Subgroups — C₂×C₆₇×#3545 #30742004

Order 17152.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3545	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#562×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×H(3,𝔽₄)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#555×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#551×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#546×C₆₇	C₂	1	4	yes	maximal, complemented
9	C₂×#542×C₆₇	C₂	1	4	yes	maximal, complemented
10	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
11	C₂×#536×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#534×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₆₇	C₂²	1	2	yes	—
16	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
19	#563×C₆₇	C₂²	1	16	yes	complemented
20	#562×C₆₇	C₂²	1	32	yes	complemented
21	H(3,𝔽₄)×C₆₇	C₂²	1	16	yes	complemented
22	#555×C₆₇	C₂²	1	32	yes	complemented
23	#551×C₆₇	C₂²	1	32	yes	complemented
24	#551×C₆₇	C₂²	1	64	yes	complemented
25	#546×C₆₇	C₂²	1	64	yes	complemented
26	#542×C₆₇	C₂²	1	64	yes	complemented
27	#538×C₆₇	C₂²	1	64	yes	complemented
28	#536×C₆₇	C₂²	1	32	yes	complemented
29	#534×C₆₇	C₂²	1	32	yes	complemented
30	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
31	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
32	#529×C₆₇	C₂²	1	32	yes	complemented
33	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
34	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
36	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
37	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
42	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
44	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
47	C₂×#124×C₆₇	C₂²	1	16	yes	complemented
48	C₂×#123×C₆₇	C₂²	1	2	yes	—
49	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
50	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
51	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
52	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
54	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
57	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
60	C₂×#121×C₆₇	C₂²	1	2	yes	—
61	C₂×#121×C₆₇	C₂²	1	4	yes	—
62	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
63	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
64	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
65	C₂×#120×C₆₇	C₂²	1	2	yes	—
66	C₂×#120×C₆₇	C₂²	1	4	yes	—
67	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
68	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
69	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
70	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
72	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
73	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
75	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
76	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
77	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
78	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
79	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂⁵×C₆₇	C₂³	1	2	yes	—
82	C₂⁵×C₆₇	C₂³	1	2	yes	—
83	C₂×#41×C₆₇	—	4	8	no	—
84	C₂×#41×C₆₇	C₂³	1	16	yes	—
85	C₂²×Q₈×C₆₇	—	4	4	no	—
86	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
87	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
89	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
90	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
92	C₂²×D₄×C₆₇	—	4	4	no	—
93	C₂²×D₄×C₆₇	—	4	8	no	—
94	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
101	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
102	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
104	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
108	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
109	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
110	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
113	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
114	#126×C₆₇	C₂³	1	32	yes	complemented
115	#126×C₆₇	C₂³	1	32	yes	complemented
116	#126×C₆₇	C₂³	1	32	yes	complemented
117	#125×C₆₇	C₂³	1	16	yes	complemented
118	#124×C₆₇	C₂³	1	8	yes	—
119	#124×C₆₇	C₂³	1	8	yes	—
120	#124×C₆₇	C₂³	1	32	yes	complemented
121	#124×C₆₇	C₂³	1	8	yes	complemented
122	#124×C₆₇	C₂³	1	8	yes	complemented
123	#124×C₆₇	C₂³	1	16	yes	complemented
124	#124×C₆₇	C₂³	1	16	yes	complemented
125	#124×C₆₇	C₂³	1	16	yes	complemented
126	#124×C₆₇	C₂³	1	32	yes	complemented
127	#124×C₆₇	C₂³	1	32	yes	complemented
128	#123×C₆₇	C₂³	1	16	yes	—
129	#123×C₆₇	C₂³	1	32	yes	complemented
130	#123×C₆₇	C₂³	1	16	yes	complemented
131	#123×C₆₇	C₂³	1	32	yes	complemented
132	#123×C₆₇	C₂³	1	32	yes	complemented
133	#123×C₆₇	C₂³	1	32	yes	complemented
134	#123×C₆₇	C₂³	1	32	yes	complemented
135	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
136	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
137	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
138	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
139	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
140	#121×C₆₇	C₂³	1	16	yes	—
141	#121×C₆₇	C₂³	1	32	yes	—
142	#121×C₆₇	C₂³	1	32	yes	complemented
143	#121×C₆₇	C₂³	1	32	yes	complemented
144	#121×C₆₇	C₂³	1	32	yes	complemented
145	#120×C₆₇	C₂³	1	32	yes	—
146	#120×C₆₇	C₂³	1	16	yes	—
147	#120×C₆₇	C₂³	1	16	yes	complemented
148	#120×C₆₇	C₂³	1	32	yes	complemented
149	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
150	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
151	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
152	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
153	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
154	#117×C₆₇	C₂³	1	32	yes	complemented
155	#117×C₆₇	C₂³	1	16	yes	complemented
156	#117×C₆₇	C₂³	1	32	yes	complemented
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
184	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
191	C₂⁴×C₆₇	—	2	8	no	—
192	C₂⁴×C₆₇	—	4	4	no	—
193	C₂⁴×C₆₇	—	4	8	no	—
194	C₂⁴×C₆₇	—	4	8	no	—
195	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
196	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
197	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
198	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
200	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
201	#41×C₆₇	—	4	32	no	—
202	C₂×Q₈×C₆₇	—	4	2	no	—
203	C₂×Q₈×C₆₇	—	4	4	no	—
204	C₂×Q₈×C₆₇	—	4	2	no	—
205	C₂×Q₈×C₆₇	—	4	16	no	—
206	C₂×Q₈×C₆₇	—	4	4	no	—
207	C₂×Q₈×C₆₇	—	4	4	no	—
208	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
209	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
210	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
211	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
212	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
213	C₂×D₄×C₆₇	—	2	16	no	—
214	C₂×D₄×C₆₇	—	4	2	no	—
215	C₂×D₄×C₆₇	—	4	4	no	—
216	C₂×D₄×C₆₇	—	4	2	no	—
217	C₂×D₄×C₆₇	—	4	16	no	—
218	C₂×D₄×C₆₇	—	4	8	no	—
219	C₂×D₄×C₆₇	—	4	8	no	—
220	C₂×D₄×C₆₇	—	4	8	no	—
221	C₂×D₄×C₆₇	—	4	4	no	—
222	C₂×D₄×C₆₇	—	4	4	no	—
223	C₂×D₄×C₆₇	—	4	32	no	—
224	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
225	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
226	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
227	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
228	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
229	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
230	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
231	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
232	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	8	no	—
235	C₂²×C₄×C₆₇	—	4	8	no	—
236	C₂²×C₄×C₆₇	—	4	4	no	—
237	C₂²×C₄×C₆₇	—	4	8	no	—
238	C₂²×C₄×C₆₇	—	4	4	no	—
239	C₂²×C₄×C₆₇	—	4	8	no	—
240	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
256	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
257	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
258	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
259	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
261	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
262	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
263	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
264	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
265	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
266	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
267	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
268	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
269	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
270	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
271	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
272	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
273	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
274	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
275	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
276	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
277	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
278	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
279	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
280	C₄²×C₆₇	C₂⁴	1	4	yes	—
281	C₄²×C₆₇	C₂⁴	1	8	yes	—
282	C₄²×C₆₇	C₂⁴	1	4	yes	—
283	C₄²×C₆₇	C₂⁴	1	8	yes	—
284	C₄²×C₆₇	C₂⁴	1	16	yes	—
285	C₄²×C₆₇	C₂⁴	1	8	yes	—
286	C₂³×C₆₇	—	2	4	no	—
287	C₂³×C₆₇	—	2	8	no	—
288	C₂³×C₆₇	—	2	4	no	—
289	C₂³×C₆₇	—	2	4	no	—
290	C₂³×C₆₇	—	2	8	no	—
291	C₂³×C₆₇	—	2	8	no	—
292	C₂³×C₆₇	—	2	8	no	—
293	C₂³×C₆₇	—	2	8	no	—
294	C₂³×C₆₇	—	2	16	no	—
295	C₂³×C₆₇	—	4	8	no	—
296	C₂³×C₆₇	—	4	16	no	—
297	C₂³×C₆₇	—	4	16	no	—
298	C₂³×C₆₇	—	8	16	no	—
299	C₂³×C₆₇	—	8	16	no	—
300	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
301	C₂³×C₆₇	C₂⁵	1	4	yes	—
302	C₂³×C₆₇	C₂⁵	1	8	yes	—
303	C₂³×C₆₇	C₂⁵	1	4	yes	—
304	C₂³×C₆₇	C₂⁵	1	2	yes	—
305	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
306	Q₈×C₆₇	—	4	4	no	—
307	Q₈×C₆₇	—	4	8	no	—
308	Q₈×C₆₇	—	4	4	no	—
309	Q₈×C₆₇	—	4	8	no	—
310	Q₈×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	2	32	no	—
312	D₄×C₆₇	—	4	4	no	—
313	D₄×C₆₇	—	4	8	no	—
314	D₄×C₆₇	—	4	4	no	—
315	D₄×C₆₇	—	4	16	no	—
316	D₄×C₆₇	—	4	16	no	—
317	D₄×C₆₇	—	4	16	no	—
318	D₄×C₆₇	—	4	8	no	—
319	D₄×C₆₇	—	4	8	no	—
320	C₂×C₄×C₆₇	—	2	4	no	—
321	C₂×C₄×C₆₇	—	2	8	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	16	no	—
326	C₂×C₄×C₆₇	—	2	8	no	—
327	C₂×C₄×C₆₇	—	2	4	no	—
328	C₂×C₄×C₆₇	—	2	8	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	8	no	—
331	C₂×C₄×C₆₇	—	4	16	no	—
332	C₂×C₄×C₆₇	—	4	8	no	—
333	C₂×C₄×C₆₇	—	4	16	no	—
334	C₂×C₄×C₆₇	—	4	8	no	—
335	C₂×C₄×C₆₇	—	4	16	no	—
336	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
337	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
338	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
339	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
340	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
341	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
342	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
343	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
344	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	2	8	no	—
348	C₂²×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	4	no	—
350	C₂²×C₆₇	—	2	8	no	—
351	C₂²×C₆₇	—	2	8	no	—
352	C₂²×C₆₇	—	2	8	no	—
353	C₂²×C₆₇	—	2	8	no	—
354	C₂²×C₆₇	—	4	16	no	—
355	C₂²×C₆₇	—	4	8	no	—
356	C₂²×C₆₇	—	4	8	no	—
357	C₂²×C₆₇	—	8	16	no	—
358	C₂²×C₆₇	—	8	16	no	—
359	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
360	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₆₇	#585	1	4	yes	—
362	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
363	C₄×C₆₇	—	2	4	no	—
364	C₄×C₆₇	—	2	2	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	2	8	no	—
368	C₄×C₆₇	—	2	4	no	—
369	C₄×C₆₇	—	2	8	no	—
370	C₄×C₆₇	—	2	4	no	—
371	C₄×C₆₇	—	2	8	no	—
372	C₂×#3545	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
373	C₂×C₆₇	—	2	4	no	—
374	C₂×C₆₇	—	4	8	no	—
375	C₂×C₆₇	—	4	4	no	—
376	C₂×C₆₇	—	4	4	no	—
377	C₂×C₆₇	#3545	1	4	yes	direct product factor
378	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₆₇	C₂×#585	1	2	yes	—
380	#3545	C₂×C₆₇	1	32	yes	direct product factor
381	C₂×#563	C₂×C₆₇	1	1	yes	characteristic, complemented
382	C₂×#562	C₂×C₆₇	1	2	yes	complemented
383	C₂×H(3,𝔽₄)	C₂×C₆₇	1	1	yes	characteristic, complemented
384	C₂×#555	C₂×C₆₇	1	2	yes	complemented
385	C₂×#551	C₂×C₆₇	1	2	yes	complemented
386	C₂×#551	C₂×C₆₇	1	4	yes	complemented
387	C₂×#546	C₂×C₆₇	1	4	yes	complemented
388	C₂×#542	C₂×C₆₇	1	4	yes	complemented
389	C₂×#538	C₂×C₆₇	1	4	yes	complemented
390	C₂×#536	C₂×C₆₇	1	2	yes	complemented
391	C₂×#534	C₂×C₆₇	1	2	yes	complemented
392	C₂×#529	C₂×C₆₇	1	2	yes	complemented
393	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₆₇	C₂×#3545	1	1	yes	characteristic, direct product factor, Sylow
395	C₂²×#41	C₂²×C₆₇	1	2	yes	—
396	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
397	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
398	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
399	#563	C₂²×C₆₇	1	16	yes	complemented
400	#562	C₂²×C₆₇	1	32	yes	complemented
401	H(3,𝔽₄)	C₂²×C₆₇	1	16	yes	complemented
402	#555	C₂²×C₆₇	1	32	yes	complemented
403	#551	C₂²×C₆₇	1	32	yes	complemented
404	#551	C₂²×C₆₇	1	64	yes	complemented
405	#546	C₂²×C₆₇	1	64	yes	complemented
406	#542	C₂²×C₆₇	1	64	yes	complemented
407	#538	C₂²×C₆₇	1	64	yes	complemented
408	#536	C₂²×C₆₇	1	32	yes	complemented
409	#534	C₂²×C₆₇	1	32	yes	complemented
410	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
411	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
412	#529	C₂²×C₆₇	1	32	yes	complemented
413	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
414	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
415	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
416	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
417	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
420	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
422	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
423	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
424	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
425	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
426	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
427	C₂×#124	C₂²×C₆₇	1	16	yes	complemented
428	C₂×#123	C₂²×C₆₇	1	2	yes	—
429	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
430	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
431	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
432	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
433	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
434	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
435	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
436	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
437	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
438	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
439	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
440	C₂×#121	C₂²×C₆₇	1	2	yes	—
441	C₂×#121	C₂²×C₆₇	1	4	yes	—
442	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
443	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
444	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
445	C₂×#120	C₂²×C₆₇	1	4	yes	—
446	C₂×#120	C₂²×C₆₇	1	2	yes	—
447	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
448	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
449	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
450	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
451	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
452	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
453	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
454	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
455	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
456	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
457	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
458	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
459	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
460	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	C₂⁵	C₂³×C₆₇	1	2	yes	—
462	C₂⁵	C₂³×C₆₇	1	2	yes	—
463	C₂×#41	—	4	8	no	—
464	C₂×#41	C₂³×C₆₇	1	16	yes	—
465	C₂²×Q₈	—	4	4	no	—
466	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
467	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
469	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
470	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₆₇	1	8	yes	complemented
472	C₂²×D₄	—	4	4	no	—
473	C₂²×D₄	—	4	8	no	—
474	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
475	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
476	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
477	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
478	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
480	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
481	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
482	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
484	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
485	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
486	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
488	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
489	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
490	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
491	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
492	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
493	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
494	#126	C₂³×C₆₇	1	32	yes	complemented
495	#126	C₂³×C₆₇	1	32	yes	complemented
496	#126	C₂³×C₆₇	1	32	yes	complemented
497	#125	C₂³×C₆₇	1	16	yes	complemented
498	#124	C₂³×C₆₇	1	8	yes	—
499	#124	C₂³×C₆₇	1	8	yes	—
500	#124	C₂³×C₆₇	1	32	yes	complemented
501	#124	C₂³×C₆₇	1	8	yes	complemented
502	#124	C₂³×C₆₇	1	8	yes	complemented
503	#124	C₂³×C₆₇	1	16	yes	complemented
504	#124	C₂³×C₆₇	1	16	yes	complemented
505	#124	C₂³×C₆₇	1	16	yes	complemented
506	#124	C₂³×C₆₇	1	32	yes	complemented
507	#124	C₂³×C₆₇	1	32	yes	complemented
508	#123	C₂³×C₆₇	1	16	yes	—
509	#123	C₂³×C₆₇	1	32	yes	complemented
510	#123	C₂³×C₆₇	1	16	yes	complemented
511	#123	C₂³×C₆₇	1	32	yes	complemented
512	#123	C₂³×C₆₇	1	32	yes	complemented
513	#123	C₂³×C₆₇	1	32	yes	complemented
514	#123	C₂³×C₆₇	1	32	yes	complemented
515	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
516	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
517	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
518	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
519	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
520	#121	C₂³×C₆₇	1	16	yes	—
521	#121	C₂³×C₆₇	1	32	yes	—
522	#121	C₂³×C₆₇	1	32	yes	complemented
523	#121	C₂³×C₆₇	1	32	yes	complemented
524	#121	C₂³×C₆₇	1	32	yes	complemented
525	#120	C₂³×C₆₇	1	32	yes	—
526	#120	C₂³×C₆₇	1	16	yes	—
527	#120	C₂³×C₆₇	1	16	yes	complemented
528	#120	C₂³×C₆₇	1	32	yes	complemented
529	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
530	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
531	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
532	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
533	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
534	#117	C₂³×C₆₇	1	32	yes	complemented
535	#117	C₂³×C₆₇	1	16	yes	complemented
536	#117	C₂³×C₆₇	1	32	yes	complemented
537	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
541	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
564	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
566	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
567	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
568	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
569	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
571	C₂⁴	—	2	8	no	—
572	C₂⁴	—	4	4	no	—
573	C₂⁴	—	4	8	no	—
574	C₂⁴	—	4	8	no	—
575	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
576	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
577	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
578	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
580	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
581	#41	—	4	32	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	—	4	16	no	—
586	C₂×Q₈	—	4	4	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
589	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
590	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
591	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
592	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
593	C₂×D₄	—	2	16	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	16	no	—
598	C₂×D₄	—	4	8	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	8	no	—
601	C₂×D₄	—	4	8	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	32	no	—
604	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
605	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
606	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
607	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
608	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
609	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
610	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
611	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
612	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	8	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	4	8	no	—
617	C₂²×C₄	—	4	8	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	8	no	—
620	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
631	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
633	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
634	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
635	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
636	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
637	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
638	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
640	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
641	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
642	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
643	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
644	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
645	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
646	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
647	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
649	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
650	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
651	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
652	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
653	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
656	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
657	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
658	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
659	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
660	C₄²	C₂⁴×C₆₇	1	4	yes	—
661	C₄²	C₂⁴×C₆₇	1	8	yes	—
662	C₄²	C₂⁴×C₆₇	1	4	yes	—
663	C₄²	C₂⁴×C₆₇	1	8	yes	—
664	C₄²	C₂⁴×C₆₇	1	16	yes	—
665	C₄²	C₂⁴×C₆₇	1	8	yes	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	8	no	—
673	C₂³	—	2	8	no	—
674	C₂³	—	2	16	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	8	16	no	—
679	C₂³	—	8	16	no	—
680	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
681	C₂³	C₂⁵×C₆₇	1	4	yes	—
682	C₂³	C₂⁵×C₆₇	1	8	yes	—
683	C₂³	C₂⁵×C₆₇	1	4	yes	—
684	C₂³	C₂⁵×C₆₇	1	2	yes	—
685	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	D₄	—	2	32	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	8	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	16	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	16	no	—
698	D₄	—	4	16	no	—
699	D₄	—	4	8	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	16	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	16	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	16	no	—
716	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
717	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
718	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
719	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
720	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
721	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
722	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
723	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
724	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
725	C₂²	—	2	8	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	4	8	no	—
735	C₂²	—	4	16	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	8	16	no	—
738	C₂²	—	8	16	no	—
739	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
740	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
741	C₂²	#585×C₆₇	1	4	yes	—
742	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	8	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	8	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	8	no	—
755	C₂	—	4	4	no	—
756	C₂	C₆₇×#3545	1	4	yes	direct product factor
757	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
758	C₂	C₂×#585×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3545	C₂	direct (N × H)
2. C₂×#563×C₆₇	C₂	semidirect
3. C₂×#562×C₆₇	C₂	semidirect
4. C₂×H(3,𝔽₄)×C₆₇	C₂	semidirect
5. C₂×#555×C₆₇	C₂	semidirect
6. C₂×#551×C₆₇	C₂	semidirect
7. C₂×#551×C₆₇	C₂	semidirect
8. C₂×#546×C₆₇	C₂	semidirect
9. C₂×#542×C₆₇	C₂	semidirect
10. C₂×#538×C₆₇	C₂	semidirect
11. C₂×#536×C₆₇	C₂	semidirect
12. C₂×#534×C₆₇	C₂	semidirect
13. C₂×#529×C₆₇	C₂	semidirect
14. C₂²×#124×C₆₇	C₂	semidirect
16. C₂³×Q₈×C₆₇	C₂²	semidirect
18. C₂³×D₄×C₆₇	C₂²	semidirect
19. #563×C₆₇	C₂²	semidirect
20. #562×C₆₇	C₂²	semidirect
21. H(3,𝔽₄)×C₆₇	C₂²	semidirect
22. #555×C₆₇	C₂²	semidirect
23. #551×C₆₇	C₂²	semidirect
24. #551×C₆₇	C₂²	semidirect
25. #546×C₆₇	C₂²	semidirect
26. #542×C₆₇	C₂²	semidirect
27. #538×C₆₇	C₂²	semidirect
28. #536×C₆₇	C₂²	semidirect
29. #534×C₆₇	C₂²	semidirect
30. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
32. #529×C₆₇	C₂²	semidirect
33. C₂×#126×C₆₇	C₂²	semidirect
34. C₂×#126×C₆₇	C₂²	semidirect
35. C₂×#126×C₆₇	C₂²	semidirect
36. C₂×#125×C₆₇	C₂²	semidirect
39. C₂×#124×C₆₇	C₂²	semidirect
40. C₂×#124×C₆₇	C₂²	semidirect
41. C₂×#124×C₆₇	C₂²	semidirect
42. C₂×#124×C₆₇	C₂²	semidirect
43. C₂×#124×C₆₇	C₂²	semidirect
44. C₂×#124×C₆₇	C₂²	semidirect
45. C₂×#124×C₆₇	C₂²	semidirect
46. C₂×#124×C₆₇	C₂²	semidirect
47. C₂×#124×C₆₇	C₂²	semidirect
49. C₂×#123×C₆₇	C₂²	semidirect
50. C₂×#123×C₆₇	C₂²	semidirect
51. C₂×#123×C₆₇	C₂²	semidirect
52. C₂×#123×C₆₇	C₂²	semidirect
53. C₂×#123×C₆₇	C₂²	semidirect
54. C₂×#123×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
57. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
58. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
62. C₂×#121×C₆₇	C₂²	semidirect
63. C₂×#121×C₆₇	C₂²	semidirect
64. C₂×#121×C₆₇	C₂²	semidirect
67. C₂×#120×C₆₇	C₂²	semidirect
68. C₂×#120×C₆₇	C₂²	semidirect
69. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
70. C₂×C₄×D₄×C₆₇	C₂²	semidirect
71. C₂×C₄×D₄×C₆₇	C₂²	semidirect
72. C₂×C₄×D₄×C₆₇	C₂²	semidirect
73. C₂×C₄×D₄×C₆₇	C₂²	semidirect
74. C₂×#117×C₆₇	C₂²	semidirect
75. C₂×#117×C₆₇	C₂²	semidirect
76. C₂×#117×C₆₇	C₂²	semidirect
77. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
78. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
79. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
80. C₂²×C₄²×C₆₇	C₂²	semidirect
91. C₂²×Q₈×C₆₇	C₂³	semidirect
104. C₂²×D₄×C₆₇	C₂³	semidirect
112. C₄⋊Q₈×C₆₇	C₂³	semidirect
113. C₄⋊Q₈×C₆₇	C₂³	semidirect
114. #126×C₆₇	C₂³	semidirect
115. #126×C₆₇	C₂³	semidirect
116. #126×C₆₇	C₂³	semidirect
117. #125×C₆₇	C₂³	semidirect
120. #124×C₆₇	C₂³	semidirect
121. #124×C₆₇	C₂³	semidirect
122. #124×C₆₇	C₂³	semidirect
123. #124×C₆₇	C₂³	semidirect
124. #124×C₆₇	C₂³	semidirect
125. #124×C₆₇	C₂³	semidirect
126. #124×C₆₇	C₂³	semidirect
127. #124×C₆₇	C₂³	semidirect
129. #123×C₆₇	C₂³	semidirect
130. #123×C₆₇	C₂³	semidirect
131. #123×C₆₇	C₂³	semidirect
132. #123×C₆₇	C₂³	semidirect
133. #123×C₆₇	C₂³	semidirect
134. #123×C₆₇	C₂³	semidirect
135. C₂²⋊Q₈×C₆₇	C₂³	semidirect
136. C₂²⋊Q₈×C₆₇	C₂³	semidirect
137. C₂²⋊Q₈×C₆₇	C₂³	semidirect
138. C₂²⋊Q₈×C₆₇	C₂³	semidirect
139. C₂²⋊Q₈×C₆₇	C₂³	semidirect
142. #121×C₆₇	C₂³	semidirect
143. #121×C₆₇	C₂³	semidirect
144. #121×C₆₇	C₂³	semidirect
147. #120×C₆₇	C₂³	semidirect
148. #120×C₆₇	C₂³	semidirect
149. C₄×Q₈×C₆₇	C₂³	semidirect
150. C₄×D₄×C₆₇	C₂³	semidirect
151. C₄×D₄×C₆₇	C₂³	semidirect
152. C₄×D₄×C₆₇	C₂³	semidirect
153. C₄×D₄×C₆₇	C₂³	semidirect
154. #117×C₆₇	C₂³	semidirect
155. #117×C₆₇	C₂³	semidirect
156. #117×C₆₇	C₂³	semidirect
181. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
182. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
183. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
190. C₂×C₄²×C₆₇	C₂³	semidirect
372. C₂×#3545	C₆₇	direct (N × H)
377. C₂×C₆₇	#3545	direct (N × H)
380. #3545	C₂×C₆₇	direct (N × H)
381. C₂×#563	C₂×C₆₇	semidirect
382. C₂×#562	C₂×C₆₇	semidirect
383. C₂×H(3,𝔽₄)	C₂×C₆₇	semidirect
384. C₂×#555	C₂×C₆₇	semidirect
385. C₂×#551	C₂×C₆₇	semidirect
386. C₂×#551	C₂×C₆₇	semidirect
387. C₂×#546	C₂×C₆₇	semidirect
388. C₂×#542	C₂×C₆₇	semidirect
389. C₂×#538	C₂×C₆₇	semidirect
390. C₂×#536	C₂×C₆₇	semidirect
391. C₂×#534	C₂×C₆₇	semidirect
392. C₂×#529	C₂×C₆₇	semidirect
393. C₂²×#124	C₂×C₆₇	semidirect
394. C₆₇	C₂×#3545	direct (N × H)
396. C₂³×Q₈	C₂²×C₆₇	semidirect
398. C₂³×D₄	C₂²×C₆₇	semidirect
399. #563	C₂²×C₆₇	semidirect
400. #562	C₂²×C₆₇	semidirect
401. H(3,𝔽₄)	C₂²×C₆₇	semidirect
402. #555	C₂²×C₆₇	semidirect
403. #551	C₂²×C₆₇	semidirect
404. #551	C₂²×C₆₇	semidirect
405. #546	C₂²×C₆₇	semidirect
406. #542	C₂²×C₆₇	semidirect
407. #538	C₂²×C₆₇	semidirect
408. #536	C₂²×C₆₇	semidirect
409. #534	C₂²×C₆₇	semidirect
410. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
411. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
412. #529	C₂²×C₆₇	semidirect
413. C₂×#126	C₂²×C₆₇	semidirect
414. C₂×#126	C₂²×C₆₇	semidirect
415. C₂×#126	C₂²×C₆₇	semidirect
416. C₂×#125	C₂²×C₆₇	semidirect
419. C₂×#124	C₂²×C₆₇	semidirect
420. C₂×#124	C₂²×C₆₇	semidirect
421. C₂×#124	C₂²×C₆₇	semidirect
422. C₂×#124	C₂²×C₆₇	semidirect
423. C₂×#124	C₂²×C₆₇	semidirect
424. C₂×#124	C₂²×C₆₇	semidirect
425. C₂×#124	C₂²×C₆₇	semidirect
426. C₂×#124	C₂²×C₆₇	semidirect
427. C₂×#124	C₂²×C₆₇	semidirect
429. C₂×#123	C₂²×C₆₇	semidirect
430. C₂×#123	C₂²×C₆₇	semidirect
431. C₂×#123	C₂²×C₆₇	semidirect
432. C₂×#123	C₂²×C₆₇	semidirect
433. C₂×#123	C₂²×C₆₇	semidirect
434. C₂×#123	C₂²×C₆₇	semidirect
435. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
436. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
437. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
438. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
439. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
442. C₂×#121	C₂²×C₆₇	semidirect
443. C₂×#121	C₂²×C₆₇	semidirect
444. C₂×#121	C₂²×C₆₇	semidirect
447. C₂×#120	C₂²×C₆₇	semidirect
448. C₂×#120	C₂²×C₆₇	semidirect
449. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
450. C₂×C₄×D₄	C₂²×C₆₇	semidirect
451. C₂×C₄×D₄	C₂²×C₆₇	semidirect
452. C₂×C₄×D₄	C₂²×C₆₇	semidirect
453. C₂×C₄×D₄	C₂²×C₆₇	semidirect
454. C₂×#117	C₂²×C₆₇	semidirect
455. C₂×#117	C₂²×C₆₇	semidirect
456. C₂×#117	C₂²×C₆₇	semidirect
457. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
458. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
459. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
460. C₂²×C₄²	C₂²×C₆₇	semidirect
471. C₂²×Q₈	C₂³×C₆₇	semidirect
484. C₂²×D₄	C₂³×C₆₇	semidirect
492. C₄⋊Q₈	C₂³×C₆₇	semidirect
493. C₄⋊Q₈	C₂³×C₆₇	semidirect
494. #126	C₂³×C₆₇	semidirect
495. #126	C₂³×C₆₇	semidirect
496. #126	C₂³×C₆₇	semidirect
497. #125	C₂³×C₆₇	semidirect
500. #124	C₂³×C₆₇	semidirect
501. #124	C₂³×C₆₇	semidirect
502. #124	C₂³×C₆₇	semidirect
503. #124	C₂³×C₆₇	semidirect
504. #124	C₂³×C₆₇	semidirect
505. #124	C₂³×C₆₇	semidirect
506. #124	C₂³×C₆₇	semidirect
507. #124	C₂³×C₆₇	semidirect
509. #123	C₂³×C₆₇	semidirect
510. #123	C₂³×C₆₇	semidirect
511. #123	C₂³×C₆₇	semidirect
512. #123	C₂³×C₆₇	semidirect
513. #123	C₂³×C₆₇	semidirect
514. #123	C₂³×C₆₇	semidirect
515. C₂²⋊Q₈	C₂³×C₆₇	semidirect
516. C₂²⋊Q₈	C₂³×C₆₇	semidirect
517. C₂²⋊Q₈	C₂³×C₆₇	semidirect
518. C₂²⋊Q₈	C₂³×C₆₇	semidirect
519. C₂²⋊Q₈	C₂³×C₆₇	semidirect
522. #121	C₂³×C₆₇	semidirect
523. #121	C₂³×C₆₇	semidirect
524. #121	C₂³×C₆₇	semidirect
527. #120	C₂³×C₆₇	semidirect
528. #120	C₂³×C₆₇	semidirect
529. C₄×Q₈	C₂³×C₆₇	semidirect
530. C₄×D₄	C₂³×C₆₇	semidirect
531. C₄×D₄	C₂³×C₆₇	semidirect
532. C₄×D₄	C₂³×C₆₇	semidirect
533. C₄×D₄	C₂³×C₆₇	semidirect
534. #117	C₂³×C₆₇	semidirect
535. #117	C₂³×C₆₇	semidirect
536. #117	C₂³×C₆₇	semidirect
561. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
562. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
563. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
570. C₂×C₄²	C₂³×C₆₇	semidirect
756. C₂	C₆₇×#3545	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3545	2
C₂×#563×C₆₇	2
C₂×#562×C₆₇	2
C₂×H(3,𝔽₄)×C₆₇	2
C₂×#555×C₆₇	2
C₂×#551×C₆₇	2
C₂×#546×C₆₇	2
C₂×#542×C₆₇	2
C₂×#538×C₆₇	2
C₂×#536×C₆₇	2
C₂×#534×C₆₇	2
C₂×#529×C₆₇	2
C₂²×#124×C₆₇	2
C₂×#3545	67

Subgroups — C2×C67×#3545 #30742004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3545 #30742004