Subgroups — C₇₃×#25626 #32935030

Order 18688.

1076 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3153	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2005	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2003	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1883	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
14	#559×C₇₃	—	2	1	no	—
15	#557×C₇₃	—	2	1	no	—
16	#556×C₇₃	—	2	1	no	—
17	#556×C₇₃	—	2	2	no	—
18	#554×C₇₃	—	2	1	no	—
19	#552×C₇₃	—	2	2	no	—
20	#539×C₇₃	—	2	2	no	—
21	#536×C₇₃	C₂²	1	2	yes	—
22	#533×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	#529×C₇₃	—	2	2	no	—
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
28	#520×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	#497×C₇₃	—	2	1	no	—
31	#496×C₇₃	—	2	1	no	—
32	#495×C₇₃	—	2	2	no	—
33	#489×C₇₃	—	2	1	no	—
34	#489×C₇₃	—	2	1	no	—
35	#488×C₇₃	—	2	2	no	—
36	C₂×#104×C₇₃	C₂²	1	2	yes	—
37	C₂×#104×C₇₃	C₂²	1	2	yes	—
38	#419×C₇₃	C₂²	1	2	yes	—
39	#418×C₇₃	C₂²	1	2	yes	—
40	C₂×#101×C₇₃	C₂²	1	2	yes	—
41	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
43	#396×C₇₃	—	2	2	no	—
44	#391×C₇₃	C₂²	1	1	yes	characteristic
45	#390×C₇₃	C₂²	1	1	yes	characteristic
46	#388×C₇₃	—	2	2	no	—
47	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
48	#343×C₇₃	C₂²	1	2	yes	—
49	#339×C₇₃	C₂²	1	2	yes	—
50	#339×C₇₃	C₂²	1	2	yes	—
51	C₂×#41×C₇₃	C₂³	1	2	yes	—
52	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
55	#137×C₇₃	—	2	4	no	—
56	#137×C₇₃	—	4	2	no	—
57	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
58	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
59	C₂×Q₁₆×C₇₃	—	2	2	no	—
60	C₂×SD₁₆×C₇₃	—	2	2	no	—
61	C₂×SD₁₆×C₇₃	—	2	2	no	—
62	C₂×D₈×C₇₃	—	2	2	no	—
63	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
64	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₇₃	—	2	2	no	—
66	C₄⋊Q₈×C₇₃	—	4	2	no	—
67	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
70	#127×C₇₃	D₄	1	1	yes	characteristic
71	#126×C₇₃	—	2	4	no	—
72	#126×C₇₃	—	2	4	no	—
73	#125×C₇₃	—	2	2	no	—
74	#125×C₇₃	—	2	4	no	—
75	#125×C₇₃	D₄	1	2	yes	—
76	#124×C₇₃	—	2	2	no	—
77	#124×C₇₃	—	2	2	no	—
78	#124×C₇₃	—	2	1	no	—
79	#124×C₇₃	—	2	1	no	—
80	#124×C₇₃	—	2	1	no	—
81	#124×C₇₃	—	2	1	no	—
82	#124×C₇₃	—	4	2	no	—
83	#124×C₇₃	D₄	1	2	yes	—
84	#123×C₇₃	—	2	4	no	—
85	#123×C₇₃	—	2	4	no	—
86	C₂²⋊Q₈×C₇₃	—	2	4	no	—
87	C₂²⋊Q₈×C₇₃	—	2	1	no	—
88	C₂²⋊Q₈×C₇₃	—	2	1	no	—
89	C₂²⋊Q₈×C₇₃	—	2	2	no	—
90	C₂²⋊Q₈×C₇₃	—	2	2	no	—
91	#121×C₇₃	—	2	1	no	—
92	#121×C₇₃	—	2	1	no	—
93	C₄×Q₈×C₇₃	—	2	2	no	—
94	C₄×Q₈×C₇₃	—	2	2	no	—
95	C₄×Q₈×C₇₃	—	2	1	no	—
96	C₄×Q₈×C₇₃	—	2	1	no	—
97	C₄×Q₈×C₇₃	—	2	1	no	—
98	C₄×Q₈×C₇₃	—	2	1	no	—
99	C₄×Q₈×C₇₃	—	2	1	no	—
100	C₄×Q₈×C₇₃	—	2	1	no	—
101	C₄×D₄×C₇₃	—	2	2	no	—
102	C₄×D₄×C₇₃	—	2	2	no	—
103	C₄×D₄×C₇₃	—	2	4	no	—
104	C₄×D₄×C₇₃	—	2	1	no	—
105	C₄×D₄×C₇₃	—	2	1	no	—
106	#117×C₇₃	—	2	4	no	—
107	#117×C₇₃	—	2	2	no	—
108	#117×C₇₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
110	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
118	C₂×C₄²×C₇₃	D₄	1	2	yes	—
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
122	#104×C₇₃	—	4	2	no	—
123	#104×C₇₃	—	4	2	no	—
124	#103×C₇₃	—	2	2	no	—
125	#103×C₇₃	—	2	2	no	—
126	#102×C₇₃	—	2	2	no	—
127	#102×C₇₃	—	2	2	no	—
128	#101×C₇₃	—	2	4	no	—
129	#97×C₇₃	—	2	1	no	—
130	#97×C₇₃	—	2	1	no	—
131	C₄×C₈×C₇₃	—	2	1	no	—
132	C₄×C₈×C₇₃	—	2	1	no	—
133	#95×C₇₃	—	2	1	no	—
134	#95×C₇₃	—	2	2	no	—
135	C₂⁴×C₇₃	—	2	1	no	—
136	#41×C₇₃	—	2	2	no	—
137	#41×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	#41×C₇₃	—	2	2	no	—
140	C₂×Q₈×C₇₃	—	2	1	no	—
141	C₂×Q₈×C₇₃	—	2	1	no	—
142	C₂×Q₈×C₇₃	—	2	1	no	—
143	C₂×Q₈×C₇₃	—	2	1	no	—
144	C₂×Q₈×C₇₃	—	2	2	no	—
145	C₂×Q₈×C₇₃	—	2	2	no	—
146	C₂×Q₈×C₇₃	—	2	1	no	—
147	C₂×Q₈×C₇₃	—	2	1	no	—
148	C₂×Q₈×C₇₃	—	2	2	no	—
149	C₂×Q₈×C₇₃	—	2	2	no	—
150	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	—	2	1	no	—
153	C₂×D₄×C₇₃	—	2	1	no	—
154	C₂×D₄×C₇₃	—	2	1	no	—
155	C₂×D₄×C₇₃	—	2	1	no	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	2	2	no	—
158	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₇₃	—	2	1	no	—
160	C₂²×C₄×C₇₃	—	2	4	no	—
161	C₂²×C₄×C₇₃	—	2	2	no	—
162	C₂²×C₄×C₇₃	—	2	1	no	—
163	C₂²×C₄×C₇₃	—	2	1	no	—
164	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₇₃	—	4	4	no	—
170	SD₁₆×C₇₃	—	4	4	no	—
171	SD₁₆×C₇₃	—	4	4	no	—
172	D₈×C₇₃	—	4	4	no	—
173	M₁₆×C₇₃	—	2	2	no	—
174	M₁₆×C₇₃	—	2	2	no	—
175	M₁₆×C₇₃	—	2	2	no	—
176	M₁₆×C₇₃	#41	1	4	yes	—
177	C₂×C₈×C₇₃	—	2	2	no	—
178	C₂×C₈×C₇₃	—	2	2	no	—
179	C₄⋊C₄×C₇₃	—	2	4	no	—
180	C₄⋊C₄×C₇₃	—	2	4	no	—
181	C₄⋊C₄×C₇₃	—	2	4	no	—
182	C₄⋊C₄×C₇₃	—	2	2	no	—
183	C₄⋊C₄×C₇₃	—	2	2	no	—
184	C₄⋊C₄×C₇₃	—	2	2	no	—
185	C₄⋊C₄×C₇₃	—	2	1	no	—
186	C₄⋊C₄×C₇₃	—	2	1	no	—
187	C₄⋊C₄×C₇₃	—	2	1	no	—
188	C₄⋊C₄×C₇₃	—	2	2	no	—
189	C₄⋊C₄×C₇₃	—	2	1	no	—
190	C₄⋊C₄×C₇₃	—	2	1	no	—
191	C₄⋊C₄×C₇₃	—	2	1	no	—
192	C₄⋊C₄×C₇₃	—	4	2	no	—
193	C₄⋊C₄×C₇₃	—	4	4	no	—
194	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
196	C₂²⋊C₄×C₇₃	—	2	4	no	—
197	C₂²⋊C₄×C₇₃	—	2	4	no	—
198	C₂²⋊C₄×C₇₃	—	2	4	no	—
199	C₂²⋊C₄×C₇₃	—	2	2	no	—
200	C₂²⋊C₄×C₇₃	—	2	2	no	—
201	C₂²⋊C₄×C₇₃	—	2	2	no	—
202	C₂²⋊C₄×C₇₃	—	4	4	no	—
203	C₂²⋊C₄×C₇₃	—	4	4	no	—
204	C₂²⋊C₄×C₇₃	—	4	1	no	—
205	C₂²⋊C₄×C₇₃	—	4	1	no	—
206	C₂²⋊C₄×C₇₃	—	4	1	no	—
207	C₂²⋊C₄×C₇₃	—	4	1	no	—
208	C₄²×C₇₃	—	2	4	no	—
209	C₄²×C₇₃	—	2	2	no	—
210	C₄²×C₇₃	—	2	2	no	—
211	C₄²×C₇₃	—	2	2	no	—
212	C₄²×C₇₃	—	2	2	no	—
213	C₄²×C₇₃	—	2	2	no	—
214	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₇₃	—	2	2	no	—
219	C₂³×C₇₃	—	4	2	no	—
220	C₂³×C₇₃	—	4	2	no	—
221	C₂³×C₇₃	—	4	1	no	—
222	C₂³×C₇₃	—	4	1	no	—
223	C₂³×C₇₃	—	4	1	no	—
224	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₇₃	—	2	2	no	—
226	Q₈×C₇₃	—	2	2	no	—
227	Q₈×C₇₃	—	4	2	no	—
228	Q₈×C₇₃	—	4	2	no	—
229	Q₈×C₇₃	—	4	2	no	—
230	Q₈×C₇₃	—	4	2	no	—
231	Q₈×C₇₃	—	4	2	no	—
232	Q₈×C₇₃	—	8	1	no	—
233	D₄×C₇₃	—	2	2	no	—
234	D₄×C₇₃	—	2	2	no	—
235	D₄×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	2	no	—
237	D₄×C₇₃	—	4	2	no	—
238	D₄×C₇₃	—	4	2	no	—
239	D₄×C₇₃	—	4	2	no	—
240	D₄×C₇₃	—	8	1	no	—
241	C₂×C₄×C₇₃	—	2	2	no	—
242	C₂×C₄×C₇₃	—	2	2	no	—
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	2	2	no	—
245	C₂×C₄×C₇₃	—	2	2	no	—
246	C₂×C₄×C₇₃	—	2	2	no	—
247	C₂×C₄×C₇₃	—	2	2	no	—
248	C₂×C₄×C₇₃	—	2	2	no	—
249	C₂×C₄×C₇₃	—	4	1	no	—
250	C₂×C₄×C₇₃	—	4	1	no	—
251	C₂×C₄×C₇₃	—	4	1	no	—
252	C₂×C₄×C₇₃	—	4	1	no	—
253	C₂×C₄×C₇₃	—	4	2	no	—
254	C₂×C₄×C₇₃	—	4	2	no	—
255	C₂×C₄×C₇₃	—	4	2	no	—
256	C₂×C₄×C₇₃	—	4	1	no	—
257	C₂×C₄×C₇₃	—	4	1	no	—
258	C₂×C₄×C₇₃	—	4	1	no	—
259	C₂×C₄×C₇₃	—	4	1	no	—
260	C₂×C₄×C₇₃	—	4	1	no	—
261	C₂×C₄×C₇₃	—	4	1	no	—
262	C₂×C₄×C₇₃	—	8	4	no	—
263	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
264	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
265	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
266	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
270	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₇₃	—	2	4	no	—
272	C₈×C₇₃	—	4	2	no	—
273	C₂²×C₇₃	—	2	1	no	—
274	C₂²×C₇₃	—	2	1	no	—
275	C₂²×C₇₃	—	4	2	no	—
276	C₂²×C₇₃	—	4	2	no	—
277	C₂²×C₇₃	—	4	2	no	—
278	C₂²×C₇₃	—	8	2	no	—
279	C₂²×C₇₃	—	8	2	no	—
280	C₂²×C₇₃	—	8	1	no	—
281	C₂²×C₇₃	—	8	1	no	—
282	C₂²×C₇₃	—	8	1	no	—
283	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
284	C₂²×C₇₃	#532	1	1	yes	characteristic
285	C₂²×C₇₃	#535	1	1	yes	characteristic
286	C₄×C₇₃	—	2	1	no	—
287	C₄×C₇₃	—	2	1	no	—
288	C₄×C₇₃	—	2	1	no	—
289	C₄×C₇₃	—	2	1	no	—
290	C₄×C₇₃	—	4	2	no	—
291	C₄×C₇₃	—	4	2	no	—
292	C₄×C₇₃	—	4	2	no	—
293	C₄×C₇₃	—	4	2	no	—
294	C₄×C₇₃	—	4	2	no	—
295	C₄×C₇₃	—	4	2	no	—
296	C₄×C₇₃	—	8	1	no	—
297	C₄×C₇₃	—	8	1	no	—
298	C₄×C₇₃	#546	1	2	yes	—
299	C₄×C₇₃	#550	1	2	yes	—
300	#25626	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂×C₇₃	—	2	1	no	—
302	C₂×C₇₃	—	2	1	no	—
303	C₂×C₇₃	—	8	2	no	—
304	C₂×C₇₃	—	16	1	no	—
305	C₂×C₇₃	#2431	1	1	yes	characteristic
306	C₂×C₇₃	#3018	1	1	yes	characteristic
307	C₂×C₇₃	#3020	1	1	yes	characteristic
308	#3507	C₂×C₇₃	1	1	yes	characteristic, complemented
309	#3153	C₂×C₇₃	1	1	yes	characteristic
310	#3140	C₂×C₇₃	1	1	yes	characteristic, complemented
311	#2545	C₂×C₇₃	1	1	yes	characteristic, complemented
312	#2005	C₂×C₇₃	1	2	yes	complemented
313	#2003	C₂×C₇₃	1	2	yes	complemented
314	#1986	C₂×C₇₃	1	1	yes	characteristic, complemented
315	#1980	C₂×C₇₃	1	1	yes	characteristic, complemented
316	#1883	C₂×C₇₃	1	2	yes	complemented
317	#1882	C₂×C₇₃	1	2	yes	complemented
318	C₄×#101	C₂×C₇₃	1	1	yes	characteristic, complemented
319	C₇₃	#25626	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#137	C₂²×C₇₃	1	2	yes	—
321	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
322	#559	—	2	1	no	—
323	#557	—	2	1	no	—
324	#556	—	2	1	no	—
325	#556	—	2	2	no	—
326	#554	—	2	1	no	—
327	#552	—	2	2	no	—
328	#539	—	2	2	no	—
329	#536	C₂²×C₇₃	1	2	yes	—
330	#533	C₂²×C₇₃	1	1	yes	characteristic
331	#532	C₂²×C₇₃	1	1	yes	characteristic
332	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
333	#529	—	2	2	no	—
334	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
335	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
336	#520	C₂²×C₇₃	1	2	yes	—
337	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
338	#497	—	2	1	no	—
339	#496	—	2	1	no	—
340	#495	—	2	2	no	—
341	#489	—	2	1	no	—
342	#489	—	2	1	no	—
343	#488	—	2	2	no	—
344	C₂×#104	C₂²×C₇₃	1	2	yes	—
345	C₂×#104	C₂²×C₇₃	1	2	yes	—
346	#419	C₂²×C₇₃	1	2	yes	—
347	#418	C₂²×C₇₃	1	2	yes	—
348	C₂×#101	C₂²×C₇₃	1	2	yes	—
349	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
350	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
351	#396	—	2	2	no	—
352	#391	C₂²×C₇₃	1	1	yes	characteristic
353	#390	C₂²×C₇₃	1	1	yes	characteristic
354	#388	—	2	2	no	—
355	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
356	#343	C₂²×C₇₃	1	2	yes	—
357	#339	C₂²×C₇₃	1	2	yes	—
358	#339	C₂²×C₇₃	1	2	yes	—
359	C₂×#41	C₂³×C₇₃	1	2	yes	—
360	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
362	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
363	#137	—	2	4	no	—
364	#137	—	4	2	no	—
365	AGL(1,ℤ/8)	—	2	4	no	—
366	AGL(1,ℤ/8)	—	4	2	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×D₈	—	2	2	no	—
371	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
372	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	—	4	2	no	—
375	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
376	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
377	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
378	#127	D₄×C₇₃	1	1	yes	characteristic
379	#126	—	2	4	no	—
380	#126	—	2	4	no	—
381	#125	—	2	2	no	—
382	#125	—	2	4	no	—
383	#125	D₄×C₇₃	1	2	yes	—
384	#124	—	2	2	no	—
385	#124	—	2	2	no	—
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#124	—	2	1	no	—
390	#124	—	4	2	no	—
391	#124	D₄×C₇₃	1	2	yes	—
392	#123	—	2	4	no	—
393	#123	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	4	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	#117	—	2	4	no	—
415	#117	—	2	2	no	—
416	#117	C₂³×C₇₃	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₄²	D₄×C₇₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
430	#104	—	4	2	no	—
431	#104	—	4	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#102	—	2	2	no	—
435	#102	—	2	2	no	—
436	#101	—	2	4	no	—
437	#97	—	2	1	no	—
438	#97	—	2	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	2	no	—
443	C₂⁴	—	2	1	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
477	Q₁₆	—	4	4	no	—
478	SD₁₆	—	4	4	no	—
479	SD₁₆	—	4	4	no	—
480	D₈	—	4	4	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	#41×C₇₃	1	4	yes	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
503	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
523	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
526	C₂³	—	2	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	2	no	—
536	Q₈	—	4	2	no	—
537	Q₈	—	4	2	no	—
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	8	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	8	4	no	—
571	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
572	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
573	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
574	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
578	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
579	C₈	—	2	4	no	—
580	C₈	—	4	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	8	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
592	C₂²	#532×C₇₃	1	1	yes	characteristic
593	C₂²	#535×C₇₃	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	#546×C₇₃	1	2	yes	—
607	C₄	#550×C₇₃	1	2	yes	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	8	2	no	—
611	C₂	—	16	1	no	—
612	C₂	C₇₃×#2431	1	1	yes	characteristic
613	C₂	C₇₃×#3018	1	1	yes	characteristic
614	C₂	C₇₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3153	C₂
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×#3507	C₂	semidirect
3. C₇₃×#3140	C₂	semidirect
4. C₇₃×#2545	C₂	semidirect
5. C₇₃×#2005	C₂	semidirect
6. C₇₃×#2003	C₂	semidirect
7. C₇₃×#1986	C₂	semidirect
8. C₇₃×#1980	C₂	semidirect
9. C₇₃×#1883	C₂	semidirect
10. C₇₃×#1882	C₂	semidirect
11. C₄×#101×C₇₃	C₂	semidirect
300. #25626	C₇₃	direct (N × H)
308. #3507	C₂×C₇₃	semidirect
310. #3140	C₂×C₇₃	semidirect
311. #2545	C₂×C₇₃	semidirect
312. #2005	C₂×C₇₃	semidirect
313. #2003	C₂×C₇₃	semidirect
314. #1986	C₂×C₇₃	semidirect
315. #1980	C₂×C₇₃	semidirect
316. #1883	C₂×C₇₃	semidirect
317. #1882	C₂×C₇₃	semidirect
318. C₄×#101	C₂×C₇₃	semidirect
319. C₇₃	#25626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3507	2
C₇₃×#3153	2
C₇₃×#3140	2
C₇₃×#2545	2
C₇₃×#2005	2
C₇₃×#2003	2
C₇₃×#1986	2
C₇₃×#1980	2
C₇₃×#1883	2
C₇₃×#1882	2
C₄×#101×C₇₃	2
#25626	73

Subgroups — C73×#25626 #32935030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25626 #32935030