Subgroups — C₄×#551×C₆₇ #30713413

Order 17152.

2732 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2374	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2372	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2343	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
11	C₄×#126×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic
17	C₄²×D₄×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#117×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	#551×C₆₇	C₄	1	16	yes	direct product factor
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂×#117×C₆₇	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
37	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
39	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#391×C₆₇	C₂²	1	2	yes	complemented
41	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#390×C₆₇	C₂²	1	1	yes	characteristic
43	#389×C₆₇	C₂²	1	2	yes	complemented
44	#388×C₆₇	C₂²	1	2	yes	—
45	#388×C₆₇	C₂²	1	2	yes	—
46	#388×C₆₇	C₂²	1	2	yes	—
47	#388×C₆₇	C₂²	1	2	yes	—
48	#388×C₆₇	C₂²	1	2	yes	—
49	#388×C₆₇	C₂²	1	2	yes	complemented
50	#388×C₆₇	C₂²	1	2	yes	complemented
51	#388×C₆₇	C₂²	1	2	yes	complemented
52	#387×C₆₇	C₂²	1	2	yes	complemented
53	#387×C₆₇	C₂²	1	2	yes	complemented
54	#387×C₆₇	C₂²	1	2	yes	complemented
55	#387×C₆₇	C₂²	1	2	yes	complemented
56	#387×C₆₇	C₂²	1	2	yes	complemented
57	#387×C₆₇	C₂²	1	2	yes	complemented
58	#387×C₆₇	C₂²	1	2	yes	complemented
59	#387×C₆₇	C₂²	1	2	yes	complemented
60	#386×C₆₇	C₂²	1	2	yes	—
61	#386×C₆₇	C₂²	1	1	yes	characteristic
62	#386×C₆₇	C₂²	1	2	yes	—
63	#386×C₆₇	C₂²	1	1	yes	characteristic
64	#385×C₆₇	C₂²	1	2	yes	—
65	#385×C₆₇	C₂²	1	1	yes	characteristic
66	#385×C₆₇	C₂²	1	2	yes	—
67	#385×C₆₇	C₂²	1	2	yes	—
68	#385×C₆₇	C₂²	1	2	yes	—
69	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#383×C₆₇	C₂²	1	2	yes	complemented
71	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#381×C₆₇	C₂²	1	2	yes	—
73	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#380×C₆₇	C₂²	1	2	yes	—
75	#379×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
78	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
82	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
83	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
85	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
86	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
87	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
88	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
89	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
90	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
91	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#376×C₆₇	C₂²	1	2	yes	complemented
103	#376×C₆₇	C₂²	1	2	yes	complemented
104	C₂×#95×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₄³×C₆₇	C₂²	1	2	yes	complemented
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	—	2	8	no	—
113	C₂³×C₄×C₆₇	—	4	2	no	—
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	#126×C₆₇	C₂×C₄	1	16	yes	complemented
126	#124×C₆₇	C₂×C₄	1	8	yes	complemented
127	#123×C₆₇	C₂×C₄	1	8	yes	complemented
128	#123×C₆₇	C₂×C₄	1	16	yes	complemented
129	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
130	#120×C₆₇	C₂×C₄	1	8	yes	—
131	C₄×Q₈×C₆₇	—	4	2	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	C₄×D₄×C₆₇	—	2	8	no	—
134	C₄×D₄×C₆₇	—	4	2	no	—
135	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
136	#117×C₆₇	—	2	8	no	—
137	#117×C₆₇	C₂×C₄	1	16	yes	complemented
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
151	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₇	—	2	8	no	—
173	C₂×C₄²×C₆₇	—	4	4	no	—
174	C₂×C₄²×C₆₇	—	4	2	no	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	C₂⁴×C₆₇	—	2	4	no	—
216	C₂⁴×C₆₇	—	2	4	no	—
217	C₂⁴×C₆₇	—	4	1	no	—
218	C₂⁴×C₆₇	—	4	1	no	—
219	C₂⁴×C₆₇	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₆₇	—	4	1	no	—
224	C₂×Q₈×C₆₇	—	4	1	no	—
225	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	complemented
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	4	1	no	—
229	C₂×D₄×C₆₇	—	4	1	no	—
230	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
231	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	4	1	no	—
249	C₂²×C₄×C₆₇	—	4	1	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	1	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	1	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	16	no	—
258	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
259	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
260	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
261	C₂²×C₄×C₆₇	#41	1	8	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	1	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	1	no	—
286	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
287	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
288	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
289	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	4	1	no	—
298	C₂²⋊C₄×C₆₇	—	4	1	no	—
299	C₂²⋊C₄×C₆₇	—	4	1	no	—
300	C₂²⋊C₄×C₆₇	—	4	1	no	—
301	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
302	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
303	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
304	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
305	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
306	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
307	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	complemented
308	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	complemented
309	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
310	C₄²×C₆₇	—	2	4	no	—
311	C₄²×C₆₇	—	2	4	no	—
312	C₄²×C₆₇	—	2	4	no	—
313	C₄²×C₆₇	—	2	4	no	—
314	C₄²×C₆₇	—	2	4	no	—
315	C₄²×C₆₇	—	2	4	no	—
316	C₄²×C₆₇	—	2	4	no	—
317	C₄²×C₆₇	—	2	4	no	—
318	C₄²×C₆₇	—	2	4	no	—
319	C₄²×C₆₇	—	2	4	no	—
320	C₄²×C₆₇	—	2	2	no	—
321	C₄²×C₆₇	—	4	2	no	—
322	C₄²×C₆₇	—	4	2	no	—
323	C₄²×C₆₇	—	4	2	no	—
324	C₄²×C₆₇	—	4	1	no	—
325	C₄²×C₆₇	—	4	2	no	—
326	C₄²×C₆₇	C₂²×C₄	1	4	yes	complemented
327	C₄²×C₆₇	C₂²×C₄	1	8	yes	complemented
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	16	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	2	1	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	1	no	—
341	C₂³×C₆₇	—	4	4	no	—
342	C₂³×C₆₇	—	4	4	no	—
343	C₂³×C₆₇	—	4	8	no	—
344	C₂³×C₆₇	—	4	4	no	—
345	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
346	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
347	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
348	C₂³×C₆₇	C₂×#41	1	4	yes	—
349	C₂³×C₆₇	C₂×#41	1	4	yes	—
350	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
351	Q₈×C₆₇	—	4	4	no	—
352	D₄×C₆₇	—	2	16	no	—
353	D₄×C₆₇	—	4	4	no	—
354	C₂×C₄×C₆₇	—	2	16	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	16	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	1	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	4	8	no	—
390	C₂×C₄×C₆₇	—	4	4	no	—
391	C₂×C₄×C₆₇	—	4	4	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	8	no	—
394	C₂×C₄×C₆₇	—	4	8	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	—	4	4	no	—
397	C₂×C₄×C₆₇	—	4	4	no	—
398	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
399	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
401	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
402	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
403	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
405	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
406	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
407	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
408	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₆₇	—	2	4	no	—
410	C₂²×C₆₇	—	2	4	no	—
411	C₂²×C₆₇	—	2	4	no	—
412	C₂²×C₆₇	—	2	4	no	—
413	C₂²×C₆₇	—	2	4	no	—
414	C₂²×C₆₇	—	2	4	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	2	no	—
418	C₂²×C₆₇	—	2	2	no	—
419	C₂²×C₆₇	—	4	16	no	—
420	C₂²×C₆₇	—	4	1	no	—
421	C₂²×C₆₇	—	4	1	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	1	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	C₄×#41	1	8	yes	—
427	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
428	C₂²×C₆₇	C₂²×#41	1	2	yes	—
429	C₂²×C₆₇	C₂²×#41	1	2	yes	—
430	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₆₇	#585	1	1	yes	characteristic
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	4	no	—
434	C₄×C₆₇	—	2	4	no	—
435	C₄×C₆₇	—	2	4	no	—
436	C₄×C₆₇	—	2	4	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	4	no	—
439	C₄×C₆₇	—	2	4	no	—
440	C₄×C₆₇	—	2	4	no	—
441	C₄×C₆₇	—	4	1	no	—
442	C₄×C₆₇	—	4	1	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	1	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	#551	1	4	yes	direct product factor
448	C₄×#551	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂×C₆₇	—	2	8	no	—
450	C₂×C₆₇	—	4	2	no	—
451	C₂×C₆₇	—	4	2	no	—
452	C₂×C₆₇	C₂×C₄×#41	1	2	yes	—
453	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
455	C₂×C₆₇	#3475	1	2	yes	—
456	C₂×C₆₇	#3481	1	1	yes	characteristic
457	C₂×#551	C₂×C₆₇	1	1	yes	characteristic
458	#2374	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2373	C₂×C₆₇	1	2	yes	complemented
460	#2372	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2368	C₂×C₆₇	1	2	yes	complemented
462	#2359	C₂×C₆₇	1	2	yes	complemented
463	#2358	C₂×C₆₇	1	1	yes	characteristic
464	#2353	C₂×C₆₇	1	2	yes	complemented
465	#2343	C₂×C₆₇	1	2	yes	complemented
466	#2342	C₂×C₆₇	1	2	yes	complemented
467	C₄×#126	C₂×C₆₇	1	2	yes	complemented
468	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
469	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
470	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
471	C₄×#123	C₂×C₆₇	1	2	yes	complemented
472	C₄×#120	C₂×C₆₇	1	1	yes	characteristic
473	C₄²×D₄	C₂×C₆₇	1	2	yes	complemented
474	C₄×#117	C₂×C₆₇	1	2	yes	complemented
475	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
476	C₆₇	C₄×#551	1	1	yes	characteristic, direct product factor, Sylow
477	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
478	#551	C₄×C₆₇	1	16	yes	direct product factor
479	C₂×#126	C₂²×C₆₇	1	2	yes	—
480	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×#123	C₂²×C₆₇	1	2	yes	—
482	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
484	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
485	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
488	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
490	C₂×#117	C₂²×C₆₇	1	2	yes	—
491	C₂×#117	C₂²×C₆₇	1	2	yes	—
492	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
493	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
494	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
495	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
496	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#391	C₂²×C₆₇	1	2	yes	complemented
499	#390	C₂²×C₆₇	1	1	yes	characteristic
500	#389	C₂²×C₆₇	1	2	yes	complemented
501	#388	C₂²×C₆₇	1	2	yes	—
502	#388	C₂²×C₆₇	1	2	yes	—
503	#388	C₂²×C₆₇	1	2	yes	—
504	#388	C₂²×C₆₇	1	2	yes	—
505	#388	C₂²×C₆₇	1	2	yes	—
506	#388	C₂²×C₆₇	1	2	yes	complemented
507	#388	C₂²×C₆₇	1	2	yes	complemented
508	#388	C₂²×C₆₇	1	2	yes	complemented
509	#387	C₂²×C₆₇	1	2	yes	complemented
510	#387	C₂²×C₆₇	1	2	yes	complemented
511	#387	C₂²×C₆₇	1	2	yes	complemented
512	#387	C₂²×C₆₇	1	2	yes	complemented
513	#387	C₂²×C₆₇	1	2	yes	complemented
514	#387	C₂²×C₆₇	1	2	yes	complemented
515	#387	C₂²×C₆₇	1	2	yes	complemented
516	#387	C₂²×C₆₇	1	2	yes	complemented
517	#386	C₂²×C₆₇	1	2	yes	—
518	#386	C₂²×C₆₇	1	2	yes	—
519	#386	C₂²×C₆₇	1	1	yes	characteristic
520	#386	C₂²×C₆₇	1	1	yes	characteristic
521	#385	C₂²×C₆₇	1	2	yes	—
522	#385	C₂²×C₆₇	1	2	yes	—
523	#385	C₂²×C₆₇	1	2	yes	—
524	#385	C₂²×C₆₇	1	2	yes	—
525	#385	C₂²×C₆₇	1	1	yes	characteristic
526	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	#383	C₂²×C₆₇	1	2	yes	complemented
528	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
529	#381	C₂²×C₆₇	1	2	yes	—
530	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	#380	C₂²×C₆₇	1	2	yes	—
532	#379	C₂²×C₆₇	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
534	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
535	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
536	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
537	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
538	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
539	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
540	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
541	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
551	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
552	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
553	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
556	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
557	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	#376	C₂²×C₆₇	1	2	yes	complemented
560	#376	C₂²×C₆₇	1	2	yes	complemented
561	C₂×#95	C₂²×C₆₇	1	2	yes	—
562	C₂×#95	C₂²×C₆₇	1	2	yes	—
563	C₄³	C₂²×C₆₇	1	2	yes	complemented
564	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
568	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂³×C₄	—	2	8	no	—
570	C₂³×C₄	—	4	2	no	—
571	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
577	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
579	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
580	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
581	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
582	#126	C₂×C₄×C₆₇	1	16	yes	complemented
583	#124	C₂×C₄×C₆₇	1	8	yes	complemented
584	#123	C₂×C₄×C₆₇	1	8	yes	complemented
585	#123	C₂×C₄×C₆₇	1	16	yes	complemented
586	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
587	#120	C₂×C₄×C₆₇	1	8	yes	—
588	C₄×Q₈	—	4	2	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	2	8	no	—
591	C₄×D₄	—	4	2	no	—
592	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
593	#117	—	2	8	no	—
594	#117	C₂×C₄×C₆₇	1	16	yes	complemented
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	—	2	8	no	—
608	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	—	2	8	no	—
630	C₂×C₄²	—	4	4	no	—
631	C₂×C₄²	—	4	2	no	—
632	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
634	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	C₂⁴	—	2	4	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	—	4	1	no	—
676	C₂⁴	C₂²×C₄×C₆₇	1	4	yes	—
677	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	1	no	—
682	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	complemented
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
688	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
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	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	16	no	—
715	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
716	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
718	C₂²×C₄	#41×C₆₇	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
744	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
745	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
746	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	1	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	1	no	—
758	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
759	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
760	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
761	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
764	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	complemented
765	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	complemented
766	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	4	no	—
769	C₄²	—	2	4	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	1	no	—
782	C₄²	—	4	2	no	—
783	C₄²	C₂²×C₄×C₆₇	1	4	yes	complemented
784	C₄²	C₂²×C₄×C₆₇	1	8	yes	complemented
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	16	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
803	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
804	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
805	C₂³	C₂×#41×C₆₇	1	4	yes	—
806	C₂³	C₂×#41×C₆₇	1	4	yes	—
807	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
808	Q₈	—	4	4	no	—
809	D₄	—	2	16	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	16	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
857	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
858	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
861	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
862	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
863	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
864	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
865	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	C₄×#41×C₆₇	1	8	yes	—
884	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₆₇	1	2	yes	—
886	C₂²	C₂²×#41×C₆₇	1	2	yes	—
887	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
888	C₂²	#585×C₆₇	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	4	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	4	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	#551×C₆₇	1	4	yes	direct product factor
905	C₂	—	2	8	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	C₂×C₄×#41×C₆₇	1	2	yes	—
909	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
910	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
911	C₂	C₆₇×#3475	1	2	yes	—
912	C₂	C₆₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#120×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2374	C₂	semidirect
3. C₆₇×#2373	C₂	semidirect
4. C₆₇×#2372	C₂	semidirect
5. C₆₇×#2368	C₂	semidirect
6. C₆₇×#2359	C₂	semidirect
8. C₆₇×#2353	C₂	semidirect
9. C₆₇×#2343	C₂	semidirect
10. C₆₇×#2342	C₂	semidirect
11. C₄×#126×C₆₇	C₂	semidirect
12. C₄×#124×C₆₇	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
14. C₄×#123×C₆₇	C₂	semidirect
15. C₄×#123×C₆₇	C₂	semidirect
17. C₄²×D₄×C₆₇	C₂	semidirect
18. C₄×#117×C₆₇	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
21. #551×C₆₇	C₄	direct (N × H)
28. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
39. C₂²×C₄²×C₆₇	C₂²	semidirect
40. #391×C₆₇	C₂²	semidirect
41. #391×C₆₇	C₂²	semidirect
43. #389×C₆₇	C₂²	semidirect
49. #388×C₆₇	C₂²	semidirect
50. #388×C₆₇	C₂²	semidirect
51. #388×C₆₇	C₂²	semidirect
52. #387×C₆₇	C₂²	semidirect
53. #387×C₆₇	C₂²	semidirect
54. #387×C₆₇	C₂²	semidirect
55. #387×C₆₇	C₂²	semidirect
56. #387×C₆₇	C₂²	semidirect
57. #387×C₆₇	C₂²	semidirect
58. #387×C₆₇	C₂²	semidirect
59. #387×C₆₇	C₂²	semidirect
69. #385×C₆₇	C₂²	semidirect
70. #383×C₆₇	C₂²	semidirect
71. #382×C₆₇	C₂²	semidirect
73. #381×C₆₇	C₂²	semidirect
76. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
77. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
78. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
79. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
80. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
81. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
82. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
83. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
102. #376×C₆₇	C₂²	semidirect
103. #376×C₆₇	C₂²	semidirect
106. C₄³×C₆₇	C₂²	semidirect
107. C₄³×C₆₇	C₂²	semidirect
125. #126×C₆₇	C₂×C₄	semidirect
126. #124×C₆₇	C₂×C₄	semidirect
127. #123×C₆₇	C₂×C₄	semidirect
128. #123×C₆₇	C₂×C₄	semidirect
129. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
135. C₄×D₄×C₆₇	C₂×C₄	semidirect
137. #117×C₆₇	C₂×C₄	semidirect
151. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
225. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
260. C₂²×C₄×C₆₇	C₂²×C₄	semidirect
286. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
287. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
288. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
289. C₄⋊C₄×C₆₇	C₂²×C₄	semidirect
307. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
308. C₂²⋊C₄×C₆₇	C₂²×C₄	semidirect
326. C₄²×C₆₇	C₂²×C₄	semidirect
327. C₄²×C₆₇	C₂²×C₄	semidirect
447. C₄×C₆₇	#551	direct (N × H)
448. C₄×#551	C₆₇	direct (N × H)
458. #2374	C₂×C₆₇	semidirect
459. #2373	C₂×C₆₇	semidirect
460. #2372	C₂×C₆₇	semidirect
461. #2368	C₂×C₆₇	semidirect
462. #2359	C₂×C₆₇	semidirect
464. #2353	C₂×C₆₇	semidirect
465. #2343	C₂×C₆₇	semidirect
466. #2342	C₂×C₆₇	semidirect
467. C₄×#126	C₂×C₆₇	semidirect
468. C₄×#124	C₂×C₆₇	semidirect
469. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
470. C₄×#123	C₂×C₆₇	semidirect
471. C₄×#123	C₂×C₆₇	semidirect
473. C₄²×D₄	C₂×C₆₇	semidirect
474. C₄×#117	C₂×C₆₇	semidirect
475. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
476. C₆₇	C₄×#551	direct (N × H)
478. #551	C₄×C₆₇	direct (N × H)
485. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
496. C₂²×C₄²	C₂²×C₆₇	semidirect
497. #391	C₂²×C₆₇	semidirect
498. #391	C₂²×C₆₇	semidirect
500. #389	C₂²×C₆₇	semidirect
506. #388	C₂²×C₆₇	semidirect
507. #388	C₂²×C₆₇	semidirect
508. #388	C₂²×C₆₇	semidirect
509. #387	C₂²×C₆₇	semidirect
510. #387	C₂²×C₆₇	semidirect
511. #387	C₂²×C₆₇	semidirect
512. #387	C₂²×C₆₇	semidirect
513. #387	C₂²×C₆₇	semidirect
514. #387	C₂²×C₆₇	semidirect
515. #387	C₂²×C₆₇	semidirect
516. #387	C₂²×C₆₇	semidirect
526. #385	C₂²×C₆₇	semidirect
527. #383	C₂²×C₆₇	semidirect
528. #382	C₂²×C₆₇	semidirect
530. #381	C₂²×C₆₇	semidirect
533. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
534. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
535. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
536. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
537. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
538. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
539. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
540. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
555. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
556. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
557. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
558. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
559. #376	C₂²×C₆₇	semidirect
560. #376	C₂²×C₆₇	semidirect
563. C₄³	C₂²×C₆₇	semidirect
564. C₄³	C₂²×C₆₇	semidirect
582. #126	C₂×C₄×C₆₇	semidirect
583. #124	C₂×C₄×C₆₇	semidirect
584. #123	C₂×C₄×C₆₇	semidirect
585. #123	C₂×C₄×C₆₇	semidirect
586. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
592. C₄×D₄	C₂×C₄×C₆₇	semidirect
594. #117	C₂×C₄×C₆₇	semidirect
608. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
682. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
717. C₂²×C₄	C₂²×C₄×C₆₇	semidirect
743. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
744. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
745. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
746. C₄⋊C₄	C₂²×C₄×C₆₇	semidirect
764. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
765. C₂²⋊C₄	C₂²×C₄×C₆₇	semidirect
783. C₄²	C₂²×C₄×C₆₇	semidirect
784. C₄²	C₂²×C₄×C₆₇	semidirect
904. C₄	#551×C₆₇	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×#551×C₆₇	2
C₆₇×#2374	2
C₆₇×#2373	2
C₆₇×#2372	2
C₆₇×#2368	2
C₆₇×#2359	2
C₆₇×#2358	2
C₆₇×#2353	2
C₆₇×#2343	2
C₆₇×#2342	2
C₄×#126×C₆₇	2
C₄×#124×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#123×C₆₇	2
C₄×#120×C₆₇	2
C₄²×D₄×C₆₇	2
C₄×#117×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₄×#551	67

Subgroups — C4×#551×C67 #30713413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#551×C₆₇ #30713413