Subgroups — C₂×C₇₃×#3314 #32970530

Order 18688.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#3314	C₂	1	16	yes	maximal, direct product factor
4	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#484×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#480×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#474×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#468×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#467×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#464×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#452×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#450×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#435×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
24	#554×C₇₃	—	2	4	no	—
25	#554×C₇₃	C₂²	1	8	yes	complemented
26	#546×C₇₃	—	2	4	no	—
27	#546×C₇₃	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#125×C₇₃	—	2	1	no	—
30	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#123×C₇₃	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₇₃	—	2	1	no	—
38	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#120×C₇₃	—	2	1	no	—
40	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₇₃	—	2	1	no	—
42	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
47	#489×C₇₃	C₂²	1	8	yes	complemented
48	#484×C₇₃	C₂²	1	8	yes	complemented
49	#480×C₇₃	C₂²	1	8	yes	complemented
50	#474×C₇₃	C₂²	1	8	yes	complemented
51	#468×C₇₃	C₂²	1	8	yes	complemented
52	#467×C₇₃	C₂²	1	8	yes	complemented
53	#464×C₇₃	C₂²	1	8	yes	complemented
54	#452×C₇₃	C₂²	1	8	yes	complemented
55	#450×C₇₃	C₂²	1	8	yes	complemented
56	#440×C₇₃	C₂²	1	8	yes	complemented
57	#435×C₇₃	C₂²	1	8	yes	complemented
58	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
62	#417×C₇₃	C₂²	1	8	yes	complemented
63	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
68	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
69	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
70	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
71	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
72	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
73	C₂×#102×C₇₃	C₂²	1	8	yes	complemented
74	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
75	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₇₃	—	2	1	no	—
78	C₂×#41×C₇₃	—	2	2	no	—
79	C₂×#41×C₇₃	—	2	4	no	—
80	C₂×#41×C₇₃	—	4	2	no	—
81	C₂×#41×C₇₃	C₂³	1	4	yes	—
82	C₂²×Q₈×C₇₃	—	2	1	no	—
83	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₇₃	—	2	4	no	—
86	C₂²×D₄×C₇₃	—	2	1	no	—
87	C₂²×D₄×C₇₃	—	2	1	no	—
88	C₂²×D₄×C₇₃	—	2	1	no	—
89	C₂²×D₄×C₇₃	—	2	2	no	—
90	C₂²×D₄×C₇₃	—	4	2	no	—
91	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
94	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇₃	—	2	1	no	—
96	C₂³×C₄×C₇₃	—	2	1	no	—
97	C₂³×C₄×C₇₃	—	2	1	no	—
98	C₂³×C₄×C₇₃	—	2	1	no	—
99	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
101	C₂×Q₁₆×C₇₃	—	4	2	no	—
102	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	complemented
103	C₂×SD₁₆×C₇₃	—	2	4	no	—
104	C₂×SD₁₆×C₇₃	—	4	2	no	—
105	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
107	C₂×M₁₆×C₇₃	—	4	2	no	—
108	C₂×M₁₆×C₇₃	C₂³	1	4	yes	complemented
109	C₂²×C₈×C₇₃	—	4	2	no	—
110	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₇₃	—	2	2	no	—
116	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	complemented
117	#125×C₇₃	—	2	8	no	—
118	#124×C₇₃	—	2	2	no	—
119	#124×C₇₃	C₂³	1	4	yes	—
120	#123×C₇₃	—	2	8	no	—
121	C₂²⋊Q₈×C₇₃	—	2	2	no	—
122	C₂²⋊Q₈×C₇₃	—	2	2	no	—
123	C₂²⋊Q₈×C₇₃	—	2	2	no	—
124	C₂²⋊Q₈×C₇₃	—	2	8	no	—
125	C₂²⋊Q₈×C₇₃	—	2	8	no	—
126	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
127	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	complemented
129	#121×C₇₃	—	2	2	no	—
130	#121×C₇₃	—	2	8	no	—
131	#121×C₇₃	C₂³	1	4	yes	—
132	#120×C₇₃	—	2	8	no	—
133	C₄×Q₈×C₇₃	—	2	2	no	—
134	C₄×Q₈×C₇₃	C₂³	1	4	yes	complemented
135	C₄×D₄×C₇₃	—	2	8	no	—
136	C₄×D₄×C₇₃	—	2	2	no	—
137	C₄×D₄×C₇₃	D₄	1	4	yes	—
138	C₄×D₄×C₇₃	C₂³	1	4	yes	—
139	C₄×D₄×C₇₃	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	complemented
156	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
164	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₇₃	—	2	1	no	—
167	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
168	#107×C₇₃	C₂³	1	4	yes	complemented
169	#107×C₇₃	C₂³	1	4	yes	complemented
170	#107×C₇₃	C₂³	1	4	yes	complemented
171	C₄⋊C₈×C₇₃	C₂³	1	4	yes	complemented
172	#103×C₇₃	C₂³	1	4	yes	complemented
173	#103×C₇₃	C₂³	1	4	yes	complemented
174	#103×C₇₃	C₂³	1	4	yes	complemented
175	#103×C₇₃	C₂³	1	4	yes	complemented
176	#102×C₇₃	C₂³	1	4	yes	—
177	#102×C₇₃	C₂³	1	4	yes	—
178	#102×C₇₃	C₂³	1	4	yes	—
179	#102×C₇₃	C₂³	1	4	yes	—
180	#102×C₇₃	C₂³	1	4	yes	—
181	#102×C₇₃	C₂³	1	4	yes	—
182	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
183	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	complemented
184	#97×C₇₃	C₂³	1	4	yes	complemented
185	C₂⁴×C₇₃	—	2	1	no	—
186	C₂⁴×C₇₃	—	2	1	no	—
187	C₂⁴×C₇₃	—	2	4	no	—
188	C₂⁴×C₇₃	—	4	4	no	—
189	C₂⁴×C₇₃	—	4	4	no	—
190	C₂⁴×C₇₃	—	8	2	no	—
191	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
193	#41×C₇₃	—	2	8	no	—
194	#41×C₇₃	—	4	4	no	—
195	#41×C₇₃	—	4	8	no	—
196	C₂×Q₈×C₇₃	—	2	1	no	—
197	C₂×Q₈×C₇₃	—	2	1	no	—
198	C₂×Q₈×C₇₃	—	2	4	no	—
199	C₂×Q₈×C₇₃	—	2	2	no	—
200	C₂×Q₈×C₇₃	—	2	2	no	—
201	C₂×Q₈×C₇₃	—	2	2	no	—
202	C₂×Q₈×C₇₃	—	2	2	no	—
203	C₂×Q₈×C₇₃	—	8	2	no	—
204	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
205	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
206	C₂×D₄×C₇₃	—	2	4	no	—
207	C₂×D₄×C₇₃	—	2	8	no	—
208	C₂×D₄×C₇₃	—	2	4	no	—
209	C₂×D₄×C₇₃	—	2	4	no	—
210	C₂×D₄×C₇₃	—	2	1	no	—
211	C₂×D₄×C₇₃	—	2	4	no	—
212	C₂×D₄×C₇₃	—	2	1	no	—
213	C₂×D₄×C₇₃	—	2	2	no	—
214	C₂×D₄×C₇₃	—	2	2	no	—
215	C₂×D₄×C₇₃	—	2	2	no	—
216	C₂×D₄×C₇₃	—	4	4	no	—
217	C₂×D₄×C₇₃	—	4	8	no	—
218	C₂×D₄×C₇₃	—	4	4	no	—
219	C₂×D₄×C₇₃	—	4	4	no	—
220	C₂×D₄×C₇₃	—	8	2	no	—
221	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₇₃	#41	1	4	yes	—
223	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₇₃	—	2	2	no	—
226	C₂²×C₄×C₇₃	—	2	2	no	—
227	C₂²×C₄×C₇₃	—	2	2	no	—
228	C₂²×C₄×C₇₃	—	2	2	no	—
229	C₂²×C₄×C₇₃	—	2	1	no	—
230	C₂²×C₄×C₇₃	—	2	1	no	—
231	C₂²×C₄×C₇₃	—	2	1	no	—
232	C₂²×C₄×C₇₃	—	2	1	no	—
233	C₂²×C₄×C₇₃	—	2	1	no	—
234	C₂²×C₄×C₇₃	—	2	1	no	—
235	C₂²×C₄×C₇₃	—	2	4	no	—
236	C₂²×C₄×C₇₃	—	2	4	no	—
237	C₂²×C₄×C₇₃	—	2	4	no	—
238	C₂²×C₄×C₇₃	—	2	4	no	—
239	C₂²×C₄×C₇₃	—	4	4	no	—
240	C₂²×C₄×C₇₃	—	8	2	no	—
241	C₂²×C₄×C₇₃	—	8	2	no	—
242	C₂²×C₄×C₇₃	—	8	2	no	—
243	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
252	Q₁₆×C₇₃	—	4	4	no	—
253	SD₁₆×C₇₃	—	2	8	no	—
254	SD₁₆×C₇₃	—	4	4	no	—
255	M₁₆×C₇₃	—	4	4	no	—
256	C₂×C₈×C₇₃	—	2	2	no	—
257	C₂×C₈×C₇₃	—	2	2	no	—
258	C₂×C₈×C₇₃	—	2	2	no	—
259	C₂×C₈×C₇₃	—	2	2	no	—
260	C₂×C₈×C₇₃	—	4	4	no	—
261	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₇₃	—	2	1	no	—
266	C₄⋊C₄×C₇₃	—	2	4	no	—
267	C₄⋊C₄×C₇₃	—	2	1	no	—
268	C₄⋊C₄×C₇₃	—	2	1	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	4	no	—
271	C₄⋊C₄×C₇₃	—	2	4	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	2	1	no	—
276	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₇₃	—	2	4	no	—
282	C₂²⋊C₄×C₇₃	—	2	4	no	—
283	C₂²⋊C₄×C₇₃	—	2	4	no	—
284	C₂²⋊C₄×C₇₃	—	2	4	no	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	—	2	4	no	—
288	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
290	C₄²×C₇₃	—	2	4	no	—
291	C₄²×C₇₃	C₂×D₄	1	2	yes	—
292	C₄²×C₇₃	C₂⁴	1	2	yes	—
293	C₂³×C₇₃	—	2	2	no	—
294	C₂³×C₇₃	—	2	2	no	—
295	C₂³×C₇₃	—	2	2	no	—
296	C₂³×C₇₃	—	2	4	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	—	4	8	no	—
302	C₂³×C₇₃	—	4	2	no	—
303	C₂³×C₇₃	—	4	2	no	—
304	C₂³×C₇₃	—	4	2	no	—
305	C₂³×C₇₃	—	4	8	no	—
306	C₂³×C₇₃	—	4	2	no	—
307	C₂³×C₇₃	—	4	2	no	—
308	C₂³×C₇₃	—	8	4	no	—
309	C₂³×C₇₃	—	8	16	no	—
310	C₂³×C₇₃	#137	1	4	yes	—
311	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
312	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
313	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₇₃	—	2	2	no	—
315	Q₈×C₇₃	—	2	2	no	—
316	Q₈×C₇₃	—	2	2	no	—
317	Q₈×C₇₃	—	2	2	no	—
318	Q₈×C₇₃	—	4	2	no	—
319	Q₈×C₇₃	—	4	2	no	—
320	Q₈×C₇₃	—	8	4	no	—
321	D₄×C₇₃	—	2	8	no	—
322	D₄×C₇₃	—	2	4	no	—
323	D₄×C₇₃	—	2	2	no	—
324	D₄×C₇₃	—	2	2	no	—
325	D₄×C₇₃	—	2	2	no	—
326	D₄×C₇₃	—	4	8	no	—
327	D₄×C₇₃	—	4	8	no	—
328	D₄×C₇₃	—	4	2	no	—
329	D₄×C₇₃	—	8	4	no	—
330	D₄×C₇₃	C₂×#41	1	4	yes	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	2	no	—
334	C₂×C₄×C₇₃	—	2	2	no	—
335	C₂×C₄×C₇₃	—	2	4	no	—
336	C₂×C₄×C₇₃	—	2	4	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	2	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	2	no	—
344	C₂×C₄×C₇₃	—	2	2	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	4	8	no	—
348	C₂×C₄×C₇₃	—	4	2	no	—
349	C₂×C₄×C₇₃	—	4	2	no	—
350	C₂×C₄×C₇₃	—	4	2	no	—
351	C₂×C₄×C₇₃	—	4	2	no	—
352	C₂×C₄×C₇₃	—	4	2	no	—
353	C₂×C₄×C₇₃	—	4	2	no	—
354	C₂×C₄×C₇₃	—	8	4	no	—
355	C₂×C₄×C₇₃	—	8	4	no	—
356	C₂×C₄×C₇₃	—	8	4	no	—
357	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
363	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
364	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
365	C₈×C₇₃	—	2	2	no	—
366	C₈×C₇₃	—	2	2	no	—
367	C₈×C₇₃	—	2	2	no	—
368	C₈×C₇₃	—	2	2	no	—
369	C₂²×C₇₃	—	2	2	no	—
370	C₂²×C₇₃	—	2	8	no	—
371	C₂²×C₇₃	—	2	2	no	—
372	C₂²×C₇₃	—	2	2	no	—
373	C₂²×C₇₃	—	2	4	no	—
374	C₂²×C₇₃	—	2	2	no	—
375	C₂²×C₇₃	—	2	2	no	—
376	C₂²×C₇₃	—	4	4	no	—
377	C₂²×C₇₃	—	4	8	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	—	8	16	no	—
384	C₂²×C₇₃	—	8	4	no	—
385	C₂²×C₇₃	#546	1	2	yes	—
386	C₂²×C₇₃	C₂×#137	1	4	yes	—
387	C₂²×C₇₃	C₂×#137	1	2	yes	—
388	C₂²×C₇₃	#576	1	2	yes	—
389	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
390	C₄×C₇₃	—	2	2	no	—
391	C₄×C₇₃	—	2	2	no	—
392	C₄×C₇₃	—	2	2	no	—
393	C₄×C₇₃	—	2	2	no	—
394	C₄×C₇₃	—	4	2	no	—
395	C₄×C₇₃	—	4	2	no	—
396	C₄×C₇₃	—	4	2	no	—
397	C₄×C₇₃	—	4	2	no	—
398	C₄×C₇₃	—	4	2	no	—
399	C₄×C₇₃	—	4	2	no	—
400	C₄×C₇₃	#546	1	2	yes	—
401	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
402	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×#3314	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₇₃	—	2	4	no	—
405	C₂×C₇₃	—	4	2	no	—
406	C₂×C₇₃	—	4	4	no	—
407	C₂×C₇₃	—	8	2	no	—
408	C₂×C₇₃	#3314	1	4	yes	direct product factor
409	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
410	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
411	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
412	C₂×#554	C₂×C₇₃	1	1	yes	characteristic, complemented
413	C₂×#546	C₂×C₇₃	1	1	yes	characteristic
414	#3314	C₂×C₇₃	1	16	yes	direct product factor
415	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
416	C₂×#484	C₂×C₇₃	1	1	yes	characteristic, complemented
417	C₂×#480	C₂×C₇₃	1	1	yes	characteristic, complemented
418	C₂×#474	C₂×C₇₃	1	1	yes	characteristic, complemented
419	C₂×#468	C₂×C₇₃	1	1	yes	characteristic, complemented
420	C₂×#467	C₂×C₇₃	1	1	yes	characteristic, complemented
421	C₂×#464	C₂×C₇₃	1	1	yes	characteristic, complemented
422	C₂×#452	C₂×C₇₃	1	1	yes	characteristic, complemented
423	C₂×#450	C₂×C₇₃	1	1	yes	characteristic, complemented
424	C₂×#440	C₂×C₇₃	1	1	yes	characteristic, complemented
425	C₂×#435	C₂×C₇₃	1	1	yes	characteristic, complemented
426	C₂×#417	C₂×C₇₃	1	1	yes	characteristic, complemented
427	C₂²×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
428	C₇₃	C₂×#3314	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
430	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
431	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
432	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
433	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
434	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
435	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
436	#554	—	2	4	no	—
437	#554	C₂²×C₇₃	1	8	yes	complemented
438	#546	—	2	4	no	—
439	#546	C₂²×C₇₃	1	8	yes	—
440	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
441	C₂×#125	—	2	1	no	—
442	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
443	C₂×#123	—	2	1	no	—
444	C₂×C₂²⋊Q₈	—	2	1	no	—
445	C₂×C₂²⋊Q₈	—	2	1	no	—
446	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
447	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
448	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
449	C₂×#121	—	2	1	no	—
450	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
451	C₂×#120	—	2	1	no	—
452	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
453	C₂×C₄×D₄	—	2	1	no	—
454	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
458	C₂²×C₂²⋊C₄	—	2	1	no	—
459	#489	C₂²×C₇₃	1	8	yes	complemented
460	#484	C₂²×C₇₃	1	8	yes	complemented
461	#480	C₂²×C₇₃	1	8	yes	complemented
462	#474	C₂²×C₇₃	1	8	yes	complemented
463	#468	C₂²×C₇₃	1	8	yes	complemented
464	#467	C₂²×C₇₃	1	8	yes	complemented
465	#464	C₂²×C₇₃	1	8	yes	complemented
466	#452	C₂²×C₇₃	1	8	yes	complemented
467	#450	C₂²×C₇₃	1	8	yes	complemented
468	#440	C₂²×C₇₃	1	8	yes	complemented
469	#435	C₂²×C₇₃	1	8	yes	complemented
470	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
471	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
472	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
473	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
474	#417	C₂²×C₇₃	1	8	yes	complemented
475	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
476	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
477	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
478	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
479	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
480	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
481	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
482	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
484	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
485	C₂×#102	C₂²×C₇₃	1	8	yes	complemented
486	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
488	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic, complemented
489	C₂⁵	—	2	1	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	4	no	—
492	C₂×#41	—	4	2	no	—
493	C₂×#41	C₂³×C₇₃	1	4	yes	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	4	2	no	—
503	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
506	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
513	C₂×Q₁₆	—	4	2	no	—
514	C₂×Q₁₆	C₂³×C₇₃	1	4	yes	complemented
515	C₂×SD₁₆	—	2	4	no	—
516	C₂×SD₁₆	—	4	2	no	—
517	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
518	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
519	C₂×M₁₆	—	4	2	no	—
520	C₂×M₁₆	C₂³×C₇₃	1	4	yes	complemented
521	C₂²×C₈	—	4	2	no	—
522	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	complemented
529	#125	—	2	8	no	—
530	#124	—	2	2	no	—
531	#124	C₂³×C₇₃	1	4	yes	—
532	#123	—	2	8	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	8	no	—
537	C₂²⋊Q₈	—	2	8	no	—
538	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	—
539	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	complemented
541	#121	—	2	2	no	—
542	#121	—	2	8	no	—
543	#121	C₂³×C₇₃	1	4	yes	—
544	#120	—	2	8	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	C₂³×C₇₃	1	4	yes	complemented
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	D₄×C₇₃	1	4	yes	—
550	C₄×D₄	C₂³×C₇₃	1	4	yes	—
551	C₄×D₄	C₂³×C₇₃	1	4	yes	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	complemented
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	8	no	—
576	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
580	#107	C₂³×C₇₃	1	4	yes	complemented
581	#107	C₂³×C₇₃	1	4	yes	complemented
582	#107	C₂³×C₇₃	1	4	yes	complemented
583	C₄⋊C₈	C₂³×C₇₃	1	4	yes	complemented
584	#103	C₂³×C₇₃	1	4	yes	complemented
585	#103	C₂³×C₇₃	1	4	yes	complemented
586	#103	C₂³×C₇₃	1	4	yes	complemented
587	#103	C₂³×C₇₃	1	4	yes	complemented
588	#102	C₂³×C₇₃	1	4	yes	—
589	#102	C₂³×C₇₃	1	4	yes	—
590	#102	C₂³×C₇₃	1	4	yes	—
591	#102	C₂³×C₇₃	1	4	yes	—
592	#102	C₂³×C₇₃	1	4	yes	—
593	#102	C₂³×C₇₃	1	4	yes	—
594	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
595	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	complemented
596	#97	C₂³×C₇₃	1	4	yes	complemented
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	1	no	—
599	C₂⁴	—	2	4	no	—
600	C₂⁴	—	4	4	no	—
601	C₂⁴	—	4	4	no	—
602	C₂⁴	—	8	2	no	—
603	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
605	#41	—	2	8	no	—
606	#41	—	4	4	no	—
607	#41	—	4	8	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	2	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	8	2	no	—
616	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	8	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	8	2	no	—
633	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
634	C₂×D₄	#41×C₇₃	1	4	yes	—
635	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
636	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	8	2	no	—
653	C₂²×C₄	—	8	2	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
660	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
664	Q₁₆	—	4	4	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	4	4	no	—
667	M₁₆	—	4	4	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	4	4	no	—
673	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
676	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
689	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
701	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
702	C₄²	—	2	4	no	—
703	C₄²	C₂×D₄×C₇₃	1	2	yes	—
704	C₄²	C₂⁴×C₇₃	1	2	yes	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	16	no	—
722	C₂³	#137×C₇₃	1	4	yes	—
723	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
724	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
725	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	2	no	—
731	Q₈	—	4	2	no	—
732	Q₈	—	8	4	no	—
733	D₄	—	2	8	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	2	no	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	2	no	—
741	D₄	—	8	4	no	—
742	D₄	C₂×#41×C₇₃	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	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	—	4	8	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	2	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
771	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
772	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
774	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
775	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
776	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	8	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	8	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	8	16	no	—
796	C₂²	—	8	4	no	—
797	C₂²	#546×C₇₃	1	2	yes	—
798	C₂²	C₂×#137×C₇₃	1	4	yes	—
799	C₂²	C₂×#137×C₇₃	1	2	yes	—
800	C₂²	#576×C₇₃	1	2	yes	—
801	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	#546×C₇₃	1	2	yes	—
813	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
814	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
815	C₂	—	2	4	no	—
816	C₂	—	4	2	no	—
817	C₂	—	4	4	no	—
818	C₂	—	8	2	no	—
819	C₂	C₇₃×#3314	1	4	yes	direct product factor
820	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
821	C₂	C₂²×#137×C₇₃	1	1	yes	characteristic
822	C₂	C₂×#576×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₂×#546×C₇₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₇₃	C₂	semidirect
3. C₇₃×#3314	C₂	direct (N × H)
4. C₂×#489×C₇₃	C₂	semidirect
5. C₂×#484×C₇₃	C₂	semidirect
6. C₂×#480×C₇₃	C₂	semidirect
7. C₂×#474×C₇₃	C₂	semidirect
8. C₂×#468×C₇₃	C₂	semidirect
9. C₂×#467×C₇₃	C₂	semidirect
10. C₂×#464×C₇₃	C₂	semidirect
11. C₂×#452×C₇₃	C₂	semidirect
12. C₂×#450×C₇₃	C₂	semidirect
13. C₂×#440×C₇₃	C₂	semidirect
14. C₂×#435×C₇₃	C₂	semidirect
15. C₂×#417×C₇₃	C₂	semidirect
16. C₂²×#102×C₇₃	C₂	semidirect
19. C₂²×Q₁₆×C₇₃	C₂²	semidirect
22. C₂²×M₁₆×C₇₃	C₂²	semidirect
25. #554×C₇₃	C₂²	semidirect
28. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
40. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₇₃	C₂²	semidirect
47. #489×C₇₃	C₂²	semidirect
48. #484×C₇₃	C₂²	semidirect
49. #480×C₇₃	C₂²	semidirect
50. #474×C₇₃	C₂²	semidirect
51. #468×C₇₃	C₂²	semidirect
52. #467×C₇₃	C₂²	semidirect
53. #464×C₇₃	C₂²	semidirect
54. #452×C₇₃	C₂²	semidirect
55. #450×C₇₃	C₂²	semidirect
56. #440×C₇₃	C₂²	semidirect
57. #435×C₇₃	C₂²	semidirect
58. C₂×#107×C₇₃	C₂²	semidirect
59. C₂×#107×C₇₃	C₂²	semidirect
60. C₂×#107×C₇₃	C₂²	semidirect
61. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
62. #417×C₇₃	C₂²	semidirect
63. C₂×#103×C₇₃	C₂²	semidirect
64. C₂×#103×C₇₃	C₂²	semidirect
65. C₂×#103×C₇₃	C₂²	semidirect
66. C₂×#103×C₇₃	C₂²	semidirect
73. C₂×#102×C₇₃	C₂²	semidirect
75. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
76. C₂×#97×C₇₃	C₂²	semidirect
102. C₂×Q₁₆×C₇₃	C₂³	semidirect
108. C₂×M₁₆×C₇₃	C₂³	semidirect
116. C₄⋊Q₈×C₇₃	C₂³	semidirect
128. C₂²⋊Q₈×C₇₃	C₂³	semidirect
134. C₄×Q₈×C₇₃	C₂³	semidirect
155. C₂×C₄⋊C₄×C₇₃	C₂³	semidirect
168. #107×C₇₃	C₂³	semidirect
169. #107×C₇₃	C₂³	semidirect
170. #107×C₇₃	C₂³	semidirect
171. C₄⋊C₈×C₇₃	C₂³	semidirect
172. #103×C₇₃	C₂³	semidirect
173. #103×C₇₃	C₂³	semidirect
174. #103×C₇₃	C₂³	semidirect
175. #103×C₇₃	C₂³	semidirect
183. C₂²⋊C₈×C₇₃	C₂³	semidirect
184. #97×C₇₃	C₂³	semidirect
403. C₂×#3314	C₇₃	direct (N × H)
408. C₂×C₇₃	#3314	direct (N × H)
412. C₂×#554	C₂×C₇₃	semidirect
414. #3314	C₂×C₇₃	direct (N × H)
415. C₂×#489	C₂×C₇₃	semidirect
416. C₂×#484	C₂×C₇₃	semidirect
417. C₂×#480	C₂×C₇₃	semidirect
418. C₂×#474	C₂×C₇₃	semidirect
419. C₂×#468	C₂×C₇₃	semidirect
420. C₂×#467	C₂×C₇₃	semidirect
421. C₂×#464	C₂×C₇₃	semidirect
422. C₂×#452	C₂×C₇₃	semidirect
423. C₂×#450	C₂×C₇₃	semidirect
424. C₂×#440	C₂×C₇₃	semidirect
425. C₂×#435	C₂×C₇₃	semidirect
426. C₂×#417	C₂×C₇₃	semidirect
427. C₂²×#102	C₂×C₇₃	semidirect
428. C₇₃	C₂×#3314	direct (N × H)
431. C₂²×Q₁₆	C₂²×C₇₃	semidirect
434. C₂²×M₁₆	C₂²×C₇₃	semidirect
437. #554	C₂²×C₇₃	semidirect
440. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
448. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
452. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
457. C₂²×C₄⋊C₄	C₂²×C₇₃	semidirect
459. #489	C₂²×C₇₃	semidirect
460. #484	C₂²×C₇₃	semidirect
461. #480	C₂²×C₇₃	semidirect
462. #474	C₂²×C₇₃	semidirect
463. #468	C₂²×C₇₃	semidirect
464. #467	C₂²×C₇₃	semidirect
465. #464	C₂²×C₇₃	semidirect
466. #452	C₂²×C₇₃	semidirect
467. #450	C₂²×C₇₃	semidirect
468. #440	C₂²×C₇₃	semidirect
469. #435	C₂²×C₇₃	semidirect
470. C₂×#107	C₂²×C₇₃	semidirect
471. C₂×#107	C₂²×C₇₃	semidirect
472. C₂×#107	C₂²×C₇₃	semidirect
473. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
474. #417	C₂²×C₇₃	semidirect
475. C₂×#103	C₂²×C₇₃	semidirect
476. C₂×#103	C₂²×C₇₃	semidirect
477. C₂×#103	C₂²×C₇₃	semidirect
478. C₂×#103	C₂²×C₇₃	semidirect
485. C₂×#102	C₂²×C₇₃	semidirect
487. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
488. C₂×#97	C₂²×C₇₃	semidirect
514. C₂×Q₁₆	C₂³×C₇₃	semidirect
520. C₂×M₁₆	C₂³×C₇₃	semidirect
528. C₄⋊Q₈	C₂³×C₇₃	semidirect
540. C₂²⋊Q₈	C₂³×C₇₃	semidirect
546. C₄×Q₈	C₂³×C₇₃	semidirect
567. C₂×C₄⋊C₄	C₂³×C₇₃	semidirect
580. #107	C₂³×C₇₃	semidirect
581. #107	C₂³×C₇₃	semidirect
582. #107	C₂³×C₇₃	semidirect
583. C₄⋊C₈	C₂³×C₇₃	semidirect
584. #103	C₂³×C₇₃	semidirect
585. #103	C₂³×C₇₃	semidirect
586. #103	C₂³×C₇₃	semidirect
587. #103	C₂³×C₇₃	semidirect
595. C₂²⋊C₈	C₂³×C₇₃	semidirect
596. #97	C₂³×C₇₃	semidirect
819. C₂	C₇₃×#3314	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#554×C₇₃	2
C₂×#546×C₇₃	2
C₇₃×#3314	2
C₂×#489×C₇₃	2
C₂×#484×C₇₃	2
C₂×#480×C₇₃	2
C₂×#474×C₇₃	2
C₂×#468×C₇₃	2
C₂×#467×C₇₃	2
C₂×#464×C₇₃	2
C₂×#452×C₇₃	2
C₂×#450×C₇₃	2
C₂×#440×C₇₃	2
C₂×#435×C₇₃	2
C₂×#417×C₇₃	2
C₂²×#102×C₇₃	2
C₂×#3314	73

Subgroups — C2×C73×#3314 #32970530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3314 #32970530