Subgroups — C₇₃×#25752 #32935156

Order 18688.

1590 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#454×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₂×#453×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2657	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2003	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2002	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
15	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
16	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	complemented
17	#548×C₇₃	—	2	2	no	—
18	#546×C₇₃	—	2	2	no	—
19	#546×C₇₃	—	2	4	no	—
20	#536×C₇₃	—	2	1	no	—
21	#536×C₇₃	C₂²	1	1	yes	characteristic
22	#535×C₇₃	—	2	1	no	—
23	#535×C₇₃	C₂²	1	1	yes	characteristic
24	#532×C₇₃	—	2	1	no	—
25	#532×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#127×C₇₃	C₂²	1	2	yes	—
27	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₇₃	—	2	1	no	—
29	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
31	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
32	#496×C₇₃	—	2	1	no	—
33	#496×C₇₃	—	2	1	no	—
34	#493×C₇₃	—	2	1	no	—
35	#492×C₇₃	—	2	1	no	—
36	#460×C₇₃	—	2	2	no	—
37	#459×C₇₃	—	2	2	no	—
38	#454×C₇₃	—	2	8	no	—
39	#453×C₇₃	—	2	8	no	—
40	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#104×C₇₃	C₂²	1	2	yes	—
42	C₂×#104×C₇₃	C₂²	1	2	yes	—
43	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
44	#418×C₇₃	C₂²	1	2	yes	complemented
45	C₂×#101×C₇₃	C₂²	1	2	yes	complemented
46	C₂×#100×C₇₃	C₂²	1	2	yes	—
47	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	#392×C₇₃	—	2	4	no	—
49	#376×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	#339×C₇₃	C₂²	1	2	yes	complemented
51	2₋¹⁺⁴×C₇₃	—	2	4	no	—
52	2₋¹⁺⁴×C₇₃	—	4	2	no	—
53	H(5,𝔽₂)×C₇₃	—	2	4	no	—
54	H(5,𝔽₂)×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	—	2	1	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂×#41×C₇₃	—	2	1	no	—
59	C₂×#41×C₇₃	—	2	2	no	—
60	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
61	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₇₃	—	2	1	no	—
64	C₂²×Q₈×C₇₃	—	2	1	no	—
65	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₇₃	—	2	2	no	—
67	C₂²×D₄×C₇₃	—	2	1	no	—
68	C₂²×D₄×C₇₃	—	2	1	no	—
69	C₂²×D₄×C₇₃	—	2	4	no	—
70	C₂²×D₄×C₇₃	—	2	2	no	—
71	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
73	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
74	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
75	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
76	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
77	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
78	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
79	C₂×SD₁₆×C₇₃	—	2	2	no	—
80	C₂×SD₁₆×C₇₃	—	2	2	no	—
81	C₂×SD₁₆×C₇₃	—	2	2	no	—
82	C₂×D₈×C₇₃	—	2	2	no	—
83	C₂×D₈×C₇₃	—	2	2	no	—
84	C₂×D₈×C₇₃	—	2	2	no	—
85	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₇₃	—	2	1	no	—
88	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic, complemented
89	#127×C₇₃	—	2	1	no	—
90	#127×C₇₃	—	2	4	no	—
91	#127×C₇₃	—	2	2	no	—
92	#127×C₇₃	—	2	1	no	—
93	#127×C₇₃	—	2	1	no	—
94	#127×C₇₃	—	4	2	no	—
95	#127×C₇₃	D₄	1	1	yes	characteristic, complemented
96	#124×C₇₃	—	2	4	no	—
97	#124×C₇₃	—	2	1	no	—
98	#124×C₇₃	—	2	1	no	—
99	#124×C₇₃	—	2	1	no	—
100	#124×C₇₃	—	2	1	no	—
101	#124×C₇₃	—	2	2	no	—
102	#124×C₇₃	—	2	4	no	—
103	#124×C₇₃	—	4	2	no	—
104	#124×C₇₃	D₄	1	1	yes	characteristic, complemented
105	#124×C₇₃	D₄	1	1	yes	characteristic, complemented
106	#123×C₇₃	—	2	4	no	—
107	#123×C₇₃	—	2	2	no	—
108	C₂²⋊Q₈×C₇₃	—	2	4	no	—
109	C₂²⋊Q₈×C₇₃	—	2	2	no	—
110	#121×C₇₃	—	2	4	no	—
111	#121×C₇₃	—	2	4	no	—
112	#121×C₇₃	—	2	2	no	—
113	#121×C₇₃	—	2	2	no	—
114	#120×C₇₃	—	2	4	no	—
115	#120×C₇₃	—	2	2	no	—
116	C₄×Q₈×C₇₃	D₄	1	2	yes	complemented
117	C₄×D₄×C₇₃	—	2	4	no	—
118	C₄×D₄×C₇₃	—	2	2	no	—
119	C₄×D₄×C₇₃	—	2	2	no	—
120	C₄×D₄×C₇₃	D₄	1	2	yes	complemented
121	#117×C₇₃	—	2	1	no	—
122	#117×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₇₃	D₄	1	4	yes	—
126	C₂×C₄²×C₇₃	—	2	1	no	—
127	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₇₃	—	2	2	no	—
130	#104×C₇₃	—	2	4	no	—
131	#104×C₇₃	—	2	4	no	—
132	#104×C₇₃	D₄	1	8	yes	complemented
133	#102×C₇₃	—	2	4	no	—
134	#101×C₇₃	—	2	4	no	—
135	#100×C₇₃	—	2	4	no	—
136	#97×C₇₃	—	2	1	no	—
137	C₄×C₈×C₇₃	—	2	1	no	—
138	#95×C₇₃	—	2	2	no	—
139	C₂⁴×C₇₃	—	2	2	no	—
140	C₂⁴×C₇₃	—	2	2	no	—
141	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
142	#41×C₇₃	—	2	2	no	—
143	#41×C₇₃	—	2	2	no	—
144	#41×C₇₃	—	2	2	no	—
145	#41×C₇₃	—	2	2	no	—
146	#41×C₇₃	—	2	2	no	—
147	#41×C₇₃	—	4	4	no	—
148	#41×C₇₃	—	4	8	no	—
149	#41×C₇₃	—	4	4	no	—
150	#41×C₇₃	—	4	2	no	—
151	#41×C₇₃	—	4	2	no	—
152	#41×C₇₃	—	4	2	no	—
153	#41×C₇₃	—	4	2	no	—
154	#41×C₇₃	C₂×D₄	1	4	yes	—
155	C₂×Q₈×C₇₃	—	2	2	no	—
156	C₂×Q₈×C₇₃	—	2	2	no	—
157	C₂×Q₈×C₇₃	—	2	1	no	—
158	C₂×Q₈×C₇₃	—	2	1	no	—
159	C₂×Q₈×C₇₃	—	2	2	no	—
160	C₂×Q₈×C₇₃	—	4	4	no	—
161	C₂×Q₈×C₇₃	—	4	2	no	—
162	C₂×Q₈×C₇₃	—	4	2	no	—
163	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
164	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
165	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
166	C₂×D₄×C₇₃	—	2	1	no	—
167	C₂×D₄×C₇₃	—	2	2	no	—
168	C₂×D₄×C₇₃	—	2	2	no	—
169	C₂×D₄×C₇₃	—	2	2	no	—
170	C₂×D₄×C₇₃	—	2	1	no	—
171	C₂×D₄×C₇₃	—	2	1	no	—
172	C₂×D₄×C₇₃	—	2	4	no	—
173	C₂×D₄×C₇₃	—	2	2	no	—
174	C₂×D₄×C₇₃	—	2	2	no	—
175	C₂×D₄×C₇₃	—	2	1	no	—
176	C₂×D₄×C₇₃	—	2	1	no	—
177	C₂×D₄×C₇₃	—	2	2	no	—
178	C₂×D₄×C₇₃	—	2	2	no	—
179	C₂×D₄×C₇₃	—	2	2	no	—
180	C₂×D₄×C₇₃	—	2	2	no	—
181	C₂×D₄×C₇₃	—	2	2	no	—
182	C₂×D₄×C₇₃	—	2	2	no	—
183	C₂×D₄×C₇₃	—	2	2	no	—
184	C₂×D₄×C₇₃	—	4	4	no	—
185	C₂×D₄×C₇₃	—	4	8	no	—
186	C₂×D₄×C₇₃	—	4	8	no	—
187	C₂×D₄×C₇₃	—	4	2	no	—
188	C₂×D₄×C₇₃	—	4	2	no	—
189	C₂×D₄×C₇₃	—	4	2	no	—
190	C₂×D₄×C₇₃	—	4	2	no	—
191	C₂×D₄×C₇₃	—	8	4	no	—
192	C₂×D₄×C₇₃	—	8	8	no	—
193	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₃	—	2	1	no	—
197	C₂²×C₄×C₇₃	—	2	2	no	—
198	C₂²×C₄×C₇₃	—	2	2	no	—
199	C₂²×C₄×C₇₃	—	2	2	no	—
200	C₂²×C₄×C₇₃	—	2	2	no	—
201	C₂²×C₄×C₇₃	—	2	1	no	—
202	C₂²×C₄×C₇₃	—	2	1	no	—
203	C₂²×C₄×C₇₃	—	2	2	no	—
204	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
207	SD₁₆×C₇₃	—	4	4	no	—
208	SD₁₆×C₇₃	—	4	4	no	—
209	SD₁₆×C₇₃	—	4	4	no	—
210	D₈×C₇₃	—	4	4	no	—
211	D₈×C₇₃	—	4	4	no	—
212	D₈×C₇₃	—	4	4	no	—
213	M₁₆×C₇₃	—	2	2	no	—
214	M₁₆×C₇₃	—	2	2	no	—
215	M₁₆×C₇₃	—	2	2	no	—
216	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
217	C₂×C₈×C₇₃	—	2	2	no	—
218	C₂×C₈×C₇₃	—	2	2	no	—
219	C₄⋊C₄×C₇₃	—	2	4	no	—
220	C₄⋊C₄×C₇₃	—	2	2	no	—
221	C₄⋊C₄×C₇₃	—	2	2	no	—
222	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
223	C₂²⋊C₄×C₇₃	—	2	4	no	—
224	C₂²⋊C₄×C₇₃	—	2	4	no	—
225	C₂²⋊C₄×C₇₃	—	2	1	no	—
226	C₂²⋊C₄×C₇₃	—	2	2	no	—
227	C₂²⋊C₄×C₇₃	—	2	4	no	—
228	C₂²⋊C₄×C₇₃	—	2	4	no	—
229	C₂²⋊C₄×C₇₃	—	2	2	no	—
230	C₂²⋊C₄×C₇₃	—	2	2	no	—
231	C₂²⋊C₄×C₇₃	—	4	8	no	—
232	C₄²×C₇₃	—	2	2	no	—
233	C₄²×C₇₃	—	2	1	no	—
234	C₄²×C₇₃	—	2	2	no	—
235	C₄²×C₇₃	C₂×D₄	1	4	yes	—
236	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₇₃	C₂×D₄	1	2	yes	—
239	C₂³×C₇₃	—	2	1	no	—
240	C₂³×C₇₃	—	2	2	no	—
241	C₂³×C₇₃	—	2	1	no	—
242	C₂³×C₇₃	—	2	1	no	—
243	C₂³×C₇₃	—	2	4	no	—
244	C₂³×C₇₃	—	4	4	no	—
245	C₂³×C₇₃	—	4	4	no	—
246	C₂³×C₇₃	—	4	8	no	—
247	C₂³×C₇₃	—	4	2	no	—
248	C₂³×C₇₃	—	4	2	no	—
249	C₂³×C₇₃	—	4	2	no	—
250	C₂³×C₇₃	—	8	4	no	—
251	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₇₃	—	2	1	no	—
253	Q₈×C₇₃	—	2	2	no	—
254	Q₈×C₇₃	—	2	2	no	—
255	Q₈×C₇₃	—	4	4	no	—
256	Q₈×C₇₃	—	4	1	no	—
257	Q₈×C₇₃	—	4	1	no	—
258	Q₈×C₇₃	—	4	2	no	—
259	Q₈×C₇₃	#127	1	2	yes	—
260	D₄×C₇₃	—	2	4	no	—
261	D₄×C₇₃	—	2	1	no	—
262	D₄×C₇₃	—	2	2	no	—
263	D₄×C₇₃	—	2	2	no	—
264	D₄×C₇₃	—	4	4	no	—
265	D₄×C₇₃	—	4	4	no	—
266	D₄×C₇₃	—	4	4	no	—
267	D₄×C₇₃	—	4	2	no	—
268	D₄×C₇₃	—	4	2	no	—
269	D₄×C₇₃	—	4	1	no	—
270	D₄×C₇₃	—	4	2	no	—
271	D₄×C₇₃	—	4	1	no	—
272	D₄×C₇₃	—	4	2	no	—
273	D₄×C₇₃	—	4	2	no	—
274	D₄×C₇₃	—	4	2	no	—
275	D₄×C₇₃	—	4	2	no	—
276	D₄×C₇₃	—	8	2	no	—
277	D₄×C₇₃	—	8	4	no	—
278	D₄×C₇₃	—	8	4	no	—
279	D₄×C₇₃	—	8	4	no	—
280	D₄×C₇₃	—	8	16	no	—
281	D₄×C₇₃	#127	1	2	yes	—
282	C₂×C₄×C₇₃	—	2	1	no	—
283	C₂×C₄×C₇₃	—	2	4	no	—
284	C₂×C₄×C₇₃	—	2	2	no	—
285	C₂×C₄×C₇₃	—	2	1	no	—
286	C₂×C₄×C₇₃	—	2	2	no	—
287	C₂×C₄×C₇₃	—	2	1	no	—
288	C₂×C₄×C₇₃	—	2	4	no	—
289	C₂×C₄×C₇₃	—	2	4	no	—
290	C₂×C₄×C₇₃	—	4	2	no	—
291	C₂×C₄×C₇₃	—	4	4	no	—
292	C₂×C₄×C₇₃	—	4	4	no	—
293	C₂×C₄×C₇₃	—	4	4	no	—
294	C₂×C₄×C₇₃	—	4	4	no	—
295	C₂×C₄×C₇₃	—	4	1	no	—
296	C₂×C₄×C₇₃	—	4	1	no	—
297	C₂×C₄×C₇₃	—	4	1	no	—
298	C₂×C₄×C₇₃	—	4	1	no	—
299	C₂×C₄×C₇₃	—	8	2	no	—
300	C₂×C₄×C₇₃	#120	1	2	yes	—
301	C₂×C₄×C₇₃	#120	1	2	yes	—
302	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
306	C₈×C₇₃	—	2	4	no	—
307	C₈×C₇₃	—	4	2	no	—
308	C₂²×C₇₃	—	2	2	no	—
309	C₂²×C₇₃	—	2	2	no	—
310	C₂²×C₇₃	—	4	2	no	—
311	C₂²×C₇₃	—	4	1	no	—
312	C₂²×C₇₃	—	4	1	no	—
313	C₂²×C₇₃	—	4	2	no	—
314	C₂²×C₇₃	—	4	2	no	—
315	C₂²×C₇₃	—	4	4	no	—
316	C₂²×C₇₃	—	4	2	no	—
317	C₂²×C₇₃	—	8	4	no	—
318	C₂²×C₇₃	—	8	4	no	—
319	C₂²×C₇₃	—	8	4	no	—
320	C₂²×C₇₃	—	8	2	no	—
321	C₂²×C₇₃	—	8	4	no	—
322	C₂²×C₇₃	—	16	4	no	—
323	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
324	C₂²×C₇₃	D₄²	1	2	yes	—
325	C₄×C₇₃	—	2	2	no	—
326	C₄×C₇₃	—	2	2	no	—
327	C₄×C₇₃	—	2	2	no	—
328	C₄×C₇₃	—	4	4	no	—
329	C₄×C₇₃	—	4	2	no	—
330	C₄×C₇₃	—	4	1	no	—
331	C₄×C₇₃	—	4	1	no	—
332	C₄×C₇₃	—	4	2	no	—
333	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
334	C₄×C₇₃	#535	1	1	yes	characteristic
335	C₄×C₇₃	D₄²	1	2	yes	—
336	#25752	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂×C₇₃	—	2	2	no	—
338	C₂×C₇₃	—	4	2	no	—
339	C₂×C₇₃	—	8	1	no	—
340	C₂×C₇₃	—	8	2	no	—
341	C₂×C₇₃	—	8	1	no	—
342	C₂×C₇₃	—	16	2	no	—
343	C₂×C₇₃	#2433	1	1	yes	characteristic
344	C₂×C₇₃	#3021	1	2	yes	—
345	#3500	C₂×C₇₃	1	1	yes	characteristic, complemented
346	#3151	C₂×C₇₃	1	1	yes	characteristic, complemented
347	#3038	C₂×C₇₃	1	1	yes	characteristic, complemented
348	C₂×#454	C₂×C₇₃	1	2	yes	complemented
349	C₂×#453	C₂×C₇₃	1	2	yes	complemented
350	#2657	C₂×C₇₃	1	1	yes	characteristic, complemented
351	#2003	C₂×C₇₃	1	2	yes	complemented
352	#2002	C₂×C₇₃	1	2	yes	complemented
353	#1967	C₂×C₇₃	1	1	yes	characteristic, complemented
354	#1963	C₂×C₇₃	1	1	yes	characteristic, complemented
355	#1759	C₂×C₇₃	1	1	yes	characteristic, complemented
356	C₇₃	#25752	1	1	yes	characteristic, direct product factor, Sylow
357	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	1	yes	characteristic
358	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	1	yes	characteristic
359	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
360	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
361	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	complemented
362	#548	—	2	2	no	—
363	#546	—	2	2	no	—
364	#546	—	2	4	no	—
365	#536	—	2	1	no	—
366	#536	C₂²×C₇₃	1	1	yes	characteristic
367	#535	—	2	1	no	—
368	#535	C₂²×C₇₃	1	1	yes	characteristic
369	#532	—	2	1	no	—
370	#532	C₂²×C₇₃	1	1	yes	characteristic
371	C₂×#127	C₂²×C₇₃	1	2	yes	—
372	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic, complemented
373	C₂×#124	—	2	1	no	—
374	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
375	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
376	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
377	#496	—	2	1	no	—
378	#496	—	2	1	no	—
379	#493	—	2	1	no	—
380	#492	—	2	1	no	—
381	#460	—	2	2	no	—
382	#459	—	2	2	no	—
383	#454	—	2	8	no	—
384	#453	—	2	8	no	—
385	#423	C₂²×C₇₃	1	1	yes	characteristic, complemented
386	C₂×#104	C₂²×C₇₃	1	2	yes	—
387	C₂×#104	C₂²×C₇₃	1	2	yes	—
388	C₂×#104	C₂²×C₇₃	1	2	yes	complemented
389	#418	C₂²×C₇₃	1	2	yes	complemented
390	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
391	C₂×#100	C₂²×C₇₃	1	2	yes	—
392	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
393	#392	—	2	4	no	—
394	#376	C₂²×C₇₃	1	1	yes	characteristic, complemented
395	#339	C₂²×C₇₃	1	2	yes	complemented
396	2₋¹⁺⁴	—	2	4	no	—
397	2₋¹⁺⁴	—	4	2	no	—
398	H(5,𝔽₂)	—	2	4	no	—
399	H(5,𝔽₂)	—	4	2	no	—
400	C₂×#41	—	2	1	no	—
401	C₂×#41	—	2	1	no	—
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	2	1	no	—
404	C₂×#41	—	2	2	no	—
405	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
406	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
407	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
408	C₂²×Q₈	—	2	1	no	—
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
411	C₂²×D₄	—	2	2	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	4	no	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
417	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
418	AGL(1,ℤ/8)	—	2	4	no	—
419	AGL(1,ℤ/8)	—	2	4	no	—
420	AGL(1,ℤ/8)	—	2	4	no	—
421	AGL(1,ℤ/8)	—	2	4	no	—
422	AGL(1,ℤ/8)	—	4	2	no	—
423	AGL(1,ℤ/8)	—	4	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₂×D₈	—	2	2	no	—
428	C₂×D₈	—	2	2	no	—
429	C₂×D₈	—	2	2	no	—
430	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
431	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic, complemented
434	#127	—	2	1	no	—
435	#127	—	2	4	no	—
436	#127	—	2	2	no	—
437	#127	—	2	1	no	—
438	#127	—	2	1	no	—
439	#127	—	4	2	no	—
440	#127	D₄×C₇₃	1	1	yes	characteristic, complemented
441	#124	—	2	4	no	—
442	#124	—	2	1	no	—
443	#124	—	2	1	no	—
444	#124	—	2	1	no	—
445	#124	—	2	1	no	—
446	#124	—	2	2	no	—
447	#124	—	2	4	no	—
448	#124	—	4	2	no	—
449	#124	D₄×C₇₃	1	1	yes	characteristic, complemented
450	#124	D₄×C₇₃	1	1	yes	characteristic, complemented
451	#123	—	2	4	no	—
452	#123	—	2	2	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#120	—	2	4	no	—
460	#120	—	2	2	no	—
461	C₄×Q₈	D₄×C₇₃	1	2	yes	complemented
462	C₄×D₄	—	2	4	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	2	no	—
465	C₄×D₄	D₄×C₇₃	1	2	yes	complemented
466	#117	—	2	1	no	—
467	#117	C₂³×C₇₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	D₄×C₇₃	1	4	yes	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
474	C₄⋊C₈	—	2	2	no	—
475	#104	—	2	4	no	—
476	#104	—	2	4	no	—
477	#104	D₄×C₇₃	1	8	yes	complemented
478	#102	—	2	4	no	—
479	#101	—	2	4	no	—
480	#100	—	2	4	no	—
481	#97	—	2	1	no	—
482	C₄×C₈	—	2	1	no	—
483	#95	—	2	2	no	—
484	C₂⁴	—	2	2	no	—
485	C₂⁴	—	2	2	no	—
486	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
487	#41	—	2	2	no	—
488	#41	—	2	2	no	—
489	#41	—	2	2	no	—
490	#41	—	2	2	no	—
491	#41	—	2	2	no	—
492	#41	—	4	4	no	—
493	#41	—	4	8	no	—
494	#41	—	4	4	no	—
495	#41	—	4	2	no	—
496	#41	—	4	2	no	—
497	#41	—	4	2	no	—
498	#41	—	4	2	no	—
499	#41	C₂×D₄×C₇₃	1	4	yes	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
509	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
510	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	4	8	no	—
531	C₂×D₄	—	4	8	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	8	4	no	—
537	C₂×D₄	—	8	8	no	—
538	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
539	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
540	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
552	SD₁₆	—	4	4	no	—
553	SD₁₆	—	4	4	no	—
554	SD₁₆	—	4	4	no	—
555	D₈	—	4	4	no	—
556	D₈	—	4	4	no	—
557	D₈	—	4	4	no	—
558	M₁₆	—	2	2	no	—
559	M₁₆	—	2	2	no	—
560	M₁₆	—	2	2	no	—
561	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
562	C₂×C₈	—	2	2	no	—
563	C₂×C₈	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	4	8	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	2	no	—
580	C₄²	C₂×D₄×C₇₃	1	4	yes	—
581	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
582	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
583	C₄²	C₂×D₄×C₇₃	1	2	yes	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	4	4	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	8	4	no	—
596	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
597	Q₈	—	2	1	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	4	4	no	—
601	Q₈	—	4	1	no	—
602	Q₈	—	4	1	no	—
603	Q₈	—	4	2	no	—
604	Q₈	#127×C₇₃	1	2	yes	—
605	D₄	—	2	4	no	—
606	D₄	—	2	1	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	4	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	4	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	2	no	—
620	D₄	—	4	2	no	—
621	D₄	—	8	2	no	—
622	D₄	—	8	4	no	—
623	D₄	—	8	4	no	—
624	D₄	—	8	4	no	—
625	D₄	—	8	16	no	—
626	D₄	#127×C₇₃	1	2	yes	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	#120×C₇₃	1	2	yes	—
646	C₂×C₄	#120×C₇₃	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
650	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
651	C₈	—	2	4	no	—
652	C₈	—	4	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	8	4	no	—
663	C₂²	—	8	4	no	—
664	C₂²	—	8	4	no	—
665	C₂²	—	8	4	no	—
666	C₂²	—	8	2	no	—
667	C₂²	—	16	4	no	—
668	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
669	C₂²	D₄²×C₇₃	1	2	yes	—
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
679	C₄	#535×C₇₃	1	1	yes	characteristic
680	C₄	D₄²×C₇₃	1	2	yes	—
681	C₂	—	2	2	no	—
682	C₂	—	4	2	no	—
683	C₂	—	8	2	no	—
684	C₂	—	8	1	no	—
685	C₂	—	8	1	no	—
686	C₂	—	16	2	no	—
687	C₂	C₇₃×#2433	1	1	yes	characteristic
688	C₂	C₇₃×#3021	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3500	C₂	semidirect
2. C₇₃×#3151	C₂	semidirect
3. C₇₃×#3038	C₂	semidirect
4. C₂×#454×C₇₃	C₂	semidirect
5. C₂×#453×C₇₃	C₂	semidirect
6. C₇₃×#2657	C₂	semidirect
7. C₇₃×#2003	C₂	semidirect
8. C₇₃×#2002	C₂	semidirect
9. C₇₃×#1967	C₂	semidirect
10. C₇₃×#1963	C₂	semidirect
11. C₇₃×#1759	C₂	semidirect
16. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
27. C₂×#127×C₇₃	C₂²	semidirect
30. C₂×#124×C₇₃	C₂²	semidirect
40. #423×C₇₃	C₂²	semidirect
43. C₂×#104×C₇₃	C₂²	semidirect
44. #418×C₇₃	C₂²	semidirect
45. C₂×#101×C₇₃	C₂²	semidirect
47. C₄×M₁₆×C₇₃	C₂²	semidirect
49. #376×C₇₃	C₂²	semidirect
50. #339×C₇₃	C₂²	semidirect
88. C₄⋊Q₈×C₇₃	D₄	semidirect
95. #127×C₇₃	D₄	semidirect
104. #124×C₇₃	D₄	semidirect
105. #124×C₇₃	D₄	semidirect
116. C₄×Q₈×C₇₃	D₄	semidirect
120. C₄×D₄×C₇₃	D₄	semidirect
132. #104×C₇₃	D₄	semidirect
336. #25752	C₇₃	direct (N × H)
345. #3500	C₂×C₇₃	semidirect
346. #3151	C₂×C₇₃	semidirect
347. #3038	C₂×C₇₃	semidirect
348. C₂×#454	C₂×C₇₃	semidirect
349. C₂×#453	C₂×C₇₃	semidirect
350. #2657	C₂×C₇₃	semidirect
351. #2003	C₂×C₇₃	semidirect
352. #2002	C₂×C₇₃	semidirect
353. #1967	C₂×C₇₃	semidirect
354. #1963	C₂×C₇₃	semidirect
355. #1759	C₂×C₇₃	semidirect
356. C₇₃	#25752	direct (N × H)
361. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
372. C₂×#127	C₂²×C₇₃	semidirect
375. C₂×#124	C₂²×C₇₃	semidirect
385. #423	C₂²×C₇₃	semidirect
388. C₂×#104	C₂²×C₇₃	semidirect
389. #418	C₂²×C₇₃	semidirect
390. C₂×#101	C₂²×C₇₃	semidirect
392. C₄×M₁₆	C₂²×C₇₃	semidirect
394. #376	C₂²×C₇₃	semidirect
395. #339	C₂²×C₇₃	semidirect
433. C₄⋊Q₈	D₄×C₇₃	semidirect
440. #127	D₄×C₇₃	semidirect
449. #124	D₄×C₇₃	semidirect
450. #124	D₄×C₇₃	semidirect
461. C₄×Q₈	D₄×C₇₃	semidirect
465. C₄×D₄	D₄×C₇₃	semidirect
477. #104	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3500	2
C₇₃×#3151	2
C₇₃×#3038	2
C₂×#454×C₇₃	2
C₂×#453×C₇₃	2
C₇₃×#2657	2
C₇₃×#2003	2
C₇₃×#2002	2
C₇₃×#1967	2
C₇₃×#1963	2
C₇₃×#1759	2
#25752	73

Subgroups — C73×#25752 #32935156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25752 #32935156