Subgroups — C₇₃×#25625 #32935029

Order 18688.

1172 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2004	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2002	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×#100×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	2	no	—
15	#556×C₇₃	—	2	1	no	—
16	#555×C₇₃	—	2	1	no	—
17	#553×C₇₃	—	2	2	no	—
18	#550×C₇₃	—	2	1	no	—
19	#547×C₇₃	—	2	1	no	—
20	#538×C₇₃	—	2	2	no	—
21	#535×C₇₃	C₂²	1	2	yes	—
22	#533×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	#525×C₇₃	—	2	2	no	—
28	#520×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×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×#100×C₇₃	C₂²	1	2	yes	—
41	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
43	#394×C₇₃	—	2	2	no	—
44	#391×C₇₃	C₂²	1	1	yes	characteristic
45	#390×C₇₃	C₂²	1	1	yes	characteristic
46	#386×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	—	2	2	no	—
52	C₂×#41×C₇₃	C₂³	1	2	yes	—
53	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₇₃	—	2	2	no	—
55	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇₃	D₄	1	2	yes	—
58	#137×C₇₃	—	2	4	no	—
59	#137×C₇₃	—	4	2	no	—
60	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
61	AGL(1,ℤ/8)×C₇₃	—	4	2	no	—
62	C₂×Q₁₆×C₇₃	—	2	2	no	—
63	C₂×SD₁₆×C₇₃	—	2	2	no	—
64	C₂×SD₁₆×C₇₃	—	2	2	no	—
65	C₂×D₈×C₇₃	—	2	2	no	—
66	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
67	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic, complemented
69	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic, complemented
70	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic, complemented
71	#127×C₇₃	—	2	2	no	—
72	#127×C₇₃	—	4	2	no	—
73	#127×C₇₃	D₄	1	1	yes	characteristic, complemented
74	#126×C₇₃	—	2	4	no	—
75	#125×C₇₃	D₄	1	2	yes	complemented
76	#124×C₇₃	—	2	4	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	complemented
84	#123×C₇₃	—	2	4	no	—
85	#123×C₇₃	—	2	4	no	—
86	C₂²⋊Q₈×C₇₃	—	2	2	no	—
87	C₂²⋊Q₈×C₇₃	—	2	1	no	—
88	C₂²⋊Q₈×C₇₃	—	2	1	no	—
89	#121×C₇₃	—	2	2	no	—
90	#121×C₇₃	—	2	4	no	—
91	#121×C₇₃	—	2	1	no	—
92	#121×C₇₃	—	2	1	no	—
93	#121×C₇₃	—	2	2	no	—
94	#121×C₇₃	—	2	2	no	—
95	#120×C₇₃	—	2	4	no	—
96	C₄×Q₈×C₇₃	—	2	2	no	—
97	C₄×Q₈×C₇₃	—	2	1	no	—
98	C₄×Q₈×C₇₃	—	2	1	no	—
99	C₄×D₄×C₇₃	—	2	4	no	—
100	C₄×D₄×C₇₃	—	2	2	no	—
101	C₄×D₄×C₇₃	—	2	4	no	—
102	C₄×D₄×C₇₃	—	2	1	no	—
103	C₄×D₄×C₇₃	—	2	1	no	—
104	C₄×D₄×C₇₃	—	2	1	no	—
105	C₄×D₄×C₇₃	—	2	1	no	—
106	C₄×D₄×C₇₃	—	2	1	no	—
107	C₄×D₄×C₇₃	—	2	1	no	—
108	#117×C₇₃	—	2	2	no	—
109	#117×C₇₃	—	2	2	no	—
110	#117×C₇₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
118	C₂×C₂²⋊C₄×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	#100×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	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
137	#41×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	#41×C₇₃	—	2	2	no	—
140	#41×C₇₃	—	2	2	no	—
141	#41×C₇₃	—	8	4	no	—
142	C₂×Q₈×C₇₃	—	2	1	no	—
143	C₂×Q₈×C₇₃	—	2	1	no	—
144	C₂×Q₈×C₇₃	—	2	1	no	—
145	C₂×Q₈×C₇₃	—	2	1	no	—
146	C₂×Q₈×C₇₃	—	2	2	no	—
147	C₂×Q₈×C₇₃	—	2	2	no	—
148	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₇₃	—	2	2	no	—
150	C₂×D₄×C₇₃	—	2	4	no	—
151	C₂×D₄×C₇₃	—	2	4	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	1	no	—
157	C₂×D₄×C₇₃	—	2	1	no	—
158	C₂×D₄×C₇₃	—	2	2	no	—
159	C₂×D₄×C₇₃	—	2	2	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	4	4	no	—
163	C₂×D₄×C₇₃	—	4	4	no	—
164	C₂×D₄×C₇₃	—	8	2	no	—
165	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇₃	—	2	1	no	—
167	C₂²×C₄×C₇₃	—	2	4	no	—
168	C₂²×C₄×C₇₃	—	2	2	no	—
169	C₂²×C₄×C₇₃	—	2	2	no	—
170	C₂²×C₄×C₇₃	—	2	2	no	—
171	C₂²×C₄×C₇₃	—	2	1	no	—
172	C₂²×C₄×C₇₃	—	2	1	no	—
173	C₂²×C₄×C₇₃	—	8	2	no	—
174	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
178	Q₁₆×C₇₃	—	4	4	no	—
179	SD₁₆×C₇₃	—	4	4	no	—
180	SD₁₆×C₇₃	—	4	4	no	—
181	D₈×C₇₃	—	4	4	no	—
182	M₁₆×C₇₃	—	2	2	no	—
183	M₁₆×C₇₃	—	2	2	no	—
184	M₁₆×C₇₃	—	2	2	no	—
185	M₁₆×C₇₃	#41	1	4	yes	complemented
186	C₂×C₈×C₇₃	—	2	2	no	—
187	C₂×C₈×C₇₃	—	2	2	no	—
188	C₄⋊C₄×C₇₃	—	2	4	no	—
189	C₄⋊C₄×C₇₃	—	2	1	no	—
190	C₄⋊C₄×C₇₃	—	2	1	no	—
191	C₄⋊C₄×C₇₃	—	2	2	no	—
192	C₄⋊C₄×C₇₃	—	2	1	no	—
193	C₄⋊C₄×C₇₃	—	2	2	no	—
194	C₄⋊C₄×C₇₃	—	2	1	no	—
195	C₄⋊C₄×C₇₃	—	2	1	no	—
196	C₄⋊C₄×C₇₃	—	2	1	no	—
197	C₄⋊C₄×C₇₃	—	4	2	no	—
198	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
200	C₂²⋊C₄×C₇₃	—	2	4	no	—
201	C₂²⋊C₄×C₇₃	—	2	4	no	—
202	C₂²⋊C₄×C₇₃	—	2	4	no	—
203	C₂²⋊C₄×C₇₃	—	2	2	no	—
204	C₂²⋊C₄×C₇₃	—	2	2	no	—
205	C₂²⋊C₄×C₇₃	—	2	2	no	—
206	C₂²⋊C₄×C₇₃	—	2	2	no	—
207	C₂²⋊C₄×C₇₃	—	2	2	no	—
208	C₂²⋊C₄×C₇₃	—	4	4	no	—
209	C₂²⋊C₄×C₇₃	—	4	1	no	—
210	C₂²⋊C₄×C₇₃	—	4	1	no	—
211	C₂²⋊C₄×C₇₃	—	4	1	no	—
212	C₂²⋊C₄×C₇₃	—	4	1	no	—
213	C₂²⋊C₄×C₇₃	—	8	2	no	—
214	C₄²×C₇₃	—	2	4	no	—
215	C₄²×C₇₃	—	2	2	no	—
216	C₄²×C₇₃	—	2	2	no	—
217	C₄²×C₇₃	—	2	2	no	—
218	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	2	2	no	—
224	C₂³×C₇₃	—	2	2	no	—
225	C₂³×C₇₃	—	2	2	no	—
226	C₂³×C₇₃	—	4	2	no	—
227	C₂³×C₇₃	—	4	2	no	—
228	C₂³×C₇₃	—	4	2	no	—
229	C₂³×C₇₃	—	4	2	no	—
230	C₂³×C₇₃	—	4	1	no	—
231	C₂³×C₇₃	—	4	1	no	—
232	C₂³×C₇₃	—	4	1	no	—
233	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₇₃	—	2	2	no	—
235	Q₈×C₇₃	—	2	2	no	—
236	Q₈×C₇₃	—	4	2	no	—
237	Q₈×C₇₃	—	4	2	no	—
238	Q₈×C₇₃	—	4	2	no	—
239	Q₈×C₇₃	—	8	1	no	—
240	D₄×C₇₃	—	2	2	no	—
241	D₄×C₇₃	—	2	2	no	—
242	D₄×C₇₃	—	4	2	no	—
243	D₄×C₇₃	—	4	2	no	—
244	D₄×C₇₃	—	4	2	no	—
245	D₄×C₇₃	—	4	2	no	—
246	D₄×C₇₃	—	4	2	no	—
247	D₄×C₇₃	—	4	2	no	—
248	D₄×C₇₃	—	4	2	no	—
249	D₄×C₇₃	—	8	1	no	—
250	D₄×C₇₃	—	8	4	no	—
251	D₄×C₇₃	—	8	4	no	—
252	D₄×C₇₃	—	8	8	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	2	2	no	—
255	C₂×C₄×C₇₃	—	2	2	no	—
256	C₂×C₄×C₇₃	—	2	2	no	—
257	C₂×C₄×C₇₃	—	2	2	no	—
258	C₂×C₄×C₇₃	—	4	1	no	—
259	C₂×C₄×C₇₃	—	4	1	no	—
260	C₂×C₄×C₇₃	—	4	4	no	—
261	C₂×C₄×C₇₃	—	4	1	no	—
262	C₂×C₄×C₇₃	—	4	1	no	—
263	C₂×C₄×C₇₃	—	4	2	no	—
264	C₂×C₄×C₇₃	—	4	2	no	—
265	C₂×C₄×C₇₃	—	4	2	no	—
266	C₂×C₄×C₇₃	—	4	1	no	—
267	C₂×C₄×C₇₃	—	4	1	no	—
268	C₂×C₄×C₇₃	—	4	1	no	—
269	C₂×C₄×C₇₃	—	4	1	no	—
270	C₂×C₄×C₇₃	—	4	1	no	—
271	C₂×C₄×C₇₃	—	4	1	no	—
272	C₂×C₄×C₇₃	—	8	2	no	—
273	C₂×C₄×C₇₃	—	8	4	no	—
274	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
275	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
276	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
277	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
278	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
281	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
282	C₈×C₇₃	—	2	4	no	—
283	C₈×C₇₃	—	4	2	no	—
284	C₂²×C₇₃	—	2	1	no	—
285	C₂²×C₇₃	—	2	1	no	—
286	C₂²×C₇₃	—	4	4	no	—
287	C₂²×C₇₃	—	4	2	no	—
288	C₂²×C₇₃	—	4	2	no	—
289	C₂²×C₇₃	—	4	2	no	—
290	C₂²×C₇₃	—	4	2	no	—
291	C₂²×C₇₃	—	4	2	no	—
292	C₂²×C₇₃	—	4	2	no	—
293	C₂²×C₇₃	—	8	2	no	—
294	C₂²×C₇₃	—	8	2	no	—
295	C₂²×C₇₃	—	8	2	no	—
296	C₂²×C₇₃	—	8	1	no	—
297	C₂²×C₇₃	—	8	1	no	—
298	C₂²×C₇₃	—	8	1	no	—
299	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
300	C₂²×C₇₃	#532	1	1	yes	characteristic
301	C₂²×C₇₃	#535	1	1	yes	characteristic
302	C₄×C₇₃	—	2	1	no	—
303	C₄×C₇₃	—	2	1	no	—
304	C₄×C₇₃	—	2	1	no	—
305	C₄×C₇₃	—	2	1	no	—
306	C₄×C₇₃	—	4	2	no	—
307	C₄×C₇₃	—	4	2	no	—
308	C₄×C₇₃	—	4	2	no	—
309	C₄×C₇₃	—	4	2	no	—
310	C₄×C₇₃	—	4	2	no	—
311	C₄×C₇₃	—	8	1	no	—
312	C₄×C₇₃	—	8	1	no	—
313	C₄×C₇₃	#546	1	2	yes	—
314	C₄×C₇₃	#550	1	2	yes	—
315	#25625	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂×C₇₃	—	2	1	no	—
317	C₂×C₇₃	—	2	1	no	—
318	C₂×C₇₃	—	8	2	no	—
319	C₂×C₇₃	—	8	2	no	—
320	C₂×C₇₃	—	16	1	no	—
321	C₂×C₇₃	#2431	1	1	yes	characteristic
322	C₂×C₇₃	#3018	1	1	yes	characteristic
323	C₂×C₇₃	#3019	1	1	yes	characteristic
324	#3506	C₂×C₇₃	1	1	yes	characteristic, complemented
325	#3153	C₂×C₇₃	1	1	yes	characteristic, complemented
326	#3140	C₂×C₇₃	1	1	yes	characteristic, complemented
327	#2544	C₂×C₇₃	1	1	yes	characteristic, complemented
328	#2004	C₂×C₇₃	1	2	yes	complemented
329	#2002	C₂×C₇₃	1	2	yes	complemented
330	#1986	C₂×C₇₃	1	1	yes	characteristic, complemented
331	#1980	C₂×C₇₃	1	1	yes	characteristic, complemented
332	#1883	C₂×C₇₃	1	2	yes	complemented
333	#1882	C₂×C₇₃	1	2	yes	complemented
334	C₄×#100	C₂×C₇₃	1	1	yes	characteristic, complemented
335	C₇₃	#25625	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×#137	C₂²×C₇₃	1	2	yes	—
337	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
338	#559	—	2	2	no	—
339	#556	—	2	1	no	—
340	#555	—	2	1	no	—
341	#553	—	2	2	no	—
342	#550	—	2	1	no	—
343	#547	—	2	1	no	—
344	#538	—	2	2	no	—
345	#535	C₂²×C₇₃	1	2	yes	—
346	#533	C₂²×C₇₃	1	1	yes	characteristic
347	#532	C₂²×C₇₃	1	1	yes	characteristic
348	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
349	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
350	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
351	#525	—	2	2	no	—
352	#520	C₂²×C₇₃	1	2	yes	—
353	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
354	#497	—	2	1	no	—
355	#496	—	2	1	no	—
356	#495	—	2	2	no	—
357	#489	—	2	1	no	—
358	#489	—	2	1	no	—
359	#488	—	2	2	no	—
360	C₂×#104	C₂²×C₇₃	1	2	yes	—
361	C₂×#104	C₂²×C₇₃	1	2	yes	—
362	#419	C₂²×C₇₃	1	2	yes	—
363	#418	C₂²×C₇₃	1	2	yes	—
364	C₂×#100	C₂²×C₇₃	1	2	yes	—
365	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
366	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
367	#394	—	2	2	no	—
368	#391	C₂²×C₇₃	1	1	yes	characteristic
369	#390	C₂²×C₇₃	1	1	yes	characteristic
370	#386	—	2	2	no	—
371	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
372	#343	C₂²×C₇₃	1	2	yes	—
373	#339	C₂²×C₇₃	1	2	yes	—
374	#339	C₂²×C₇₃	1	2	yes	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	C₂³×C₇₃	1	2	yes	—
377	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
381	C₂³×C₄	D₄×C₇₃	1	2	yes	—
382	#137	—	2	4	no	—
383	#137	—	4	2	no	—
384	AGL(1,ℤ/8)	—	2	4	no	—
385	AGL(1,ℤ/8)	—	4	2	no	—
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×D₈	—	2	2	no	—
390	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
391	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
392	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic, complemented
393	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic, complemented
394	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic, complemented
395	#127	—	2	2	no	—
396	#127	—	4	2	no	—
397	#127	D₄×C₇₃	1	1	yes	characteristic, complemented
398	#126	—	2	4	no	—
399	#125	D₄×C₇₃	1	2	yes	complemented
400	#124	—	2	4	no	—
401	#124	—	2	2	no	—
402	#124	—	2	1	no	—
403	#124	—	2	1	no	—
404	#124	—	2	1	no	—
405	#124	—	2	1	no	—
406	#124	—	4	2	no	—
407	#124	D₄×C₇₃	1	2	yes	complemented
408	#123	—	2	4	no	—
409	#123	—	2	4	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	#121	—	2	2	no	—
414	#121	—	2	4	no	—
415	#121	—	2	1	no	—
416	#121	—	2	1	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#120	—	2	4	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×D₄	—	2	4	no	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	1	no	—
427	C₄×D₄	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	#117	—	2	2	no	—
433	#117	—	2	2	no	—
434	#117	C₂³×C₇₃	1	2	yes	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	2	2	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
443	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
446	#104	—	4	2	no	—
447	#104	—	4	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	2	2	no	—
452	#100	—	2	4	no	—
453	#97	—	2	1	no	—
454	#97	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	C₄×C₈	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	2	no	—
459	C₂⁴	—	2	1	no	—
460	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	#41	—	8	4	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	8	2	no	—
489	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	8	2	no	—
498	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
502	Q₁₆	—	4	4	no	—
503	SD₁₆	—	4	4	no	—
504	SD₁₆	—	4	4	no	—
505	D₈	—	4	4	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	#41×C₇₃	1	4	yes	complemented
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
523	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	4	4	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₂²⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	8	2	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	2	no	—
542	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
543	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	4	2	no	—
563	Q₈	—	8	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	8	1	no	—
574	D₄	—	8	4	no	—
575	D₄	—	8	4	no	—
576	D₄	—	8	8	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	8	2	no	—
597	C₂×C₄	—	8	4	no	—
598	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
599	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
600	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
601	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
603	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
604	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
605	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
606	C₈	—	2	4	no	—
607	C₈	—	4	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	8	2	no	—
618	C₂²	—	8	2	no	—
619	C₂²	—	8	2	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
624	C₂²	#532×C₇₃	1	1	yes	characteristic
625	C₂²	#535×C₇₃	1	1	yes	characteristic
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	#546×C₇₃	1	2	yes	—
638	C₄	#550×C₇₃	1	2	yes	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	8	2	no	—
642	C₂	—	8	2	no	—
643	C₂	—	16	1	no	—
644	C₂	C₇₃×#2431	1	1	yes	characteristic
645	C₂	C₇₃×#3018	1	1	yes	characteristic
646	C₂	C₇₃×#3019	1	1	yes	characteristic

	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×#3506	C₂	semidirect
2. C₇₃×#3153	C₂	semidirect
3. C₇₃×#3140	C₂	semidirect
4. C₇₃×#2544	C₂	semidirect
5. C₇₃×#2004	C₂	semidirect
6. C₇₃×#2002	C₂	semidirect
7. C₇₃×#1986	C₂	semidirect
8. C₇₃×#1980	C₂	semidirect
9. C₇₃×#1883	C₂	semidirect
10. C₇₃×#1882	C₂	semidirect
11. C₄×#100×C₇₃	C₂	semidirect
68. C₄⋊Q₈×C₇₃	D₄	semidirect
69. C₄⋊Q₈×C₇₃	D₄	semidirect
70. C₄⋊Q₈×C₇₃	D₄	semidirect
73. #127×C₇₃	D₄	semidirect
75. #125×C₇₃	D₄	semidirect
83. #124×C₇₃	D₄	semidirect
185. M₁₆×C₇₃	#41	semidirect
315. #25625	C₇₃	direct (N × H)
324. #3506	C₂×C₇₃	semidirect
325. #3153	C₂×C₇₃	semidirect
326. #3140	C₂×C₇₃	semidirect
327. #2544	C₂×C₇₃	semidirect
328. #2004	C₂×C₇₃	semidirect
329. #2002	C₂×C₇₃	semidirect
330. #1986	C₂×C₇₃	semidirect
331. #1980	C₂×C₇₃	semidirect
332. #1883	C₂×C₇₃	semidirect
333. #1882	C₂×C₇₃	semidirect
334. C₄×#100	C₂×C₇₃	semidirect
335. C₇₃	#25625	direct (N × H)
392. C₄⋊Q₈	D₄×C₇₃	semidirect
393. C₄⋊Q₈	D₄×C₇₃	semidirect
394. C₄⋊Q₈	D₄×C₇₃	semidirect
397. #127	D₄×C₇₃	semidirect
399. #125	D₄×C₇₃	semidirect
407. #124	D₄×C₇₃	semidirect
509. M₁₆	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3506	2
C₇₃×#3153	2
C₇₃×#3140	2
C₇₃×#2544	2
C₇₃×#2004	2
C₇₃×#2002	2
C₇₃×#1986	2
C₇₃×#1980	2
C₇₃×#1883	2
C₇₃×#1882	2
C₄×#100×C₇₃	2
#25625	73

Subgroups — C73×#25625 #32935029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25625 #32935029