Subgroups — C₇₃×#59654 #32969058

Order 18688.

3104 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#548×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#547×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2681	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2536	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2491	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2461	C₂	1	4	yes	maximal, complemented
10	C₇₃×#2440	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2428	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2409	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2407	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2361	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₇₃	C₂²	1	2	yes	—
19	C₂³×Q₈×C₇₃	C₂²	1	2	yes	—
20	D₄×Q₈×C₇₃	—	2	8	no	—
21	#548×C₇₃	—	2	16	no	—
22	#547×C₇₃	—	2	8	no	—
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	4	yes	—
27	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#123×C₇₃	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
30	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
33	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
34	C₂×#121×C₇₃	C₂²	1	2	yes	—
35	C₂×#121×C₇₃	C₂²	1	2	yes	—
36	C₂×#121×C₇₃	C₂²	1	4	yes	—
37	C₂×#121×C₇₃	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
43	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
48	#398×C₇₃	C₂²	1	4	yes	—
49	#396×C₇₃	C₂²	1	4	yes	—
50	#395×C₇₃	C₂²	1	4	yes	—
51	#394×C₇₃	C₂²	1	4	yes	—
52	#394×C₇₃	C₂²	1	4	yes	—
53	#394×C₇₃	C₂²	1	4	yes	—
54	#393×C₇₃	C₂²	1	4	yes	—
55	#392×C₇₃	C₂²	1	4	yes	—
56	#391×C₇₃	C₂²	1	1	yes	characteristic
57	#391×C₇₃	C₂²	1	2	yes	—
58	#390×C₇₃	C₂²	1	2	yes	—
59	#390×C₇₃	C₂²	1	1	yes	characteristic
60	#390×C₇₃	C₂²	1	2	yes	—
61	#390×C₇₃	C₂²	1	1	yes	characteristic
62	#390×C₇₃	C₂²	1	1	yes	characteristic
63	#390×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	2	yes	—
65	#389×C₇₃	C₂²	1	2	yes	—
66	#389×C₇₃	C₂²	1	2	yes	—
67	#388×C₇₃	C₂²	1	2	yes	—
68	#388×C₇₃	C₂²	1	4	yes	—
69	#388×C₇₃	C₂²	1	4	yes	—
70	#388×C₇₃	C₂²	1	2	yes	—
71	#386×C₇₃	C₂²	1	4	yes	—
72	#386×C₇₃	C₂²	1	4	yes	—
73	#385×C₇₃	C₂²	1	4	yes	—
74	#385×C₇₃	C₂²	1	4	yes	—
75	#384×C₇₃	C₂²	1	1	yes	characteristic
76	#384×C₇₃	C₂²	1	1	yes	characteristic
77	#382×C₇₃	C₂²	1	1	yes	characteristic
78	#380×C₇₃	C₂²	1	2	yes	—
79	#380×C₇₃	C₂²	1	2	yes	—
80	#380×C₇₃	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
85	C₄³×C₇₃	C₂²	1	1	yes	characteristic
86	C₂×#41×C₇₃	—	2	8	no	—
87	C₂×#41×C₇₃	—	2	8	no	—
88	C₂×#41×C₇₃	—	4	4	no	—
89	C₂²×Q₈×C₇₃	—	2	8	no	—
90	C₂²×Q₈×C₇₃	—	2	8	no	—
91	C₂²×Q₈×C₇₃	—	4	4	no	—
92	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
93	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
106	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
107	C₄⋊Q₈×C₇₃	—	2	8	no	—
108	C₄⋊Q₈×C₇₃	D₄	1	8	yes	complemented
109	#127×C₇₃	—	2	4	no	—
110	#124×C₇₃	—	2	16	no	—
111	#124×C₇₃	D₄	1	8	yes	complemented
112	#123×C₇₃	—	2	16	no	—
113	C₂²⋊Q₈×C₇₃	—	2	8	no	—
114	C₂²⋊Q₈×C₇₃	—	2	8	no	—
115	C₂²⋊Q₈×C₇₃	—	2	8	no	—
116	C₂²⋊Q₈×C₇₃	—	2	16	no	—
117	C₂²⋊Q₈×C₇₃	—	2	16	no	—
118	#121×C₇₃	—	2	8	no	—
119	#121×C₇₃	—	2	8	no	—
120	#121×C₇₃	—	2	8	no	—
121	#121×C₇₃	—	2	16	no	—
122	C₄×Q₈×C₇₃	—	2	8	no	—
123	C₄×Q₈×C₇₃	—	2	4	no	—
124	C₄×D₄×C₇₃	—	2	8	no	—
125	C₄×D₄×C₇₃	—	2	16	no	—
126	C₄×D₄×C₇₃	—	2	4	no	—
127	C₄×D₄×C₇₃	—	2	4	no	—
128	C₄×D₄×C₇₃	—	2	8	no	—
129	C₄×D₄×C₇₃	—	2	4	no	—
130	C₄×D₄×C₇₃	—	4	4	no	—
131	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
170	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
174	#95×C₇₃	C₂³	1	2	yes	—
175	#95×C₇₃	C₂³	1	2	yes	—
176	#95×C₇₃	C₂³	1	2	yes	—
177	#95×C₇₃	C₂³	1	2	yes	—
178	#95×C₇₃	C₂³	1	4	yes	—
179	#95×C₇₃	C₂³	1	4	yes	—
180	#95×C₇₃	C₂³	1	4	yes	—
181	#95×C₇₃	C₂³	1	4	yes	—
182	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
183	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
184	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
185	#41×C₇₃	—	4	32	no	—
186	C₂×Q₈×C₇₃	—	2	2	no	—
187	C₂×Q₈×C₇₃	—	2	4	no	—
188	C₂×Q₈×C₇₃	—	2	8	no	—
189	C₂×Q₈×C₇₃	—	2	8	no	—
190	C₂×Q₈×C₇₃	—	2	2	no	—
191	C₂×Q₈×C₇₃	—	2	4	no	—
192	C₂×Q₈×C₇₃	—	4	4	no	—
193	C₂×Q₈×C₇₃	—	4	32	no	—
194	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
195	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
196	C₂×D₄×C₇₃	—	2	8	no	—
197	C₂×D₄×C₇₃	—	2	8	no	—
198	C₂×D₄×C₇₃	—	2	8	no	—
199	C₂×D₄×C₇₃	—	2	4	no	—
200	C₂×D₄×C₇₃	—	2	4	no	—
201	C₂×D₄×C₇₃	—	2	2	no	—
202	C₂×D₄×C₇₃	—	2	2	no	—
203	C₂×D₄×C₇₃	—	2	4	no	—
204	C₂×D₄×C₇₃	—	2	2	no	—
205	C₂×D₄×C₇₃	—	2	8	no	—
206	C₂×D₄×C₇₃	—	2	2	no	—
207	C₂×D₄×C₇₃	—	2	2	no	—
208	C₂×D₄×C₇₃	—	2	2	no	—
209	C₂×D₄×C₇₃	—	2	4	no	—
210	C₂×D₄×C₇₃	—	2	2	no	—
211	C₂×D₄×C₇₃	—	4	2	no	—
212	C₂×D₄×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	—	4	4	no	—
214	C₂×D₄×C₇₃	—	4	4	no	—
215	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
216	C₂×D₄×C₇₃	#41	1	4	yes	complemented
217	C₂²×C₄×C₇₃	—	2	8	no	—
218	C₂²×C₄×C₇₃	—	2	4	no	—
219	C₂²×C₄×C₇₃	—	2	8	no	—
220	C₂²×C₄×C₇₃	—	2	8	no	—
221	C₂²×C₄×C₇₃	—	2	4	no	—
222	C₂²×C₄×C₇₃	—	2	8	no	—
223	C₂²×C₄×C₇₃	—	2	4	no	—
224	C₂²×C₄×C₇₃	—	2	4	no	—
225	C₂²×C₄×C₇₃	—	2	4	no	—
226	C₂²×C₄×C₇₃	—	2	4	no	—
227	C₂²×C₄×C₇₃	—	2	4	no	—
228	C₂²×C₄×C₇₃	—	2	4	no	—
229	C₂²×C₄×C₇₃	—	2	4	no	—
230	C₂²×C₄×C₇₃	—	4	4	no	—
231	C₂²×C₄×C₇₃	—	4	4	no	—
232	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₇₃	—	2	2	no	—
247	C₄⋊C₄×C₇₃	—	2	8	no	—
248	C₄⋊C₄×C₇₃	—	2	8	no	—
249	C₄⋊C₄×C₇₃	—	2	2	no	—
250	C₄⋊C₄×C₇₃	—	2	4	no	—
251	C₄⋊C₄×C₇₃	—	2	2	no	—
252	C₄⋊C₄×C₇₃	—	2	8	no	—
253	C₄⋊C₄×C₇₃	—	2	4	no	—
254	C₄⋊C₄×C₇₃	—	2	4	no	—
255	C₄⋊C₄×C₇₃	—	2	2	no	—
256	C₄⋊C₄×C₇₃	—	2	8	no	—
257	C₄⋊C₄×C₇₃	—	2	4	no	—
258	C₄⋊C₄×C₇₃	—	4	2	no	—
259	C₄⋊C₄×C₇₃	—	4	2	no	—
260	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
261	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
262	C₂²⋊C₄×C₇₃	—	2	8	no	—
263	C₂²⋊C₄×C₇₃	—	2	8	no	—
264	C₂²⋊C₄×C₇₃	—	2	4	no	—
265	C₂²⋊C₄×C₇₃	—	2	8	no	—
266	C₂²⋊C₄×C₇₃	—	2	4	no	—
267	C₂²⋊C₄×C₇₃	—	2	4	no	—
268	C₂²⋊C₄×C₇₃	—	2	4	no	—
269	C₂²⋊C₄×C₇₃	—	2	4	no	—
270	C₂²⋊C₄×C₇₃	—	2	8	no	—
271	C₂²⋊C₄×C₇₃	—	2	8	no	—
272	C₂²⋊C₄×C₇₃	—	2	4	no	—
273	C₂²⋊C₄×C₇₃	—	4	2	no	—
274	C₂²⋊C₄×C₇₃	—	4	4	no	—
275	C₂²⋊C₄×C₇₃	—	4	2	no	—
276	C₂²⋊C₄×C₇₃	—	4	2	no	—
277	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
278	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
279	C₄²×C₇₃	—	2	8	no	—
280	C₄²×C₇₃	—	2	4	no	—
281	C₄²×C₇₃	—	2	2	no	—
282	C₄²×C₇₃	—	2	2	no	—
283	C₄²×C₇₃	—	2	2	no	—
284	C₄²×C₇₃	—	2	2	no	—
285	C₄²×C₇₃	—	4	1	no	—
286	C₄²×C₇₃	C₂×D₄	1	4	yes	—
287	C₄²×C₇₃	C₂×D₄	1	4	yes	—
288	C₂³×C₇₃	—	2	2	no	—
289	C₂³×C₇₃	—	2	2	no	—
290	C₂³×C₇₃	—	2	2	no	—
291	C₂³×C₇₃	—	2	2	no	—
292	C₂³×C₇₃	—	2	2	no	—
293	C₂³×C₇₃	—	2	2	no	—
294	C₂³×C₇₃	—	2	2	no	—
295	C₂³×C₇₃	—	2	2	no	—
296	C₂³×C₇₃	—	2	2	no	—
297	C₂³×C₇₃	—	2	2	no	—
298	C₂³×C₇₃	—	2	2	no	—
299	C₂³×C₇₃	—	2	2	no	—
300	C₂³×C₇₃	—	2	2	no	—
301	C₂³×C₇₃	—	2	2	no	—
302	C₂³×C₇₃	—	2	2	no	—
303	C₂³×C₇₃	—	2	2	no	—
304	C₂³×C₇₃	—	2	2	no	—
305	C₂³×C₇₃	—	2	2	no	—
306	C₂³×C₇₃	—	2	2	no	—
307	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
308	C₂³×C₇₃	C₂×#41	1	4	yes	—
309	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
310	Q₈×C₇₃	—	2	8	no	—
311	Q₈×C₇₃	—	2	16	no	—
312	Q₈×C₇₃	—	4	16	no	—
313	D₄×C₇₃	—	2	8	no	—
314	D₄×C₇₃	—	2	8	no	—
315	D₄×C₇₃	—	4	8	no	—
316	D₄×C₇₃	—	4	8	no	—
317	D₄×C₇₃	—	4	16	no	—
318	D₄×C₇₃	—	4	16	no	—
319	D₄×C₇₃	—	4	4	no	—
320	C₂×C₄×C₇₃	—	2	4	no	—
321	C₂×C₄×C₇₃	—	2	2	no	—
322	C₂×C₄×C₇₃	—	2	1	no	—
323	C₂×C₄×C₇₃	—	2	1	no	—
324	C₂×C₄×C₇₃	—	2	1	no	—
325	C₂×C₄×C₇₃	—	2	4	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	1	no	—
328	C₂×C₄×C₇₃	—	2	1	no	—
329	C₂×C₄×C₇₃	—	2	1	no	—
330	C₂×C₄×C₇₃	—	2	1	no	—
331	C₂×C₄×C₇₃	—	2	1	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	4	no	—
334	C₂×C₄×C₇₃	—	2	2	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	2	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	4	no	—
341	C₂×C₄×C₇₃	—	2	1	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	2	no	—
344	C₂×C₄×C₇₃	—	2	1	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	2	1	no	—
348	C₂×C₄×C₇₃	—	2	2	no	—
349	C₂×C₄×C₇₃	—	2	4	no	—
350	C₂×C₄×C₇₃	—	4	16	no	—
351	C₂×C₄×C₇₃	—	4	16	no	—
352	C₂×C₄×C₇₃	—	4	8	no	—
353	C₂×C₄×C₇₃	—	4	8	no	—
354	C₂×C₄×C₇₃	—	4	8	no	—
355	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
359	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
360	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
364	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
365	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
367	C₂²×C₇₃	—	2	4	no	—
368	C₂²×C₇₃	—	2	4	no	—
369	C₂²×C₇₃	—	2	4	no	—
370	C₂²×C₇₃	—	2	4	no	—
371	C₂²×C₇₃	—	2	4	no	—
372	C₂²×C₇₃	—	2	4	no	—
373	C₂²×C₇₃	—	4	2	no	—
374	C₂²×C₇₃	—	4	2	no	—
375	C₂²×C₇₃	—	4	2	no	—
376	C₂²×C₇₃	—	4	2	no	—
377	C₂²×C₇₃	—	4	2	no	—
378	C₂²×C₇₃	—	4	2	no	—
379	C₂²×C₇₃	—	4	2	no	—
380	C₂²×C₇₃	—	4	2	no	—
381	C₂²×C₇₃	—	4	2	no	—
382	C₂²×C₇₃	—	4	2	no	—
383	C₂²×C₇₃	—	4	2	no	—
384	C₂²×C₇₃	—	4	2	no	—
385	C₂²×C₇₃	—	4	2	no	—
386	C₂²×C₇₃	—	4	2	no	—
387	C₂²×C₇₃	—	4	2	no	—
388	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
389	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
390	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
394	C₂²×C₇₃	#585	1	1	yes	characteristic
395	C₄×C₇₃	—	2	8	no	—
396	C₄×C₇₃	—	2	4	no	—
397	C₄×C₇₃	—	2	2	no	—
398	C₄×C₇₃	—	2	2	no	—
399	C₄×C₇₃	—	2	2	no	—
400	C₄×C₇₃	—	2	2	no	—
401	C₄×C₇₃	—	4	2	no	—
402	C₄×C₇₃	—	4	2	no	—
403	C₄×C₇₃	—	4	2	no	—
404	C₄×C₇₃	—	4	4	no	—
405	C₄×C₇₃	—	4	2	no	—
406	C₄×C₇₃	—	4	1	no	—
407	C₄×C₇₃	D₄²	1	4	yes	—
408	C₄×C₇₃	#548	1	4	yes	complemented
409	#59654	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
410	C₂×C₇₃	—	4	4	no	—
411	C₂×C₇₃	—	4	4	no	—
412	C₂×C₇₃	—	8	2	no	—
413	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
414	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
415	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
416	C₂×C₇₃	#3497	1	1	yes	characteristic
417	C₂×C₇₃	#3499	1	1	yes	characteristic
418	C₂×C₇₃	#3520	1	1	yes	characteristic
419	C₂×C₇₃	#3547	1	1	yes	characteristic
420	C₂×D₄×Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
421	C₂×#548	C₂×C₇₃	1	2	yes	complemented
422	C₂×#547	C₂×C₇₃	1	1	yes	characteristic, complemented
423	#2681	C₂×C₇₃	1	4	yes	complemented
424	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
425	#2537	C₂×C₇₃	1	1	yes	characteristic, complemented
426	#2536	C₂×C₇₃	1	2	yes	complemented
427	#2491	C₂×C₇₃	1	2	yes	complemented
428	#2461	C₂×C₇₃	1	4	yes	complemented
429	#2440	C₂×C₇₃	1	2	yes	complemented
430	#2428	C₂×C₇₃	1	2	yes	complemented
431	#2409	C₂×C₇₃	1	2	yes	complemented
432	#2407	C₂×C₇₃	1	2	yes	complemented
433	#2361	C₂×C₇₃	1	2	yes	complemented
434	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
435	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
436	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
437	C₇₃	#59654	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²×#41	C₂²×C₇₃	1	2	yes	—
439	C₂³×Q₈	C₂²×C₇₃	1	2	yes	—
440	D₄×Q₈	—	2	8	no	—
441	#548	—	2	16	no	—
442	#547	—	2	8	no	—
443	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
444	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
445	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
446	C₂×#124	C₂²×C₇₃	1	4	yes	—
447	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
448	C₂×#123	C₂²×C₇₃	1	4	yes	—
449	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
450	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
452	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
454	C₂×#121	C₂²×C₇₃	1	2	yes	—
455	C₂×#121	C₂²×C₇₃	1	2	yes	—
456	C₂×#121	C₂²×C₇₃	1	4	yes	—
457	C₂×#121	C₂²×C₇₃	1	2	yes	—
458	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
459	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
460	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
462	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
464	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
465	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
467	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
468	#398	C₂²×C₇₃	1	4	yes	—
469	#396	C₂²×C₇₃	1	4	yes	—
470	#395	C₂²×C₇₃	1	4	yes	—
471	#394	C₂²×C₇₃	1	4	yes	—
472	#394	C₂²×C₇₃	1	4	yes	—
473	#394	C₂²×C₇₃	1	4	yes	—
474	#393	C₂²×C₇₃	1	4	yes	—
475	#392	C₂²×C₇₃	1	4	yes	—
476	#391	C₂²×C₇₃	1	2	yes	—
477	#391	C₂²×C₇₃	1	1	yes	characteristic
478	#390	C₂²×C₇₃	1	1	yes	characteristic
479	#390	C₂²×C₇₃	1	2	yes	—
480	#390	C₂²×C₇₃	1	2	yes	—
481	#390	C₂²×C₇₃	1	1	yes	characteristic
482	#390	C₂²×C₇₃	1	1	yes	characteristic
483	#390	C₂²×C₇₃	1	2	yes	—
484	#389	C₂²×C₇₃	1	2	yes	—
485	#389	C₂²×C₇₃	1	2	yes	—
486	#389	C₂²×C₇₃	1	2	yes	—
487	#388	C₂²×C₇₃	1	4	yes	—
488	#388	C₂²×C₇₃	1	2	yes	—
489	#388	C₂²×C₇₃	1	2	yes	—
490	#388	C₂²×C₇₃	1	4	yes	—
491	#386	C₂²×C₇₃	1	4	yes	—
492	#386	C₂²×C₇₃	1	4	yes	—
493	#385	C₂²×C₇₃	1	4	yes	—
494	#385	C₂²×C₇₃	1	4	yes	—
495	#384	C₂²×C₇₃	1	1	yes	characteristic
496	#384	C₂²×C₇₃	1	1	yes	characteristic
497	#382	C₂²×C₇₃	1	1	yes	characteristic
498	#380	C₂²×C₇₃	1	2	yes	—
499	#380	C₂²×C₇₃	1	2	yes	—
500	#380	C₂²×C₇₃	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
505	C₄³	C₂²×C₇₃	1	1	yes	characteristic
506	C₂×#41	—	2	8	no	—
507	C₂×#41	—	2	8	no	—
508	C₂×#41	—	4	4	no	—
509	C₂²×Q₈	—	2	8	no	—
510	C₂²×Q₈	—	2	8	no	—
511	C₂²×Q₈	—	4	4	no	—
512	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
513	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
515	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
516	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
517	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
518	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
519	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
520	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
523	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
524	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
525	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
526	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
527	C₄⋊Q₈	—	2	8	no	—
528	C₄⋊Q₈	D₄×C₇₃	1	8	yes	complemented
529	#127	—	2	4	no	—
530	#124	—	2	16	no	—
531	#124	D₄×C₇₃	1	8	yes	complemented
532	#123	—	2	16	no	—
533	C₂²⋊Q₈	—	2	8	no	—
534	C₂²⋊Q₈	—	2	8	no	—
535	C₂²⋊Q₈	—	2	8	no	—
536	C₂²⋊Q₈	—	2	16	no	—
537	C₂²⋊Q₈	—	2	16	no	—
538	#121	—	2	8	no	—
539	#121	—	2	8	no	—
540	#121	—	2	8	no	—
541	#121	—	2	16	no	—
542	C₄×Q₈	—	2	8	no	—
543	C₄×Q₈	—	2	4	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	16	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	4	no	—
548	C₄×D₄	—	2	8	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	4	4	no	—
551	C₂×C₄⋊C₄	—	2	8	no	—
552	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
585	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
587	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
588	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
594	#95	C₂³×C₇₃	1	2	yes	—
595	#95	C₂³×C₇₃	1	2	yes	—
596	#95	C₂³×C₇₃	1	2	yes	—
597	#95	C₂³×C₇₃	1	2	yes	—
598	#95	C₂³×C₇₃	1	4	yes	—
599	#95	C₂³×C₇₃	1	4	yes	—
600	#95	C₂³×C₇₃	1	4	yes	—
601	#95	C₂³×C₇₃	1	4	yes	—
602	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
603	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
604	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
605	#41	—	4	32	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	4	no	—
608	C₂×Q₈	—	2	8	no	—
609	C₂×Q₈	—	2	8	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	4	4	no	—
613	C₂×Q₈	—	4	32	no	—
614	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
615	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	8	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
636	C₂×D₄	#41×C₇₃	1	4	yes	complemented
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	8	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	8	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	4	4	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	8	no	—
668	C₄⋊C₄	—	2	8	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	8	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
681	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
682	C₂²⋊C₄	—	2	8	no	—
683	C₂²⋊C₄	—	2	8	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	8	no	—
691	C₂²⋊C₄	—	2	8	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
698	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
699	C₄²	—	2	8	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	4	1	no	—
706	C₄²	C₂×D₄×C₇₃	1	4	yes	—
707	C₄²	C₂×D₄×C₇₃	1	4	yes	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
728	C₂³	C₂×#41×C₇₃	1	4	yes	—
729	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
730	Q₈	—	2	8	no	—
731	Q₈	—	2	16	no	—
732	Q₈	—	4	16	no	—
733	D₄	—	2	8	no	—
734	D₄	—	2	8	no	—
735	D₄	—	4	16	no	—
736	D₄	—	4	8	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	16	no	—
739	D₄	—	4	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	4	16	no	—
771	C₂×C₄	—	4	16	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
776	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
777	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
779	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
780	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
783	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
784	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
785	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
786	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
809	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
810	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
811	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
812	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
813	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
814	C₂²	#585×C₇₃	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	8	no	—
820	C₄	—	2	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	4	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	D₄²×C₇₃	1	4	yes	—
828	C₄	#548×C₇₃	1	4	yes	complemented
829	C₂	—	4	4	no	—
830	C₂	—	4	4	no	—
831	C₂	—	8	2	no	—
832	C₂	C₂×D₄²×C₇₃	1	1	yes	characteristic
833	C₂	C₂×#548×C₇₃	1	1	yes	characteristic
834	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
835	C₂	C₇₃×#3497	1	1	yes	characteristic
836	C₂	C₇₃×#3499	1	1	yes	characteristic
837	C₂	C₇₃×#3520	1	1	yes	characteristic
838	C₂	C₇₃×#3547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₇₃	C₂	semidirect
2. C₂×#548×C₇₃	C₂	semidirect
3. C₂×#547×C₇₃	C₂	semidirect
4. C₇₃×#2681	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2537	C₂	semidirect
7. C₇₃×#2536	C₂	semidirect
8. C₇₃×#2491	C₂	semidirect
9. C₇₃×#2461	C₂	semidirect
10. C₇₃×#2440	C₂	semidirect
11. C₇₃×#2428	C₂	semidirect
12. C₇₃×#2409	C₂	semidirect
13. C₇₃×#2407	C₂	semidirect
14. C₇₃×#2361	C₂	semidirect
15. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
16. C₄×#127×C₇₃	C₂	semidirect
17. C₄×#124×C₇₃	C₂	semidirect
108. C₄⋊Q₈×C₇₃	D₄	semidirect
111. #124×C₇₃	D₄	semidirect
216. C₂×D₄×C₇₃	#41	semidirect
408. C₄×C₇₃	#548	semidirect
409. #59654	C₇₃	direct (N × H)
420. C₂×D₄×Q₈	C₂×C₇₃	semidirect
421. C₂×#548	C₂×C₇₃	semidirect
422. C₂×#547	C₂×C₇₃	semidirect
423. #2681	C₂×C₇₃	semidirect
424. #2538	C₂×C₇₃	semidirect
425. #2537	C₂×C₇₃	semidirect
426. #2536	C₂×C₇₃	semidirect
427. #2491	C₂×C₇₃	semidirect
428. #2461	C₂×C₇₃	semidirect
429. #2440	C₂×C₇₃	semidirect
430. #2428	C₂×C₇₃	semidirect
431. #2409	C₂×C₇₃	semidirect
432. #2407	C₂×C₇₃	semidirect
433. #2361	C₂×C₇₃	semidirect
434. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
435. C₄×#127	C₂×C₇₃	semidirect
436. C₄×#124	C₂×C₇₃	semidirect
437. C₇₃	#59654	direct (N × H)
528. C₄⋊Q₈	D₄×C₇₃	semidirect
531. #124	D₄×C₇₃	semidirect
636. C₂×D₄	#41×C₇₃	semidirect
828. C₄	#548×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₇₃	2
C₂×#548×C₇₃	2
C₂×#547×C₇₃	2
C₇₃×#2681	2
C₇₃×#2538	2
C₇₃×#2537	2
C₇₃×#2536	2
C₇₃×#2491	2
C₇₃×#2461	2
C₇₃×#2440	2
C₇₃×#2428	2
C₇₃×#2409	2
C₇₃×#2407	2
C₇₃×#2361	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
#59654	73

Subgroups — C73×#59654 #32969058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59654 #32969058