³×C₇₃	—	4	1	no	—
184	C₂³×C₇₃	—	4	2	no	—
185	C₂³×C₇₃	—	4	2	no	—
186	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₇₃	—	2	4	no	—
188	Q₈×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	2	4	no	—
190	D₄×C₇₃	—	2	4	no	—
191	D₄×C₇₃	—	2	4	no	—
192	D₄×C₇₃	—	4	8	no	—
193	D₄×C₇₃	—	4	8	no	—
194	D₄×C₇₃	—	4	2	no	—
195	D₄×C₇₃	—	4	2	no	—
196	D₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	1	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	4	1	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	1	no	—
222	C₂×C₄×C₇₃	—	4	1	no	—
223	C₂×C₄×C₇₃	—	8	4	no	—
224	C₂×C₄×C₇₃	—	8	8	no	—
225	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₇₃	—	2	4	no	—
234	C₈×C₇₃	—	4	2	no	—
235	C₂²×C₇₃	—	4	2	no	—
236	C₂²×C₇₃	—	4	4	no	—
237	C₂²×C₇₃	—	4	4	no	—
238	C₂²×C₇₃	—	4	4	no	—
239	C₂²×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	4	2	no	—
241	C₂²×C₇₃	—	8	1	no	—
242	C₂²×C₇₃	—	8	2	no	—
243	C₂²×C₇₃	—	8	1	no	—
244	C₂²×C₇₃	—	8	2	no	—
245	C₂²×C₇₃	—	8	2	no	—
246	C₂²×C₇₃	—	8	1	no	—
247	C₂²×C₇₃	—	8	2	no	—
248	C₂²×C₇₃	—	8	1	no	—
249	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₇₃	#535	1	1	yes	characteristic
251	C₂²×C₇₃	#535	1	1	yes	characteristic
252	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₂²×C₇₃	#575	1	1	yes	characteristic
255	C₂²×C₇₃	#575	1	1	yes	characteristic
256	C₄×C₇₃	—	2	2	no	—
257	C₄×C₇₃	—	2	2	no	—
258	C₄×C₇₃	—	2	2	no	—
259	C₄×C₇₃	—	2	2	no	—
260	C₄×C₇₃	—	4	2	no	—
261	C₄×C₇₃	—	4	1	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	8	1	no	—
264	C₄×C₇₃	—	8	1	no	—
265	C₄×C₇₃	—	8	2	no	—
266	C₄×C₇₃	#518	1	2	yes	—
267	C₄×C₇₃	#540	1	2	yes	—
268	#22272	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂×C₇₃	—	8	4	no	—
270	C₂×C₇₃	—	8	2	no	—
271	C₂×C₇₃	#2328	1	1	yes	characteristic
272	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂×C₇₃	#3213	1	1	yes	characteristic
275	C₂×C₇₃	#3214	1	1	yes	characteristic
276	C₂×C₇₃	#3217	1	1	yes	characteristic
277	C₂×C₇₃	#3219	1	1	yes	characteristic
278	C₂×#496	C₂×C₇₃	1	1	yes	characteristic
279	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
280	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
281	#1961	C₂×C₇₃	1	1	yes	characteristic, complemented
282	#1959	C₂×C₇₃	1	1	yes	characteristic, complemented
283	#1880	C₂×C₇₃	1	2	yes	complemented
284	#1879	C₂×C₇₃	1	2	yes	complemented
285	#1879	C₂×C₇₃	1	2	yes	complemented
286	#1877	C₂×C₇₃	1	2	yes	complemented
287	#1836	C₂×C₇₃	1	1	yes	characteristic, complemented
288	#1745	C₂×C₇₃	1	1	yes	characteristic, complemented
289	C₇₃	#22272	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
291	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
292	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
293	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
299	#496	C₄×C₇₃	1	8	yes	complemented
300	C₂×#103	C₂²×C₇₃	1	2	yes	—
301	C₂×#102	C₂²×C₇₃	1	2	yes	—
302	C₂×#102	C₂²×C₇₃	1	2	yes	—
303	C₂×#102	C₂²×C₇₃	1	2	yes	—
304	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
306	#391	C₂²×C₇₃	1	1	yes	characteristic
307	#390	—	2	1	no	—
308	#390	—	2	1	no	—
309	#390	C₂²×C₇₃	1	2	yes	—
310	#390	C₂²×C₇₃	1	1	yes	characteristic
311	#388	—	2	1	no	—
312	#388	—	2	1	no	—
313	#384	C₂²×C₇₃	1	1	yes	characteristic
314	#382	C₂²×C₇₃	1	1	yes	characteristic
315	C₄×C₂²⋊C₄	—	2	1	no	—
316	C₄×C₂²⋊C₄	—	2	1	no	—
317	C₄³	C₂²×C₇₃	1	1	yes	characteristic
318	#340	C₂²×C₇₃	1	2	yes	—
319	#340	C₂²×C₇₃	1	2	yes	—
320	#336	C₂²×C₇₃	1	2	yes	—
321	#336	C₂²×C₇₃	1	2	yes	—
322	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	2	1	no	—
329	C₂×SD₁₆	—	4	2	no	—
330	C₂×SD₁₆	—	4	2	no	—
331	C₂×SD₁₆	C₂×C₄×C₇₃	1	8	yes	complemented
332	C₂×D₈	—	4	2	no	—
333	C₂×D₈	—	4	2	no	—
334	C₂×D₈	C₂×C₄×C₇₃	1	8	yes	complemented
335	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
337	#127	—	2	2	no	—
338	#127	C₂×C₄×C₇₃	1	4	yes	complemented
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₇₃	1	4	yes	complemented
341	C₄×Q₈	—	4	2	no	—
342	C₄×D₄	—	4	2	no	—
343	C₄×D₄	—	4	2	no	—
344	C₄×D₄	—	4	2	no	—
345	C₄×D₄	—	4	4	no	—
346	C₄×D₄	—	4	4	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
363	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
369	#103	—	4	2	no	—
370	#102	—	4	2	no	—
371	#102	—	4	2	no	—
372	#102	—	4	2	no	—
373	#97	—	2	2	no	—
374	#97	C₂×C₄×C₇₃	1	4	yes	complemented
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	2	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	4	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂²×C₄×C₇₃	1	2	yes	—
400	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
418	SD₁₆	—	4	8	no	—
419	D₈	—	4	8	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	C₂²×C₄×C₇₃	1	4	yes	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	4	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	4	1	no	—
446	C₄²	—	4	1	no	—
447	C₄²	—	4	2	no	—
448	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
449	C₄²	#41×C₇₃	1	2	yes	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	—	8	8	no	—
503	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
504	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
505	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
506	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
507	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
509	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
510	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
511	C₈	—	2	4	no	—
512	C₈	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	1	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	1	no	—
527	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
528	C₂²	#535×C₇₃	1	1	yes	characteristic
529	C₂²	#535×C₇₃	1	1	yes	characteristic
530	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
531	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
532	C₂²	#575×C₇₃	1	1	yes	characteristic
533	C₂²	#575×C₇₃	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	2	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	2	no	—
544	C₄	#518×C₇₃	1	2	yes	—
545	C₄	#540×C₇₃	1	2	yes	—
546	C₂	—	8	4	no	—
547	C₂	—	8	2	no	—
548	C₂	C₇₃×#2328	1	1	yes	characteristic
549	C₂	C₄×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
550	C₂	C₄×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
551	C₂	C₇₃×#3213	1	1	yes	characteristic
552	C₂	C₇₃×#3214	1	1	yes	characteristic
553	C₂	C₇₃×#3217	1	1	yes	characteristic
554	C₂	C₇₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#496×C₇₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#127×C₇₃	C₂	semidirect
3. C₄×#124×C₇₃	C₂	semidirect
4. C₇₃×#1961	C₂	semidirect
5. C₇₃×#1959	C₂	semidirect
6. C₇₃×#1880	C₂	semidirect
7. C₇₃×#1879	C₂	semidirect
8. C₇₃×#1879	C₂	semidirect
9. C₇₃×#1877	C₂	semidirect
10. C₇₃×#1836	C₂	semidirect
11. C₇₃×#1745	C₂	semidirect
21. #496×C₇₃	C₄	semidirect
53. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
56. C₂×D₈×C₇₃	C₂×C₄	semidirect
60. #127×C₇₃	C₂×C₄	semidirect
62. #124×C₇₃	C₂×C₄	semidirect
96. #97×C₇₃	C₂×C₄	semidirect
268. #22272	C₇₃	direct (N × H)
279. C₄×#127	C₂×C₇₃	semidirect
280. C₄×#124	C₂×C₇₃	semidirect
281. #1961	C₂×C₇₃	semidirect
282. #1959	C₂×C₇₃	semidirect
283. #1880	C₂×C₇₃	semidirect
284. #1879	C₂×C₇₃	semidirect
285. #1879	C₂×C₇₃	semidirect
286. #1877	C₂×C₇₃	semidirect
287. #1836	C₂×C₇₃	semidirect
288. #1745	C₂×C₇₃	semidirect
289. C₇₃	#22272	direct (N × H)
299. #496	C₄×C₇₃	semidirect
331. C₂×SD₁₆	C₂×C₄×C₇₃	semidirect
334. C₂×D₈	C₂×C₄×C₇₃	semidirect
338. #127	C₂×C₄×C₇₃	semidirect
340. #124	C₂×C₄×C₇₃	semidirect
374. #97	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#496×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
C₇₃×#1961	2
C₇₃×#1959	2
C₇₃×#1880	2
C₇₃×#1879	2
C₇₃×#1877	2
C₇₃×#1836	2
C₇₃×#1745	2
#22272	73

Subgroups — C73×#22272 #32931676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#22272 #32931676